Jan 2, 1992 - Maltese Cristiano (MAPEI S.p.A., Milan, Italy). 37. Martinelli Paolo (Polimi-DIS, Milan, Italy). 38. Massone Giovanni (SINECO-ASTM Group, ...
Politecnico di Milano
Università di Bergamo
Università di Brescia
Proceedings of the Workshop
Fire Design of Concrete Structures: What now? What next?
Held at Milan University of Technology Milan, Italy, December 2-3, 2004 Workshop organized by fib Task Group 4.3 “Fire Design of Concrete Structures”
Proceedings edited by Pietro G. Gambarova Roberto Felicetti Alberto Meda Paolo Riva
Editors: Pietro G. Gambarova, Roberto Felicetti, Alberto Meda, Paolo Riva Title: Proceedings of the Workshop Fire Design of Concrete Structures: What now? What next? All rights reserved © 2005 Pietro G. Gambarova © 2005 Starrylink Editrice Brescia Contrada S. Urbano, 14 - 25121 Brescia, Italy Thesis and Research www.starrylink.it All rights reserved. No part of this pubblication may be reproduced or transmitted, in any form or by any means, without the prior written permission of the Editors. ISBN 88-88847-91-X Cover photo: fire in a high-rise building, courtesy of Dr. Tom Lennon of British Research Establishment, Garston – Watford, UK
Fire Design of Concrete Structures: What now? What next? Proceedings of the 2nd International Workshop held at the Milan University of Technology, Milan, Italy December 2-3, 2004 Edited by
Pietro G. Gambarova Professor of Structural Engineering Department of Structural Engineering Milan University of Technology Milan, Italy
Roberto Felicetti Associate Professor of Structural Engineering Department of Structural Engineering Milan University of Technology Milan, Italy
Paolo Riva Associate Professor of Structural Engineering Department of Civil Engineering University of Brescia Brescia, Italy
Alberto Meda Assistant Professor of Structural Engineering Dept. of Engineering Technologies and Design University of Bergamo Bergamo, Italy
Milan, March 2005
FOREWORD BY THE CONVENER OF fib WP 4.3.2 The idea of organising this workshop originated from fib TG 4.3 "Fire Design of Concrete Structures", and in particular from WP 4.3.2 "Structural Behaviour" which deals with the structural aspects of fire design. The main emphasis of the activities of WP 4.3.2 is on the influence that a local fire has on the complete structure, as opposed to the classical, codified approach, where fire resistance is judged on a member basis. Within the working party, many numerical simulations have been performed in order to quantify the indirect actions of a fire on concrete structures. During the progress of the work within WP 4.3.2 it was felt necessary to have sufficient exchange of information with other specialists in the field of fire design and to show the most recent results to a broader group of experts, in order to take advantage of the feedback for further work. The themes of the workshop sessions more or less coincide with the titles of the different chapters of the fib-bulletin, whose preparation is under way. Many aspects of the behaviour of concrete and concrete structures were covered during the workshop. The high number of contributions shows that fire resistance is still a "hot" topic and that there is really a need for a systematic design approach, based on models for both the material behaviour and the structural behaviour. In the many tests performed so far, several parameters were modified, making it difficult to understand what really happened and favouring a mostly-empirical approach to fire design. As a consequence, though a lot of progress has been recently made at the modelling level, many problems are still waiting for an answer. This latter aspect is also related to the new cementitious materials and new types of concrete, that have been recently introduced. Since the number of the constituents added to the mix has increased, their influence on concrete microstructure and thermo-mechanical properties requires further in-depth studies. Finally, I would like to thank Professors Gambarova, Riva, Felicetti and Meda, and their co-workers, for all the work they have done in preparing the workshop very efficiently and in arranging all the practical aspects in an almost perfect way. The friendly and open atmosphere during the workshop stimulated many useful discussions and contacts among the participants. Luc Taerwe Professor Magnel Laboratory for Concrete Research Ghent, Belgium
I
FOREWORD BY THE LOCAL ORGANIZING COMMITTEE The often devastating effects that fires have on entire structures or single structural members have been lately brought back to the scene, because of the increasing road traffic (fires in the tunnels), structural complexity (tall buildings), extreme environmental conditions (off-shore platforms), terrorism and war-related events. In all these cases, what matters is not only the fire duration of a given structure, but also its safety and serviceability level after a fire, the latter having to do with structural repair and strengthening, which is often a must, like in historical and monumental buildings, as well as in vital infrastructures. The increasing implications of fire-related effects in structural design have been lately dealt with in a few international research projects and committees’ activities. These initiatives are favoring the collection of new test data, the development of innovative theoretical models and computational tools, and the refinement and/or extension of the design rules, by means of code improvements and specific guidelines. Within this context, the workshop was meant to be focused on the engineering aspects of structural fire design, starting from the application of the most recent results that the scientific and technological community has brought on to the scene, in terms of materials properties and structural modeling . The workshop was organized by the Task Group 4.3 “Fire Design of Concrete Structures” of fib (International Federation for Structural Concrete). Since it was established early in 2000, the scope of the group has been to consider the implications that fire has on conceptual design, in order to achieve a satisfactory balance between materials response and structural response. A first workshop was held in Malta in March 2001, and in that occasion two Working Parties were formed, with the aim of preparing a set of guidelines on concrete modeling in fire conditions (WP 4.3.1), and on the global response of fire-exposed structures (WP 4.3.2). The Task Group and the Working Parties count many experts coming from all around the world, all active in the field of concrete and R/C exposed to fire and high temperature. This was considered by the Organizing Committee as the best prerequisite for the success of the workshop, that has fostered also three remarkable pre- and post-events: the meeting of RILEM Committee TCHTC (Mechanical Concrete Properties at High Temperature, chaired by Prof. Ulrich Schneider), a seminar on the failure of concrete-like materials under extreme temperatures (given by Prof. Kaspar Willam) and the joint meeting of fib Task Group 4.3 (Fire Design of Concrete Structures, convened by Dr. Niels Peter Hoj) and fib Working Party 4.3.2 (Structural Behaviour, convened by Prof. Luc Taerwe). As recognized by the participants, the workshop came up to the expectations, with reference not only to the presentation of past and present activities on fire design, but also to the exchange of ideas and to possible joint research projects. Pietro G. Gambarova
Roberto Felicetti
Paolo Riva
Patrick Bamonte
Matteo Colombo
Marco Lamperti
III
Alberto Meda
Members of TG 4.3 Yngve Anderberg, Angel Arteaga Patrick Bamonte Mamoud Behloul Kese Both Anthony Caserta Jean-Francois Denoël Jean-Claude Dotreppe Roberto Felicetti Joris Fellinger Jean-Marc Franssen Pietro Gambarova Niels Peter Høj (Convener TG 4.3) José Maria Izquerdo Xianyu Jin Ulla-Maija Jumppanen Gabriel Khoury (Convener WP 4.3.1) Tom Lennon Zongjin Li Carmelo Majorana Stuart Matthews Alberto Meda Ulrich Neck Yoshikazu Ota Josko Ožbolt Ekkehard Richter Paolo Riva Fabienne Robert Joao Paulo C. Rodrigues Luc Taerwe (Convener WP 4.3.2) Franz-Josef Ulm Arnold van Acker Andrea Vanni
IV
Organizing Committee Pietro G. Gambarova (Chairman) Luc Taerwe (Vicechairman) Alberto Meda (Secretary) Roberto Felicetti Niels Peter Høj (Convener fib TG. 4.3) Paolo Riva Patrick Bamonte Matteo Colombo Marco Lamperti Supporters and Sponsors DIS – Department of Structural Engineering LPM – Laboratory for Testing Materials (Milan University of Technology) AICAP – Italian Association for R/C and P/C Structures (Rome, Italy) CIS-E – Constructions and Structural Engineering in Europe (Milan, Italy) CTE – Italian Society of Building Engineers (Milan, Italy) fib CEB-FIP – Italian Group University of Padova (Padua, Italy) A22-Autobrennero – Brenner Motorway (Trent, Italy) ASSOBETON – Italian Federation of Manufacturers of PrecastConcrete Products (Milan, Italy) ASTM Group – Turin-Milan Motorway (Milan, Italy) CTG-Italcementi Group (Bergamo, Italy) Ruredil (Milan, Italy)
V
Sessions, Contents and Events
Opening Session Opening Address on Some Key Issues Concerning R/C Fire Design Pietro G. Gambarova
Page 1
Session 1: Actual State of the Codes on Fire Design in the Different Countries
9
Actual State of the Codes on Fire Design in Japan Kazunori Harada*
11
Actual State of the Codes on Fire Design in Europe Tauno Hietanen*
21
Codes and Standards for Fire Safety Design of Concrete Structures in the US Long Phan*
25
Session 2: Properties, Constitutive Models and Sectional Analysis
35
The Effects of the Constitutive Models on the Prediction of Concrete Mechanical Behaviour and on the Design of Concrete Structures Exposed to Fire Yngve Anderberg*
37
Finite-Element Modelling of Concrete Subjected to High Temperature Francesco Pesavento*, Darek Gawin, Carmelo E. Majorana and Bernhard A. Schrefler
49
On the Fire Behavior of R/C Sections Subjected to an Eccentric Axial Force Patrick Bamonte and Alberto Meda
57
High-Temperature Performance of a HPFRC for Heavy-Duty Road Pavements Stefano Cangiano and Patrick Bamonte
63
FRC Bending Behaviour: a Damage Model for High Temperatures Matteo Colombo, Marco di Prisco and Roberto Felicetti
69
Mass Transport through Concrete Walls Subjected to High Temperature and Gas Pressure Gérard Debicki and Abdelslam Laghcha
81
Microstructure of High-Strength Concrete Subjected to High Temperature Gian-Luca Guerrini, Pietro G. Gambarova and Gianpaolo Rosati
89
Mechanical Properties of HPC at High Temperature Izabela Hager and Pierre Pimienta
95
VII
Measurement of Concrete Thermal Properties at High Temperature Robert Jansson
Page 101
Experimental Investigation on Concrete Spalling in Fire Robert Jansson and Lars Boström
109
Fire Tests on Fibre-Modified Concrete Sven J. Seirer
115
Constitutive Aspects of High Temperature Material Models Kaspar Willam, Holger D. Basche and Yunping Xi
121
Session 3: Structural Behavior and Plastic Analysis
131
Plastic Analysis of Concrete Structures Subjected to Fire Jean-Marc Franssen*
133
Nonlinear and Plastic Analysis of Reinforced-Concrete Beams Paolo Riva*
147
Structural Behavior and Failure Modes of R/C at High Temperature: R/C Sections and 2-D Membersi Patrick Bamonte, Roberto Felicetti, Pietro G. Gambarova and Alberto Meda
159
Plastic-Fracturing Model for the Analysis of Reinforced-Concrete Structures in Fire Jan Cervenka, Jiri Surovec and Vladimir Cervenka
175
Session 4: Detailing and Connections
183
Transient Thermal 3D FE Analysis of Headed Stud Anchors Exposed to Fire Josko Ožbolt*, Rolf Eligehausen, Ivica Kožar and Goran Periskic
185
Preliminary Pull-out Tests on Post-Installed Mechanical Fasteners Embedded in Thermally-Damaged Concrete Patrick Bamonte, Pietro G. Gambarova, Lorenzo D’Agostino and Alessandro Genoni
199
Session 5: Assessment after Fire and Structural Repair
209
Digital Camera Colorimetry for the Assessment of Fire-Damaged Concrete Roberto Felicetti*
211
Petrografic Analysis of Fire - Damaged Concrete Neil Short and John Purkiss*
221
Damage Assessment in Actual Fire Situations by Means of Non-Destructive Techniques and Concrete Tests Andrea Benedetti and Enrico Mangoni The Drilling-Resistance Test for the Assessment of the Thermal Damage in Concrete Roberto Felicetti
VIII
231 241
Session 6: Real Fires, Large-Scale Tests and Model Validation Fire Engineering Design of Concrete Structures Tom Lennon*
Page 249 251
Fire Tests on Single-Shell Tunnel Segments Made of a New High-Performance Fireproof Concrete Ekkehard Richter*
261
On the Role of Concrete Slabs in Composite Steel-Concrete Structures Subjected to Fire Ahmed Allam, Richard Witasse and Giovanna Lilliu
269
The Effects of the Restraint Conditions on the Fire Resistance of Tunnel Linings Céline Féron
271
Test Results on the Fire Resistance of Precast Plates and Panels Provided with Polystyrene Void Formers Andrea Franchi
281
Spalling of Self-Compacting Calcareous High-Strength Concrete after a Firei Karl Kordina
285
Fire Behaviour of HPLWC Hollow-Core Slabs: Full-Scale Furnace Tests and Numerical Modelling Annibale L. Materazzi and Marco Breccolotti
289
Slender Steel-Concrete Columns in Fire: Testing and Modelling by Means of Simplified Approaches Annibale L. Materazzi, Emidio Nigro and Marco Breccolotti
295
Fire-Resistance of Precast Elements: Research Activity within the Italian National Project “Ulisse”i Sergio Tattoni
307
Session 7: Future Work in the Light of Science-Industry Cooperation
311
Fire Safe Design: Make it Concrete! Joris Fellinger* Research versus Industry Arnold Van Acker*
313
Participants
327
Authors
329
Subject Index
331
315
IX
Supporters and Sponsors
Page 335
Program of the Workshop
337
RILEM Committee TCHTC: Agenda of the meeting of December 1st, 2004
339
Seminar: Issues in Failure Analysis of Concrete Materials under Extreme Temperatures, December 1st, 2004 (Kaspar Willam)
341
fib Task Group 4.3 – fib Working Party 4.3.2: Agenda of the meeting of December 4th, 2004
343
(*) Key Speaker
(i) Available at the workshop, but not presented
X
Opening Address on Some Key Issues Concerning R/C Fire Design
Pietro G. GAMBAROVA Professor of Structural Engineering Milan University of Technology Milan, Italy
Fire has always been a “hot” issue for mankind, for the worst and for the best, as demonstrated by the many ways fire is mentioned and recalled in the history and in the literature, as well as in everyday life. In winter’s tedious nights, seat by the fire with good old folks, says Shakespeare, but don’t play with fire is a common saying whenever risky matters are at hand! One sets the world on fire, when he achieves worldwide success, but the Great Fires of London (1666) and Chicago (1871) have been a long-lasting nightmare for many Britons and Americans! The duplicity of fire – which is a mark of warmth (= life) and danger (= death) – is probably the reason why in the past fire was not considered a major problem in some countries (the “warm” countries, where winters are short and open-air living is common) and was instead a sort of obsession in other countries (especially in the “cold” countries, where woods are plenty and timber is extensively used for buildings). In our construction world, fire is definitely a danger (and often a nightmare), which has to be prevented and fought by all possible means. Although with a low level of probability, fire may occur anywhere, in any season, but when fib Task Group 4.3 met in Braunschweig in the cold November 2003, fire as a means to stay hot and comfortable was – in my opinion - the hidden thought of many task-group’s members! Consequently, this inexpressed thought was probably the driving force behind the proposal to organize a workshop on fire design in the coldest season, either in Belgium or Northern Italy, that are hardly appreciated for their mild Decembers! Then Milan was chosen, and the workshop was organized. More than 60 scholars, experts, designers, researchers and managers registered for the two intensive days of the workshop and for the other events, with more than 50% of the attendees coming from abroad. More than thirty papers were submitted to the organizing committee of the workshop and are published in the proceedings. These papers are the backbone of the seven sessions of the workshop, that cover most of the issues concerning Structural Fire Design. Going to specific issues, numerous topics are still open to investigation and discussion, and at least one of the workshop sessions is devoted to each topic: x Materials: thermal properties and thermal diffusivity as a function of the temperature (first heating, cooling and reheating); aggregate and cement roles; fibers role (metallic and/or polymeric fibers); stress-crack opening law at high temperature; fracture parameters at high temperature; modeling of mass transport of water and water vapor. x Sectional analysis: M-N envelopes and failure modes of the reinforced sections made of different cementitious composites (NSC, LWC, HPC, HPLWC, FRC, HPFRC, SCC, HPSCC); validity of the reduced-section approach under an eccentric axial force, at high temperature and after cooling (reference temperature).
1
x Structural analysis: transient creep and its role in structural behavior; failure modes during and after a fire; effects of the restrained thermal expansion; cover spalling (local, extended, in highperformance concrete with/without silica fume). x Assessment after fire: non-destructive methods based on the residual concrete color and on the resistance to drilling, in order to evaluate the maximum temperature locally reached by the concrete; shear sensitivity and bond sensitivity in damaged R/C and P/C structures; residual strength of ordinary reinforcement (outwardly-tempered, stainless-steel and low-/high-carbon rebars) and prestressing tendons (high-strength wires and strands). x Real fires, large-scale tests and model validation: failure modes (because of materials decay, restrained thermal expansion, thermal expansion of nearby members and loss of bond in P/C members); temperature distribution in hollow-core slabs; actual temperature of the reinforcement. x Connections: ultimate capacity of the different types of fasteners at high temperature and after cooling (failure modes under axial and shear forces; design models). x Codes: should they be more detailed, more general, more material-oriented, more memberoriented, more structure-oriented? With reference to cementitious materials, their behavior in direct tension at high temperature is still a challenge, and the test results available in the literature are scanty indeed (Figs. 1-5 [1-5]). Further results are badly needed, since they are instrumental in evaluating such fracture parameters as materials specific fracture energy, toughness and characteristic length, not to speak of the whole stress-crack opening curve. These parameters have been extensively investigated after cooling, with reference to the maximum temperature reached in the material, but there is mixed evidence in terms of loss of toughness, increased ultimate strains and greater damage diffusion. On the whole, the material becomes more strain-tolerant. However, the question is: what happens at high temperature? With reference to sectional analysis, the reduced-section (or effective-section) approach is known to work well in pure bending, but its validity in the case of combined bending and axial loading is not completely proved, even if some results show that this approach is conservative. However, we know that being too conservative is not the key to sound design. With reference to the structural behavior, more or less extended cover spalling, with sectional reductions and rebar live-fire exposure is still a “hot” topic (Fig. 6 [6,7]), which requires the study of concrete mass-transport phenomena, and the modeling of its hygro-chemo-mechanical behavior, to work out “safety envelopes” in the (moisture content)-(applied stress) domain, in standard-fire conditions. Of course, also the failure mode of the various members is generally affected by high temperature, during and/or after a fire, often with less bending sensitivity and more shear sensitivity, as recently demonstrated by a few dramatic collapses (Fig. 7 [8]). With reference to repair and assessment, there are several approaches aimed to assess the properties of the damaged concrete and to evaluate the maximum temperature reached locally, but user-friendly methods are still to be developed. However, remarkable headway has been recently made in such diversified fields as concrete drilling resistance (Fig. 8 [9]) and concrete colorimetry, both – needless to say - after the fire. Another very specific subject that has captured the interest of an increasing number of researchers – both in the industry and in the academy – is the behavior of the fastening devices in extreme environmental conditions because of fire and/or corrosion. The data available so far at high temperature come mostly from Stuttgart, but further studies are needed, to formulate user-friendly design methods. As a matter of fact, there is a strong demand in this field, since heavy-duty fasteners are increasingly used in very severe conditions, such as those occurring in the tunnels,
2
where fasteners support various primary systems, that should work even in fire conditions (for ventilation, electric-power supply, fire extinguishment and traffic control). Finally, a few words on codes: since the sectional and member behaviors are strictly related to temperature space- and time-evolution, the thermal properties of the materials should be introduced as exhaustively as possible. To make an example, Fig. 9 [10,11] shows the actual dependence of the thermal diffusion on the temperature, for a normal-strength, mixed-aggregate concrete and for two light-weight concretes (normal-strength and high-performance), while the full and dashed curves are the upper and lower bounds proposed in the most recent version of EC 2 – Fire Design (2002). A little too much attention is paid to materials behavior, and more attention should be devoted to structures? It is probably true, but one should remember that most of the funds allotted to fire research today comes from cement and concrete producers, under the pressure of the many new or highly-innovative cementitious composites coming onto the scene. Furthermore, durability – even under fire – is a key issue, that has to do more with the materials, than with the structures. However, there is no doubt that the fire behavior of any newly-developed material should be checked against its structural advantages. To sum up, matching materials and structures, and assessing the structural advantages of the new materials are still the real challenges!
Fig. 1 - Tests at high temperature by Takeuchi et al. (1993 [1]): relative compressive strength; relative tensile strength; and relative Young’s modulus; fc = 40 (43) MPa; fct = 2.7 (3.3) MPa; and Ec = 34 (40) GPa at 20°C, curing at 65% (100%) R.H.
Fig. 2 - Mechanical properties of 3 HPC/UHPC at high temperature and after cooling (Felicetti et al., 2000 [2]): (a) HSC with mixed aggregates, fc = 92 MPa; (b) CRC with vf = 6% steel microfibers, fc = 158 MPa; and (c) RPC with vf = 2% steel microfibers + 2% polypropylene fibers, fc = 165 MPa.
3
Fig. 3 - Residual fracture energy for different heating temperatures: (a) NSC and HPC at 15 days (fcc = 57 and 78 MPa at 28 days, no silica-fume, w/c = 0.54 and 0.30, see Zhang et al., 2000 [3], and Zhang and Bicanic, 2002 [4]); and (b) HPC/HSC and UHPC at 90-120 days (fc = 92 and 158,165 MPa at 28 days, see the caption in Fig. 2, Felicetti et al., 2000 [2]).
Fig. 4 - Residual fracture energy (a) and characteristic length (b) for various normal-strength concretes (Barragán et al., 2001 [5]): control concretes (virgin materials); , (,) cooling from 500°C (700°C); O slow cooling (controlled inside the furnace); quick cooling (under sprayed water); crushed granite as coarse aggregate; (boxed values) natural (river) gravel as coarse aggregate; the connecting lines identify the tests referring to the same concrete mix-design.
4
Fig. 5 - Plots of the toughness (a) and of the characteristic length (b) for different heating temperatures (Zhang et al., 2000 [3]; Zhang and Bicanic, 2002 [4] ).
(b) (a)
(d)
(c)
Fig. 6 - Cover spalling: (a) possible causes due to preloading VL, restrained thermal expansion VT and pore pressure VP (Khoury, 2000 [6]); (b) cross-sectional damages to beams and columns; (c) local spalling; and (d) extended spalling; for (b,c,d) see Mlakar et al. (2003 [7]).
5
Fig. 7 - Fire-induced roof collapse in the underground parking lot of Gretzenbach (Switzerland, November 2004): view of the tops of the R/C columns supporting the slab, after the collapse of the roof (90’ past the beginning of the fire, and while the firemen were still at work); the slab was covered by a thick soil layer; the column-slab joints failed in punching [8].
Relative drilling resistance
140% 120%
540°C 100%
430°C 80% 60% 40% ordinary lightweight
20% 0% 0
200
400
600
800
Temperature °C Fig. 8 - Evaluation of the maximum temperature reached by the concrete during a fire: example of the correlation between the drilling resistance (after the fire) and the temperature, as obtained with a modified commercial hammer-drill (Felicetti, 2004 [9]); NSC, LWC: fc20 | 42 MPa.
6
1 NSC LWC HPLWC EC2 lower bound EC2 upper bound
0.8
Fig. 9 - Plots of the thermal diffusivity of various concretes, as a function of the temperature: tests and code; NSC, fc = 30 MPa, mixed aggregates; LWC, fc = 39 MPa; and HPLWC, fc = 56 MPa (Felicetti et al., 2002 [10]; EC-2 “Structural Fire Design”, 2003 [11]).
0.6
D x 103 [m2/h] 0.4
0.2
0 0
400
T [°C]
800
1200
Fundamental References [1] TAKEUCHI M., HIRAMOTO M., KUMAGAI N., YAMAZAKI N., KODAIRA A. and SUGIYAMA K., “Material Properties of Concrete and Steel Bars at Elevated Temperatures”, Proc. SMiRT-12, Paper H04/4, Elsevier Science Publ., June 1993, pp.133-138. [2] FELICETTI R., GAMBAROVA P.G., KHOURY G.A. and NATALI-SORA M.P., “Mecha-nical Behaviour of HPC and UHPC in Direct Tension at High Temperature and after Cooling”, Proc. 5th RILEM Symposium BEFIB’2000, Lyon (France), September 2000, pp.749-758. [3] ZHANG B., BICANIC N., PEARCE C.J. and BALABANIC G., “Residual Fracture Properties of Normal- and High-Strength Concrete Subject to Elevated Temperatures”, Magazine of Concrete Research, V.52, No.2, 2000, pp.123-136.
[4] ZHANG B. and BICANIC N., “Residual Fracture Toughness of Normal- and High-Strength Gravel Concrete after Heating to 600°C”, ACI-Materials Journal, V.99, No.3, 2002, pp.217-226.
[5] BARRAGAN B.E., GIACCIO G.M. and ZERBINO R.L., “Fracture and Failure of Thermally-Damaged Concrete under Tensile Loading”, Materials and Structures, V.34, No.239, 2001, pp.312-319. [6] KHOURY G.A., “ Effect of Fire on Concrete and Concrete Structures”, Progress in Structural Engineering Materials, V.2, 2000, pp.429-447. [7] MLAKAR P.F., DUSENBERRY D.O., HARRIS J.R., HAYNES G., PHAN L.T. and SOZEN M.A., “The Pentagon Building Performance Report”, ASCE – SEI, January 2003, 77 pp. [8] http://www.feuerwehr-hinwil.ch/info/gretzenbach medien.htm [9] FELICETTI R., “Drilling November 2004.
Resistance
of
Fire-Damaged
Concrete”, private communication,
[10] FELICETTI R., GAMBAROVA P.G., SILVA M. and VIMERCATI M., “ Thermal Diffusivity and Residual Strength of High-Performance Light-Weight Concrete Exposed to High Temperature”, Proc. 6th Int. Symposium on the Utilization of High-Strength/High-Performance Concrete, V.2, Leipzig (Germany), June 2002, pp.935-948. [11] EC-2, “Design of Concrete Structures – Part 1.2: General Rules – Structural Fire Design”, CEN, prEN 1992-1-2, October 2002.
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Session 1
Actual State of the Codes on Fire Design in the Different Countries
Actual State of the Codes on Fire Design in Japan Kazunori Harada*
Page 11
Actual State of the Codes on Fire Design in Europe Tauno Hietanen*
21
Codes and Standards for Fire Safety Design of Concrete Structures in the US Long Phan*
25
9
Actual State of the Codes on Fire Design in Japan Kazunori HARADA Associate Professor Dept. of Architecture and Architectural Engrg. Kyoto University Kyoto, Japan
Summary The Japanese building standards were revised five years ago (2000), in order to include performance-based criteria in the area of fire resistance of structural members. However, the new approach did not substitute the conventional prescriptive-design methods, and both approaches coexist at the moment. With reference to performance-based criteria, this paper summarizes the main points of their technical basis. The new standards consist of two parts, with the first aimed to evaluate the severity and duration of the natural fires to be expected in building compartments, and the second aimed to calculate the fire duration leading to the collapse of any given structural member. Beside prescriptive design, simplified performance-based rules are available for conventional R/C members made of normal-strength concrete. As for high-strength concrete, rational design methods are under development. Finally, simple design rules based on experimental evidence are available for concrete-filled tube columns. Keywords:
1.
building standards law, performance evaluation, natural fires, deterioration depth.
Introduction
Historically, reinforced concrete structures had been deemed to be fire resistant. It was true for most of conventional concrete structures. In fire records, there is almost no building that collapsed during fire. However, recent development of new type of concrete such as high strength concrete changes the situation. It is getting obvious that in some cases, fire resistance of concrete structures must be explicitly designed based on performance. In this paper, the state-of-the-art of fire resistance design of concrete in Japan is summarized in two parts. First part corresponds with structure of building regulations on fire resistance of buildings. The second part is associated technical standards for reinforced concrete and composite structures of steel and concrete.
2.
Summary of performance-based changes in Building Standards Law of Japan
The building code of Japan (Building Standards Law of Japan, BSLJ, hereafter) was revised in 2000, including performance-based sentences for fire resistance. A simplified performance evaluation method was provided for various types of structures including concrete. 2.1
Requirements
The BSLJ was revised in 1998 to include functional requirements in place of detailed technical specifications of materials and constructions. Even though it is not perfect, the law has shifted towards performance-based format. Following the changes in law, enforcement order (detailed items of regulation) and notifications (technical standards) were revised in June 2000. Concerning with the structural fire resistance, performance evaluation framework and a set of simplified calculation formula have been added as Kenshoho (verification method) for fire resistance. By using verification method, it is possible to check the adequacy of fire resistance of structural elements easily and quickly.
11
2.2
Functional approach
After the revision, it is possible to adopt functional approach in fire resistance design. The objective implied in BSLJ is to prevent; (1) collapse due to fires that are foreseeable to take place in the building, (2) fire spread to the buildings during fires that normally takes place around the building. The functional requirements to satisfy the objective are; (1) Load-bearing structural part shall sustain load throughout the complete process of fire. (2) Building envelope (exterior walls and roofs) shall not create a gap that may penetrate flame from inside to outside (3) Floors and internal firewalls shall not create a gap to penetrate flame nor transmit heat enough to ignite combustibles in the opposite side of fire compartment in both directions. (4) Exterior walls shall not transmit heat enough to ignite combustibles in the building. The above requirements are summarized in Figure 1.
external fire (nominal)
functional requirements principal structural part openings functional requirements insulation integrity load bearing (structural frame) property line internal fire (foreseeable)
Fig. 1 - Functional requirements for fire resistance.
2.3
Performance evaluation
To satisfy the requirement of BSLJ, planning body can choose among Route A, B and C. as shown in Fig. 2. Route A is a conventional method that follows prescriptions in the code. Code specifies required fire resistance time of principal structural part depending on size (number of stories) of buildings. The principal part shall be made of fire resistive constructions listed in approved constructions. As to concrete-frame buildings, minimum dimensions (diameter and cover thickness) are prescribed as shown in Table 1. Performance-based routes were provided as in Route B and C. Route B is to apply simplified design formula specified in MoC’s notification 1433(2000fy). The chance is at most increased if they choose Route C. The difference between Route B and C are the degree of sophistication and complicity of design process, and the body that will review design solution. In the Route B, design process is simplified enough so that local building authority can review the design solutions themselves. In practice, it means that review and approval process is finished quickly, but at the same time, the design would have to be conservative. In route C submittals, it is possible to adopt any design procedure as long as it follows the requirements of law and as long as it is correct in engineering sense. The appropriateness is judged by a peer- review body, followed an approval by MLIT (Minister of Land, Infrastructure and Transportation).
12
Building Design
Prescribed Design Route Route A (prescribed fire resistance time of structural elements)
Performance-based Design Routes Route B (simplified design calculation of fire severity, thermal & mechanical actions)
Design verification by local building authority
Route C (detailed design calculation of fire severity, thermal & mechanical actions) Evaluation by peerreview body Approval by MLIT
Planning approval by local building authority
Fig. 2 - Three Routes to Conform with Fire Resistance Requirements in BSLJ.
Table 1 - Deemed-to-satisfy Specifications in BSLJ. element of construction wall, floor column beam
fire resistance rating [min] 60 120 60 120. 180 60 120 180
minimum dimension [mm] 70 100 (not specified) 250 400 (not specified) (not specified) (not specified)
minimum cover thickness [mm] (not specified)* 30 30 50 60 (not specified)* 50 60
* Minimum value are specified in terms of durability (20mm for floors, 30mm for columns and beams)
3.
Design methods
Depending on the type of concrete, design methods are selected as follows for most cases. 3.1
Reinforced concrete of ordinary strength
For ordinary strength concrete (design strength Fc > 60N/mm2), simplified design method can be applied. 3.1.1 General principle The general principle for structural fire resistance is to prevent the strength reduction of load bearing elements. Namely the strength (resistance) R must be larger than the service load S throughout the fire process,
R(t ) ! S (t ) , t
13
0~f
(1)
fire temperature
fire duration
time
load and strength
fire temperature
strength reduction
heat impact
R(t) R(tf)
S(t)
thermal stress nominal service load S
S time
tf tfr
Fig. 3 - Typical changes in load and strength of steel column during fire.
The typical changes in strength and service load are shown in Figure 3. Service load increases due to the thermal stress in the early stage of fire. However, at the critical condition of structural endpoint, thermal stress is negligible. This assumption is valid for ductile structures designed against wind and earthquake motion. As a result of seismic resistance design, structural frame is equipped with enough deformation capacity so that the frame is insensitive to perturbations caused by thermal stress in the early stage of fire. Following above assumption, it is practical to check the strength at the fire duration (plus some post fire period) t t f . Equation (1) could be
M
t fr ( S ) t f ! 0 ,
(2)
where S is the load applied by external force. It is more convenient to express by time margin, tfr(S) is the critical time to failure under the service load S. Calculation procedure consists of two parts. The first half is to calculate the fire severity of all the potential fire rooms. The second half is to calculate the time to failure of structural element. The detailed method of application and practical design examples are described in publication [1]. 3.1.2 Calculation of fire severity and duration Figure 4 shows the procedure for calculation of fire severity and duration. First of all, fire compartment boundaries are determined. At the same time, principal structural part is identified. For each fire room, total fire load (Qr[MJ]), heat release rate (qb[kW]), fire temperature coefficient ( D [K/min1/6], where Tf=Dt1/6, Tf [K] is fire temperature) and local fire temperature coefficient ( D l , where Tfl=Dlt1/6, Tfl is local fire temperature) are calculated. Summarizing the calculation results, we can identify the fire- temperature time curve as shown in the last box of Figure 4. As examples, calculation results of fire temperature is shown for various size of openings for a compartment of 10m x 10m x 3m. Fire load density was 480MJ/m2 (30kg-wood/m2).
14
setting fire compartment identifying principal structural part
identification of fire room
total fire load of fire room for all identified fire rooms
heat release rate and fire duration
fire temperature rise coefficient
local temperature rise coefficient
Dt
local fire temperature Dlt1/6
fire temp.
fire temp.
average fire room temperature
1/6
time
tf
time
20min.
Fig. 4 - Calculation Procedure of Fire Severity by Simplified Verification Method. 1200 5m fire temperature [oC]
1000
3m B=1m
800 600 400
1~39
39 (80)
3.5m
2m
200
10m
10m
0 0
60
120 time [min]
180
240
Fig. 5 - Compartment Fire Temperature for Various Opening Size.
15
3.1.3 Calculation of time to structural failure Figure 6 shows the calculation procedure for time to structural end point. The procedure starts with calculation of structural forces during normal condition to determine minimum cross sectional area for load bearing. Then the time to critical thermal deterioration depth (ineffective section, usually taken by 500oC isothermal line) is calculated. structural load G+P
fire temperature rise coefficientD local fire temperature rise coefficient Dl
dimension WxH, ds
calculation of structural forces applied to element (dairy condition)
P
d
critical depth of thermal deterioration (minimum cross sectional area to support structural load)
for all structural steel element
thermal deterioration depth versus time (temperature profile)
T(t) Tcr d(t)
critical time to failure > fire duration tfr > tf
Fig. 6 - Calculation Procedure of Critical Time to Failure by Simplified Verification Method. 1) Design strength at high temperature Fig. 7 shows existing results of compressive strength of concrete at high temperature. For most cases, strength is reduced gradually in the temperature range of 300 and 800oC. At 500oC, strength decreases to about 2/3 of nominal design strength at normal temperature. To make conservative estimate of strength at high temperature, it is assumed that Fc (T )
(2 / 3) Fc ( 20) (20 d T d 500) ® 0 (500 T ) ¯
(3)
where Fc(20) is nominal design compressive strength at normal temperature. 2) Temperature profiles For a concrete members heated by ISO834 standard fires
T f T0
345 log10 (8t 1) | 460t 1 / 6
(4)
the temperature profile can be approximated by
T ( x, t ) T0 460t
1/ 6
16
exp(
cx t
)
(5)
where c is a coefficient depending on the type of material (c=0.21 for normal weight concrete, 0.23 for lightweight concrete). After mathematical approximations, the final form is
713(cx)1 / 3 exp(1.4
T ( x, t )
cx t
) T0 ,
(6)
reduction factor of compressive strength [-]
which is graphically shown in Fig. 8. 1.5
Furumura Hattori Furumura
Schneider Malhotra Abrams
Abe Abe Fc>60N/mm2
1.0
0.5 design strength assumed in calculation
0.0
0
200
400 600 temperature [oC]
800
1000
Fig. 7 - Compressive strength of concrete at high temperatures and design strength [2-8].
temperature [oC]
1200
accurate values
1000
valid range
approx. values
800 time =240 min.
600 60
400 200 0
120
30min 0
100 distance from exposed surface [mm]
200
Fig. 8 - Temperature Profiles against Distance from Fire-exposed Surface as a Function of Time. 3) An example As an example, time to failure of centrally loaded column is calculated. In case of columns, heat is penetrated in two-dimensional way. Corner part is more intensely heated than the flat part. As a result, typical isothermal line would be rounded at corners as shown in Fig. 9. To take into account of the corner effect, thermal deterioration is selected as indicated by hatched area. The cross sectional area of deterioration is calculated by the product of heated perimeter length Hc and thermal deterioration depth d. The remaining cross sectional area is (Ac-d Hc), which has effective strength at least (2/3) of room temperature strength.
17
Thus we get
P ( Ac d H c )(2 / 3) Fc
(7)
by solving for d we get critical value for thermal deterioration depth. Further consideration is made to limit the temperature rise of reinforcing steel. Referring the temperature profile shown in Fig. 8, maximum value for d is limited to twice of cover thickness. This corresponds with limiting the steel temperature less than 600oC. d
½ P min ®( Ac ) / H c , 2d s ¾ (2 / 3) Fc ¿ ¯
(8)
A column shown in Fig. 9 was tested by ISO 834 standard fire [9]. Concrete was normal weight. Room temperature strength was Fc=26.7[N/mm2]. Axial force was P㧩1,391kN(142[tonf]). Using formula (8), critical thermal deterioration depth is
d
3 u1391600 ½ °°160,000 2 u 26.7 °° min ® ,2 u 40¾ 1,600 ° ° ¯° ¿°
min(51.1,80)
51.1 [mm]
(9)
Then the time to failure is calculated by inverse function of (6) as 16772(0.21 u 51.1) 2
t fr 460
3/ 2
§ · 0.673 ¨¨ log e ¸ 1/ 3 ¸ u ( 0 . 21 51 . 1 ) © ¹
2
139 [min.],
(10)
which result in conservative evaluation compared with actual time to failure of 279 minutes. main reinforcement (D16) thermal deterioration depth, d hoop (D6) 400mm
area of thermal deterioration, d Hc
Fig. 9 - Cross sectional shape of fire tested column.
3.2
High-Strength reinforced concrete
The simplified verification method cannot be applied to high strength concrete structures (design strength Fc > 60 N/mm2) due to the following two reasons. 1) spalling of surface layer During the initial stage of fire, spalling of surface layer would take place. In case of high strength concrete, spalling gives significant decrease in surface layers. Quite often, steel rods are exposed to fire, to result in quick increase of temperature. At this moment, it is hard to predict the degree of spalling, thus it is difficult to calculate temperature profile in concrete section. Several design methods are in development. One of the idea is to reduce cover thickness in calculation than it actually has in order to have conservative results.
18
An example is shown in Fig. 10. Spalling depth proceeds almost to the hoop tie bars. Using this cross sectional area, they carried out finite element analysis to calculate temperature profile. Then they proposed the change in M-N (moment- axial force) reaction curve as a function of fire duration.
Fig. 10 - Examples of remaining cross section of high strength concrete columns (Nishigaki et al [10]). 2) mechanical failures High strength concrete members are slender. As a result, members are subjected to the possibility of failure by structural actions such as buckling, lateral actions caused by thermal expansion of several elements within fire compartment. To investigate the mechanical actions of whole and/or partial structural frame, calculation methods are being proposed. Fig. 11 shows an example. 12MN
12MN
12MN
30kN/m ISO 834 fire
deformation (30, 60, 90, 120 and 180 min.)
Fig. 11 - An example of calculation of structural response of partial frame (Niwa et al. [11]).
3.3
Concrete Filled Tube (CFT) columns
A practical design method is published for buildings using CFT columns by ANUHT[12]. Based on the results of ISO 834 fire resistance tests, the relationship between time to structural failure (collapse) and load ratio P/AcFc is summarized as shown in Fig. 12. For practical design purpose, time to failure is calculated by
P Ac Fc
° 5.75 u 10 5 u F 2.63 u t 1 -0.214 c ® -0.225 °¯ 3.06 u 10 3 u Fc1.735 u t 1
19
(for circular tube) (for rectangular tube)
(11)
axial load ratio, P/AcFc [-]
1.0
circular tube 0.8
Fc=34N/mm
2
0.6
Fc=37.4~42.1 Fc=33~34 Fc=54.5~57.8
0.4 0.2
Fc=57.8
Fc=37.4
0.0 0
60
120 180 time to structural failure [min.]
240
Fig. 12 - Time to structural failure of circular CFT columns (Fc=33~57.8N/mm2).
4. Conclusions The state of the art in fire resistance design methods in Japan is reviewed. Most conventional concrete are designed by prescriptive specifications. However explicit design methods for fire resistance is developed for conventional concrete in a conservative way. Several new proposals are being made for high-strength concrete. Practical method is available for CFT columns.
References [1]
[2] [3]
Ministry of Construction, Ed., “Taika Seinou Kenshouhou no Kaisetu Oyobi Keisanrei tosono Kaisetu” (A Guideline on Verification Method for Fire Resistance and Examples) (in Japanese), Inoue Shoin, 2001. FURUMURA F., Transactions of Architectural Institute of Japan, No. 172 and 173, 1970.
[4]
HATTORI T., “Design Method for Thermal Stress in Nuclear Plant Concrete”, Architectural Institute of Japan, 1985. ABE T., Transactions of Architectural Institute of Japan, January, 1999.
[5] [6]
FURUMURA F., Transactions of Architectural Institute of Japan, February, 1988. SCHNEIDER U., “Behaviour of Concrete at High Temperatures”, 1982.
[7]
MALHOTRA H., K., “The Effect of Temperature on the Compressive Strength of Concrete”, Magazine of Concrete Research, Vol. 8, No. 23,84, 1956, p. 84.
[8]
ABRAMS M.S., “Compressive Strength of Concrete at Elevated Temperatures to 1600F (871 °C)”, ACI SP-25, 1971, pp. 33-58.
[9] BRI (Building Research Institute) Experimental Data, 1998. [10] NISHIGAKI T. et al., “Fire Resistance of RC Structure with High Strength Concrete (fc = 100 N/mm2)”, Summaries of Technical Papers, Architectural Institute of Japan, 1995. [11] NIWA H., NAGAO K., NAGANUMA K., ETO H. and TANAKA K., “Analytical Study on Fire Resistance of Reinforced Concrete Structures Using High-Strength Concrete” (in Japanese), Journal of Structural Engineering, Vol. 49B, Architectural Institute of Japan, March 2003, pp. 407-414. [12] Association of New Urban Housing Technology Housing, “Mutaikahifuku CFT-zou Hasira Taika Sekkei Sisin” (in Japanese, Fire Resistance Design of Non-Insulated CFT columns – Guidelines, Technical Explanations and Design Examples), March, 2004.
20
Actual State of the Codes on Fire Design in Europe Tauno HIETANEN Civil Engineer Finnish Concrete Industry Association Helsinki, Finland
Summary The new European standard for fire design of concrete structures is recalled and commented in this paper. Being an integral part of the Eurocodes, this standard will replace the national standards after a coexistence period. With respect to the ENV prestandard and to other CEB bulletins, there are three novelties: (a) two sets of tabulated data for columns; (b) a number of clauses on high-strength concrete; and (c) a few informative rules on shear design of R/C members. Keywords:
buildings, concrete structures, design, European standards, fire resistance.
1. Status and background European standard EN 1992-1-2 Eurocode 2: Design of concrete structures – Part 1.2: General rules – Structural fire design was approved in Formal Vote in June 2004 and it is expected to be published by the end of 2004. European countries have to implement it as national standard. Some safety related numerical values may be chosen or modified in National Annex which should be published in two years. Present national standards may coexist until year 2010. EN 1992-1-2 is revised version of European prestandard ENV 1992-1-2, published in 1995 for experimental use. Fire design rules in Eurocode 2 are based on CEB Bulletins on Fire Design of Concrete Structures, latest edition N° 208 July 1991. Adaptation to the Eurocode system has been done, tabulated data on columns has been completely revised, high strength concrete has been added and some other modifications have been made. EN 1992-1-2 is intended to be used in conjunction with - EN 1990 Basis of structural design - EN 1991-series Actions on structures - EN 1992-1-1 Design of concrete structures – General rules and rules for buildings Background documentation is available on DIN Livelink for European Standard Bodies.
2. Fire actions and load level Actions in fire situation are taken from EN 1991-1-2 Actions on structures exposed to fire. Mechanical actions are reduced by combination factors ȥ which depend on the type of load. Recommended partial factors for actions and materials are = 1,0. As a simplification the effects of actions may be obtained from a structural analysis for normal temperature design as: Ed,fi = Kfi Ed where Ed is the design value of the corresponding force or moment for normal temperature design, for a fundamental combination of actions, Kfi is the reduction factor for the design load level for the fire situation. Reduction factor Kfi is explained in Figure 1. A safe side estimation Kfi = 0,7 may be used.
21
ACTIONS
RESISTANCES
Rd
Ed
Ed,fi with
JF
with
with
JF,fi
JM
and
\fi time Rd Rd,fi Ed u K fi = Ed,fi Pfi = Ed,fi / Rd takes into account if the structure is not fully loaded
Fig. 1 - Load level in fire design.
3. Design methods In principle there are three assessment methods: tabulated data, simplified calculation methods and advanced calculation methods. For advanced calculation methods the principles only are given. Two optional simplified calculation methods are included: 500°C isotherm method as in CEB N° 208 and zone method as in ENV 1992-1-2. In the first one concrete with temperature above 500°C is disregarded and full strength is used for the rest of cross-section. In the second one the cross section is divided into zones and more accurate strength value in each zone is used in calculations. Design methods are illustrated in Figure 2.
Nominal fire Member analysis
Analysis of part of the structure
Global structural analysis
Determination of mechanical actions and boundary conditions
Determination of mechanical actions and boundary conditions
Selection of mechanical actions
Tabulated data
Simplified calculation
Advanced calculation
Fig. 2 - Design methods for standard fire.
22
4. Slender columns Tabulated data on columns has been completely revised. There are two optional methods. Method A is empirical, developed in Belgium from analysis of approximately 80 full scale tests. It is easy to use but the field of application is limited to typical building construction slenderness and eccentricity values. Load level is taken into account in the Table. Other values for tabulated data may be assessed by an equation with load level, reinforcement, concrete cover, buckling length and cross section dimensions as parameters. Method B is based on calculations. The field of application covers practically all columns, but it is more complicated to use, often requiring interpolations, and it gives more conservative results than method A.
5. High strength concrete Rules for high strength concrete have been included. Strength reduction at elevated temperatures depends on the composition and constituents of concrete. National Annex may choose strength reduction from three recommended classes, see Figure 3. There are four optional methods against spalling: surface reinforcement mesh, tested type of concrete, protective layers or polypropylene fibres. 1
Strength reduction
0,9 0,8 0,7
Class 1 Class 2 Class 3
0,6 0,5 0,4 0,3 0,2 0,1 0 0
100
200
300
400
500
600
700
800
Temperature
Fig. 3 - High strength concrete, strength reduction classes.
Fig. 4 - Reference temperature for shear reinforcement.
23
6. Shear, torsion and anchorages Simplified calculation rules for shear, torsion and anchorage are given in an informative annex. These rules give guidance how to define the reference temperature of shear reinforcement. It is reminded that non-linear temperature distributions may cause tensile stresses, reducing shear capacity for some types of cross sections The reference temperature T p should be evaluated at points P along the line ‘a -a’ for the calculation of the shear resistance. The effective tension area A may be obtained from EN 1992-1 (SLS of cracking), see Figure 4.
References [1] EN 1990 Basis of structural design [2] EN 1991 Actions on structures [3] EN 1992-1-1 Design of concrete structures – General rules and rules for buildings [4] EN 1992-1-2 Design of concrete structures – Structural fire design
24
Codes and Standards for Fire Safety Design of Concrete Structures in the U.S.
Long PHAN Research Structural Engineer National Institute of Standards and Technology Gaithersburg, Maryland, USA
Summary This paper summarizes current mandatory codes, standards, and non-mandatory design guides pertaining to fire safety design of concrete structures in the U.S. The paper also discusses existing research gaps and barriers that prevent structural fire safety design from being a more common practice at present, and describe current efforts being undertaken at the National Institute of Standards and Technology (NIST) to develop the technical basis for moving from the current prescriptive design methods to performance-based fire safety design.
Keywords:
1.
codes, concrete, fire, fire protection, fire safety design, performance-based, spalling, temperature.
Introduction
At present, regulatory procedures for fire safety design of structures, including concrete structures, in the United States are principally based on the provisions of two model building codes: The International Building Code 2000 (IBC 2000) [1], published by the International Code Council (ICC), and the Building Construction and Safety Code NFPA 5000 (NFPA 5000) [2], published by the National Fire Protection Association (NFPA). These model codes prescribe minimum fire safety requirements, in terms of fire endurance ratings, and methods for obtaining fire endurance ratings for building elements, as well as other prescriptive fire protection measures such as the locations and types of fire protection systems (fire walls, fire and smoke barriers, automatic sprinkler systems, standpipe systems, fire alarm and detection systems, smoke and heat vents, etc.) and the means of egress. These code provisions are prescriptive and component-oriented. When complied with, the building is deemed to have met the code intent for fire protection, which is primarily to ensure life safety of building occupants and emergency fire responders by providing sufficient time for evacuation in a conventional building fire and, to a lesser extent, to provide a measure of property protection. Developing fire protection strategies for a building is primarily the responsibility of the architect of record. The architect often specifies the fire protection features and, through the interpretation and application of the prescriptive code requirements, ensures that they comply with the intent of the codes. This is usually done separately and after the structural design for other conventional load conditions, such as loads caused by earthquake, wind, and snow, is complete. Calculation of structural response due to fire exposure is not a common practice nor it is required in the current code requirements. Recent incidences of large building fires caused by terrorist attacks have brought into sharper focus the need for a more science-based fire safety design methodology where the structural responses due to exposure to various design fire scenarios can be evaluated and designed for. The need for a science or performance-based approach for structural fire safety design is further
25
emphasized for concrete structures given the adverse structural and material responses observed in many recent structural and material fire tests [8-18]. In the sections that follow, a summary of applicable provisions of current model codes and standards in the US is provided, a discussion on the applicability of the current codes to concrete structures is outlined, and issues that need to be addressed for the development of a performance-based structural fire safety design approach are discussed.
2.
Summary of current US Codes and Standards and their applicability
Provisions for fire protection of structures prescribed by the model codes are adopted, in whole or in part, by the building codes of different states or local jurisdictions in the U.S. These fire protection provisions are handled separately from the structural design procedures for other loads such as snow, wind, gravity, and earthquake loads. The sections below summarize the scope the fire protection provisions of the two current US model codes and the relevant standards that are referenced by these codes. 2.1
IBC 2000
The objectives of IBC 2000’s fire protection provisions are primarily to ensure life safety (of building occupants and emergency fire responders) and, to a lesser extent, to provide a measure of property protection. These objectives can be achieved by using fire-resistance-rated-constructions with fire resistance ratings that meet the prescribed minimum requirements and by complying with other requirements for active fire protection measures. IBC 2000 prescribes the following methods for determining fire resistance ratings of different building components or subassemblies: x x x x
Qualification testing: based on standard fire exposure and test procedure set forth in ASTM E 119 Standard Test Methods for Fire Tests of Building Construction and Materials [3]. Fire resistance designs documented in approved sources. Prescriptive designs of fire-resistance-rated building elements: based on tabulated data provided by the code for different structural parts Calculated fire resistance method: for concrete, the prescribed methods for calculated fire resistance ratings of different assemblies are those prescribed by ACI/TMS 216 Standard Method for Determining Fire Resistance of Concrete and Masonry Assemblies [4]
In addition to these methods for determining fire resistance ratings of structural components, IBC 2000 also specifies prescriptive requirements for other fire protection measures such as the types and locations of fire protection systems (automatic sprinkler systems, standpipe systems, fire alarm and protection systems, smoke control systems, smoke and heat vents, etc…) and the means of egress. A brief description of ASTM E 119 and ACI/TMS 216, which are referenced by IBC 2000, is given below. 2.1.1 ASTM E 119 ASTM E 119 specifies laboratory procedure and criteria for determining fire resistance ratings of building components or assemblies exposed to a prescribed standard time-temperature history. This standard time-temperature history does not represent real fire conditions, which can vary with compartment size and configuration, ventilation, and fuel loads. The results of this standard test are meant to provide a relative measure of the fire test response, in terms of fire resistance ratings, of comparative test components and assemblies, and are not meant to provide an assessment the structural performance of the tested elements. Fire testing of concrete components and assemblies in accordance with ASTM E 119 is often controlled by the following two acceptance criteria: x Heat Transmission Criterion: which requires sufficient thickness of concrete is provided to limit unexposed surface temperature rise of walls, floors, and roofs. x Load Carrying Ability Criterion: which requires sufficient thickness of concrete cover is provided so that the yield strength of steel reinforcement is at least 50% of that at ambient temperature.
26
2.1.2 ACI/TMS 216 Standard ACI/TMS 216 is referenced by IBC 2000 as an approved method for calculating fire resistance ratings of concrete, concrete masonry, clay brick and tile masonry assemblies. This standard does not apply to composite metal deck floor or roof assemblies. Except for continuous concrete slabs and beams, where ACI/TMS 216 provides procedures for calculating fire resistance ratings, guidance for concrete columns and walls are strictly based on prescriptive tabulated data. The fire resistance rating calculated or determined by methods prescribed by ACI/TMS 216 is also based on the standard fire exposure prescribed in ASTM E 119. The current version of ACI/TMS 216 does not specify a range of concrete compressive strengths for which its provisions and calculation methods are applicable. In the calculation methods prescribed for concrete slabs and beams, ACI/TMS 216 allows the concrete compressive strength, f’cT, to vary as a function of temperature. However, this compressive strength-temperature relationship is mainly based on one set of experimental data obtained for normal strength concrete [5] and thus might not be applicable when concrete with higher strength grade is concerned. 2.2
NFPA 5000
In terms of fire protection, the objectives of model code NFPA 5000 are similar to IBC 2000’s. NFPA 5000 provides prescriptive requirements for fire protection of fire walls, fire barrier walls, horizontal assemblies, exterior walls, smoke barrier, vertical openings, mezzanine, joints, concealed spaces, etc. and specifies the following methods for determining fire resistance ratings of fireresistive materials and constructions: x x x
Qualification testing: based on standard fire exposure and test procedure set forth in NFPA 251 Standard Methods of Tests of Fire Endurance of Building Construction and Materials [6]. Analytical methods: as prescribed by ASCE/SFPE 29 Standard Calculation Methods for Structural Fire Protection for Structural Elements or Assemblies [7] or ACI/TMS 216 Standard Methods for Determining Fire Resistance of Concrete and Masonry Assemblies. Other approved analytical methods based on the fire exposure and acceptance criteria specified in NFPA 251.
A brief summary of ASCE/SFPE 29 and NFPA 251 is provided below. ACI/TMS 216 is also referenced by model code NFPA 5000 and its summary has been provided in the above section. 2.2.1 ASCE/SFPE 29 ASCE/SFPE 29 provides calculation methods for determining equivalent fire resistance ratings for selected structural members and barrier assemblies made of steel, concrete, concrete masonry, clay masonry, and wood that would have been achieved in the ASTM E 119 standard fire test. Thus, as is the case for ACI/TMS 216 standard, the fire resistance ratings calculated using this standard do not necessarily describe performance for natural fires having a time-temperature relationship different from that prescribed by ASTM E 119. The concrete provisions of ASCE/SFPE 29 are applicable to: (1) plain, reinforced, and prestressed concrete made with cementitious materials, aggregates (siliceous, carbonate, sand-lightweight, lightweight); (2) concrete with specified compressive strength f’c not exceeding 69 MPa; (3) cast-in-place, precast, and slabs cast on stay-inplace steel forms where slab is designed to carry all superimposed loads including the slab dead load; (4) walls – single and multi-wythe; (5) floors – single and multi-layer, restrained and unrestrained; (6) roofs – with and without insulation, restrained and unrestrained; (7) beams – restrained and unrestrained; and (8) columns. Except for the method for calculating the fire resistance ratings and concrete cover for flexural members (provided by ACI/TMS 216 and not provided by ASCE/SFPE 29) and the range of applicable concrete compressive strength (limited to 69 MPa in ASCE/SFPE 29 and not defined in ACI/TMS 216), the calculation methods for concrete components prescribed by ASCE/SFPE 29 are mostly identical to those prescribed by ACI/TMS 216.
27
2.2.2 NFPA 251 NFPA 251 Standard Methods of Tests of Fire Endurance of Building Construction and Materials prescribes laboratory procedures and methods for qualification testing of building materials and assemblies subjected to a standard time-temperature history. The standard time-temperature history and most of the test procedure and requirements specified by NFPA 251 are identical to those specified by ASTM E 119. One minor difference between these two standards is that NFPA requires the furnace temperatures to be recorded at intervals not exceeding 1 min during the test period, while ASTM E 119 requires the furnace temperature to be recorded at intervals not exceeding 5 min during the first 2 h of the test, and thereafter at intervals not exceeding 10 min. 2.3 Discussion Current codified methods for fire safety design of structures in the US are prescriptive and component or subassembly oriented. The fire endurance ratings obtained using these methods are not based on real fires but on a prescribed standard time-temperature history, and thus do not represent the actual structural behavior of the building components. Because the methods are based on tests of individual components or subassemblies, the effects on global structural response due to interaction between building components, as would occur in a 3-D structure, are ignored and the fire resistance rating of the entire structure is often assumed to be equal to that of the component with the least fire resistance rating.
Fig. 1 – Lateral column displacement [8,9]. It is important to note that instances of actual collapse of concrete buildings or large numbers of fatality of concrete building occupants due to conventional building fires are rare. This suggests that the current prescriptive fire safety design procedures are adequate to satisfy the code intent, which is to provide life safety. On the other hand, recent incidences of fire in high rise buildings caused by terrorist attacks, coupled with adverse structural and material behaviors observed in laboratory studies when concrete is exposed to fire, do indicate that there are structural performance issues unique to concrete that are not adequately considered in the current prescriptive design methods. At the global structural response level, a full-scale fire test of a 7-story concrete building, conducted at the Building Research Establishment (BRE) Laboratories at Cardington [8,9], revealed
28
(1) significant lateral displacements of the columns at the slab-column joints due to thermal expansion of the heated concrete slab (see Fig. 1) and (2) massive, early spalling (12 min after fire ignition at an ambient temperature of about 750 qC for a 60 min fire resistance rated structure) of the floor slab (C37 normal weight concrete), probably due to the high compressive stress induced by the restraint to thermal expansion of the heated region of the slab by the cooler surrounding region, resulting in loss of large areas of concrete cover for slab reinforcement. While the test structure did not collapse, these observations indicate potential for structural instability and premature loss of structural capacity and underscore the potentially detrimental effects of fire on the structural performance of concrete structures that are not considered in the current prescriptive codes. 1.2 Other NSC Tests Castillo Diederichs Abrams (Carbonate) Abrams (Siliceous)
1
Other HSC Tests
ht g n er t S e vti al e R
Castillo Hammer Diederichs Furumura Khoury
0.8
0.6
RakMK B4 K70-K100 RakMK B4 NSC No Preload
0.4
NIST HSC Tests Mixture I Mixture II Mixture III Mixture IV
0.2
0 0
200
400
600
800
1000
o
Temperature ( C)
Fig. 2 - Unstressed test data vs. codes [16-18].
Relative Strength
At the material response level, it is well known that concrete, depending on its w/c ratio and strength grade, is susceptible to loss of mechanical properties and spalling when exposed to elevated temperatures. A compilation of results of various studies [5,10-21] where concrete specimens were subjected to steady-state temperature exposure also shows that the degradation of mechanical properties is different for 1.2 normal and high strength concrete in NIST HSC Tests the intermediate temperature range NIST Mixture I NIST Mixture II (100 qC to 400 qC) . A comparison of NIST Mixture III 1 NIST Mixture IV these test results, in terms of relative compressive strengths of normal 0.8 strength (NSC) and high strength concretes (HSC) with respect to room temperature compressive strength, with RakMK B4 K70-K100 0.6 RakMK B4 NSC 30% Preload each other and with existing European code provisions [19-21] are shown in Other HSC Tests 0.4 Castillo Figures 2 and 3. These adverse material Khoury responses are unique to concrete and, CEB Other NSC Tests while well known, are not yet 0.2 Abrams (Carbonate) adequately accounted for in the fire Eurocode Siliceous Abrams (Siliceous) Eurocode Calcareous safety design provisions of current US 0 model codes and standards. 0 200 400 600 800 1000 o
Temperature ( C)
Fig. 3 - Stressed test data vs. codes [16-18].
29
Given these observations, an argument can be made for the need to develop a more sciencebased approach for structural fire safety design that can take into account these uniquely-concrete behaviors, at least for some signature or critical structures where continuing function and collapse prevention are part of the design objectives.
3.
Performance-based structural fire calculation: what are needed?
The NIST’s Building and Fire Research Laboratory, as the US national laboratory responsible for research into building fires, has been conducting research to put structural fire protection on a stronger scientific footing. As part of this effort, NIST, in collaboration with the Society of Fire Protection Engineers, organized a workshop (Baltimore, October 2003) [22] to provide a forum where input from the global fire safety engineering community was sought for use in the development of a comprehensive research and development roadmap for structural fire safety design and retrofit of structures. The workshop was attended by US and international experts in areas of structural and fire protection engineering, research and testing, as well as architecture, academia, building regulation, insurance, and professional associations. The workshop brought into focus many issues that need to be addressed before performance-based structural fire calculation methods can be developed and become widely used for fire safety design. These issues include not only engineering issues, but also non-engineering issues such as the challenges to code officials in the approval process and the change in professional responsibility for structural engineers if they are to be involved in the fire protection calculation. 3.1
Engineering issues
Unlike current prescriptive method where relative performance of building components are rated based on a pre-defined standard fire exposure, performance-based methods for structural fire response calculation will require an integrated approach involving both the characterization of fire exposure (as imposed load) and the calculation of thermal and structural response to the specified fire exposure. 3.1.1 Characterization of Fire Exposure Characterization of fire exposure for fire safety design of concrete structures involves two issues: Determining the location and spatial distribution of fire hazards on structures and estimating the fire boundary conditions of the fires for thermal and structural response calculations. For design purposes, the location and spatial distribution of the fire hazard in a structure need to be specified. However, at present, there is not yet a codified or recommended risk-based method for specifying the locations and spatial distributions of the fire hazard that constitutes different design fire scenarios in a building. Assuming the location and spatial distribution of the fire hazard can be selected, the fire boundary conditions, i.e., temperature-time history for a fire, can be estimated using two available methods: computerized fire models and closed-form equations. Computerized fire models, such as the NIST’s Fire Dynamics Simulator [23,24], exist for predicting temperature-time history in a compartment. However, use of these models requires a high level of sophistication that makes them unsuitable for routine design purposes. A more design-oriented option for predicting the fire boundary conditions for fire safety design is by using methods based on simple, closed form equations, such as those compiled in the SFPE Engineering Guide-Fire Exposures to Structural Elements [25]. This comprehensive guide summarizes, evaluates, and recommends various methods for predicting the fire boundary conditions for fully developed enclosure fires and for local fire plumes. For fully developed enclosure fires, SFPE Engineering Guide recommends Law’s method for all roughly cubic compartments. For long, narrow compartments, depending on the value of the opening factor (calculated as (AoHo1/2)/A, where A is the total surface area of the compartment in m2, Ho is the height of vertical openings in m, and Ao is the area of vertical openings in m2), either method by Law, Magnusson and Thelandersson, or Lie is recommended. The conditions within the compartment (gas temperatures, velocities, and smoke levels) and the distribution of fuel loads are
30
assumed to be uniform for these methods to be applicable. The input needed include fuel load, dimensions of compartment and openings, and wall thermal properties. For local fire plumes, SFPE Engineering Guide presented methods for estimating heat transfer boundary conditions for two different types of exposure: bounding, or elements immersed in a fire plume and fire in specific geometries including flat vertical walls, corners with a ceiling, unbounded flat ceilings, and I-beam mounted below a ceiling. 3.1.2 Calculation of Thermal and Structural Responses In the current prescriptive method, thermal isotherms for different cross sections of concrete structural members exposed to standard fire exposure ASTM E 119 are available in graphical forms or tabulated data. In a performance-based method where the fire exposure is other than the standard fire, a thermal response analysis will need to be conducted to determine the temperature distribution through the cross section of the structural components or at selected locations. Several methods are available for the thermal response calculation. These include closed form methods such as the Lumped heat capacity, the Steady state heat balances, and the Semi-infinite slab, as well as numerical finite element and finite difference methods. However, there are many limitations to these methods when applied to concrete. For example, the closed form methods assume that any incident heat from the fire causes a uniform temperature increase in the exposed subject. This assumption of homogeneity, while necessary to simplify the methods, makes the predicted temperature development in concrete assembly using these closed forms method inaccurate since they neglect the heat-induced moisture movement and changes in composition that occur in concrete at high temperatures. Some of the available numerical finite element and finite difference programs for evaluating the thermal response of fire exposed elements include FIREST3, TASEF-2, SAFIR, SUPER-TEMPCALC, FIRETRANS, and CEFICOSS. These programs can perform one to three-dimensional heat transfer calculations. However, the accuracy of the predicted thermal response for concrete elements depends significantly on accurate models for thermal properties as functions of temperature. For structural response calculation, while there are simplified design methods for predicting structural response of a concrete structural element exposed to standard fire exposures, design methods that allow the prediction of structural response of a concrete structural element exposed to fires other than the standard fires, or the global response of an entire concrete structure subjected to fires are not currently available. However, there exist sophisticated finite element programs, such as ANSYS, LS-DYNA, ABAQUS, and other research program such as SAFIR, that can been used for structural response calculation under user-defined fire exposures. These programs typically calculate the thermal and structural response by first performing the thermal analysis and then using the resulting temperatures as input for the structural response calculations. This lack of coupling between the thermal and structural analyses, combined with the lack of accurate models for mechanical properties of concrete, represent a major limitation in using these analytical tools for thermal and structural calculation since it is well known that geometric and cross sectional changes (due to spalling), as well as crack formation and heat-induced strength reduction in concrete vary differently at different temperature levels and with different mixture proportion and strength grade. 3.2 Non-Engineering issues Besides the engineering issues discussed above, there are other non-engineering issues that must be addressed for a performance-based fire safety design method to be accepted for use in practice. These include issues facing the building code enforcement officials in the approval process and issues concerning the professional responsibility for fire safety design. More detailed discussions on these issues may be found in [22]. Briefly, moving away from the prescriptive code requirements, which are familiar to building code enforcement officials and are easy to enforce, to performance-based methods requires the code officials to develop expertise in structural fire engineering in order to properly evaluate different engineered fire safety proposals. The code officials must also be able to justify the design fire event selected by the fire safety engineers, i.e., the size of the design fire, its endurance and spatial
31
distribution, and to decide whether the proposed fire safety strategy meet a standard performance goal. Another barrier to code official acceptance of engineered fire safety proposal is the lack of actual performance data to validate the models and assumptions used in the design and analysis process. Professional responsibility for fire safety design is traditionally the role of the architect of record who, in the current prescriptive approach, often specifies the fire protection features and, through the interpretation and application of the prescriptive code requirements, ensures that they comply with the intent of the codes and are accepted by the building code enforcement officials. This task is usually done separately and after the structural design process is complete. In a performance-based fire safety design approach, structural engineers will have to be involved and fire protection strategy will have to be developed during the structural design process. This change in responsibility will incur additional cost to the design of the building that needs to be considered by the building owners.
4.
Concluding remarks
Current fire safety design methods prescribed by U.S. model codes are prescriptive and do not consider many performance issues unique to concrete in fire. In lights of the findings from numerous studies regarding the adverse structural and material performance of concrete when exposed to fire, an argument can be made for the need to move structural fire safety engineering onto a stronger scientific footing, such as a performance-based fire safety methodology. While more information on concrete material, calculation procedures, and analytical tools have become available in recent years, many gaps remain to be addressed before a performance-based fire safety design method can be integrated into the current structural design procedure and routinely used. First, an overall design methodology framework will need to be developed for performance-based structural fire safety calculation. Then, within this performance-based fire safety design framework, issues related to selection of design fire scenarios and methods for thermal and structural response calculation will need to be addressed. Finally, performance goals and design failure criteria will need to be defined and codified to allow an evaluation of whether the proposed fire safety design meet the design objectives. Specifically, for the design fire scenarios, a risk-based methodology for selecting the location and spatial distribution of the design fire in the building, as well as its intensity and duration will need to be developed. Computerized and closed-form methods for estimating the fire boundary conditions exist but require data on fuel loads for today’s occupancies and actual fire data for validation. Simplified and sophisticated methods are also available for thermal response calculation based on the design fire boundary conditions. However, the application of these methods to concrete structures is constrained by the lack of appropriate material models for thermal properties that can account for the effects on temperature development of heat absorption and heat-induced moisture transport in concrete. Similarly, the shortcomings in current methods for predicting structural response of concrete structures exposed to fires are principally in the area of material modeling. Issues of heat-induced moisture transport, pore pressure buildup and spalling, different rates of degradation of mechanical properties between normal and high strength concrete, stressstrain relationships at elevated temperatures, all have a first order effect on the structural response calculation and thus will need to be incorporated into a material model for used in the structural analysis. Finally, since concrete is prone to sudden losses of stiffness due to crack formation, spalling, and strength degradation at different temperature levels, a coupled thermo-mechanical method for predicting structural response in fires is desirable.
32
References [1]
INTERNATIONAL CODE COUNCIL, International Building Code 2000, Falls Church, VA, March 2000.
[2]
NATIONAL FIRE PROTECTION ASOCIATION, Building Construction and Safety Code NFPA 5000, Quincy, MA, 2003. AMERICAN SOCIETY FOR TESTING AND MATERIALS, ASTM E 119 Standard Test Methods for Fire Tests of Building Construction and Materials, West Conshohocken, PA, 1995.
[3]
[4]
[5]
AMERICAN CONCRETE INSTITUTE, ACI/TMS 216 Standard Method for Determining Fire Resistance of Concrete and Masonry Construction Assemblies, Farmington Hills, MI, 1997. ABRAMS M.S., “Compressive Strength of Concrete at Temperatures to 1600 qF,” American Concrete Institute (ACI) SP 25, Temperature and Concrete, Detroit, Michigan, 1971.
NATIONAL FIRE PROTECTION ASOCIATION, NFPA 251 Standard Methods for Tests of Fire Endurance of Building Construction and Materials, Quincy, MA, 2003. [7] AMERICAN SOCIETY OF CIVIL ENGINEERS, ASCE/SFPE 29-99 Standard Calculation Methods for Structural Fire Protection, Reston, VA, 1999. [8] BAILEY C., “Holistic Behavior of Concrete Buildings in Fire,” Structures and Buildings, 152 Issue 3, Behavior of Concrete in Fire, pp. 199-212. [9] LENNON T., BAILEY, C., and CLAYTON N., “The Performance of High Grade Concrete Columns in Fire,” High Strength/High Performance Concrete, Vol. 1, Leipzig, Germany, 2002, pp. 341-353. [10] CASTILLO C. and DURRANI A. J., “Effect of transient high temperature on high-strength concrete,” ACI Materials Journal, v. 87, no. 1, Jan-Feb 1990, p 47-53. [6]
[11] FELICETTI R.; GAMBAROVA P.G.; ROSATI G.P.; CORSI F.; GIANNUZZI G.; “Residual Mechanical Properties of HSC Subjected to High-Temperature Cycles,” Proceedings, 4th International Symposium on Utilization of High-Strength/High-Performance Concrete, Paris, France, 1996, pp. 579-588. [12] HAMMER T.A.; “High Strength Concrete Phase 3: Compressive Strength and E-modulus at Elevated Temperatures,” SP6 Fire Resistance, Report 6.1, SINTEF Structures and Concrete, STF70 A95023, February, 1995. [13] DIEDERICHS U., JUMPPANEN U-M., SCHNEIDER U., “High temperature properties and spalling behavior of high strength concrete,” Proceedings, Fourth Weimar Workshop on High Performance Concrete: Material Properties and Design, Weimar, Germany, October 4-5, 1995, pp. 219-236. [14] KHOURY G.; and ALGAR S., “Mechanical behavior of HPC and UHPC concretes at high temperatures in compression and tension”, paper presented at ACI International Conference on State-of-the-Art in High Performance Concrete, Illinois, March 1999. [15] FURUMURA F.; ABE T.; SHINOHARA Y.; “Mechanical properties of high strength concrete at high temperatures,” Proceedings of the Fourth Weimar Workshop on High Performance Concrete: Material Properties and Design, Weimar, Germany, October 4-5, 1995, pp. 237-254. [16] PHAN L.T.; CARINO N.J., “Effects of test conditions and mixture proportions on behavior of high-strength concrete exposed to high temperatures,” ACI Materials Journal, American Concrete Institute, v. 99 (1), January-February, 2002, pp. 54-66. [17] PHAN L.T.; CARINO N.J., Mechanical Properties of High Strength Concrete at Elevated Temperatures, NISTIR 6726, Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland, March 2001.
33
[18] PHAN L.T.; CARINO N.J., “Code Provisions for High Strength Concrete StrengthTemperature Relationship at Elevated Temperature,” RILEM Materials and Structures, Volume 36, No. 264, December 2003, pp. 91-98. [19] COMITE EUROPEEN de NORMALISATION; prENV 1992-1-2: Eurocode 2: Design of Concrete Structures. Part 1 -2: Structural Fire Design, CEN/TC 250/SC 2, 1993. [20] COMITE EUROPEEN de NORMALISATION; Eurocode 4: Design of Composite Steel and Concrete Structures. Part 1 -2: General Rules - Structural Fire Design, CEN ENV, 1994. [21] CONCRETE ASSOCIATION of FINLAND, High Strength Concrete Supplementary Rules and Fire Design, RakMK B4, 1991. [22] ALMAND H.K., et al.; NIST-SFPE Workshop for Development of National R&D Roadmap for Structural Fire Safety Design and Retrofit of Structures: Proceedings, NISTIR 7133, Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland, April, 2004. [23] McGRATTAN K., et al., Fire Dynamic Simulator (Version 3)-Technical Reference Guide, NISTIR 6783, Gaithersburg, Md., National Institute of Standards and Technology, 2002 [24] McGRATTAN K., et al., Fire Dynamic Simulator (Version 3)-User’s Guide, NISTIR 6784, Gaithersburg, Md., National Institute of Standards and Technology, 2002 [25] SOCIETY OF FIRE PROTECTION ENGINEERS, SFPE Engineering Guide Fire Exposures to Structural Elements, Bethesda, MD, 2004
34
Session 2
Properties, Constitutive Models and Sectional Analysis
The Effects of the Constitutive Models on the Prediction of Concrete Mechanical Behaviour and on the Design of Concrete Structures Exposed to Fire Yngve Anderberg*
Page 37
Finite - Element Modelling of Concrete Subjected to High Temperature Francesco Pesavento*, Darek Gawin, Carmelo E. Majorana and Bernhard A. Schrefler
49
On Fire Behavior of R/C Sections Subjected to an Eccentric Axial Force Patrick Bamonte and Alberto Meda
57
High-Temperature Performance of a HPFRC for Heavy-Duty Road Pavements Stefano Cangiano and Patrick Bamonte
63
FRC Bending Behaviour: a Damage Model for High Temperature Matteo Colombo, Marco di Prisco and Roberto Felicetti
69
Mass Transport through Concrete Walls Subjected to High Temperature and Gas Pressure Gérard Debicki and Abdelslam Laghcha
81
Microstructure of High-Strength Concrete Subjected to High Temperature Gian-Luca Guerrini, Pietro G. Gambarova and Gianpaolo Rosati
89
Mechanical Properties of HPC at High Temperature Izabela Hager and Pierre Pimienta
95
Measurement of Concrete Thermal Properties at High Temperature Robert Jansson
101
Experimental Investigation on Concrete Spalling in Fire Robert Jansson and Lars Boström
109
Fire Tests on Fibre-Modified Concrete Sven J. Seirer
115
Constitutive Aspects of High-Temperature Material Models Kaspar Willam, Holger D. Basche and Yunping Xi
121
35
The Effects of the Constitutive Models on the Prediction of Concrete Mechanical Behaviour and on the Design of Concrete Structures Exposed to Fire Yngve ANDERBERG PhD, Docent Fire Safety Design Malmö, Sweden
Summary Structural-concrete modelling at high temperature must reflect the true behaviour of the material, independently of how sophisticated finite-element codes are used. Unfortunately, this is not always the case when scholars publish their theoretical predictions on the behaviour of R/C structures exposed to fire, since some aspects of concrete thermal behaviour are still elusive. As a matter of fact, the key aspect in understanding concrete mechanical behaviour at high temperature was discovered during the extensive studies made in Sweden [1,2] and Germany [3] in the seventies of the past century. A load-induced compressive strain, unknown till then, called “transient strain” develops during the first heating of the concrete, and is unrecoverable, time-independent and large. This strain was later brought back to the attention of the scientific community by Khoury [4,5] in 1983 and 1985. The first complete constitutive model of concrete for structural calculations was introduced by Anderberg in 1976 [6]. Since then, this model has opened the door to predict the behaviour of concrete structures under fire and to develop new design methods and codes. Keywords: constitutive model, structural behaviour and design, instantaneous stress-related strain, transient strain, stress distribution, load-bearing capacity, fire resistance.
1. Introduction The understanding of the mechanical behaviour of concrete at high temperature was until the mid of the 1970s very poor. All attempts to use elastic theory when calculating the stress distribution of a concrete member failed. If a concrete member is unloaded and restrained against thermal expansion during heating and the elastic theory is applied, failure will occur at about 350 °C due to high thermal stresses. This behaviour was of course not true. An unloaded and restrained specimen will never fail by itself. Thermal stresses will be relieved by a new strain component called “transient strain” or by some authors called “transitional thermal creep” discovered about 30 years ago. This strain contributes to a significant relaxation and redistribution of thermal stresses in heated concrete structures. A complete constitutive law of concrete at high temperatures was published in 1976 [2 & 6] to be used in structural analysis of fire exposed concrete members. The first realistic analytical prediction based on a true constitutive model and successfully compared with a great number of fire tests on statically indeterminate concrete slabs was also published in 1976 [6]. The software used for this purpose was a further development and extension of the computer program “Fires-RC” developed by Becker & Bresler within “Fire Research Group” at University of California, Berkeley in 1974 [7]. An improved structural software called “CONFIRE” was developed by Forsén 1982 [8]. This software was based on the constitutive law of concrete developed in 1976. Better understanding of the mechanical properties of concrete and new computer program for predicting structural behaviour opened the possibilities to apply a performance-based design and to develop simplified design methods for evaluating fire resistance of concrete structures in general. The result of that was a sectional analysis approach “500°C isotherm method”. This hand calculation method was presented at a FIP-congress in London 1978 [9]. The method was then introduced in the CEB-Bulletin Information No 145 “Design of concrete structures for fire
37
resistance” [10] in 1982 and later on in the CEB-FIP Model Code. In the Eurocodes today, where some still are under a voting process, three approaches are presented: x Tabulated data x Simplified calculation methods x Advanced calculation methods In Eurocode 2, Part 1-2 (EN 1992-1-2), applicable for concrete structures, the 500 °C isotherm method is presented under “Simplified calculation methods” [11]. To facilitate for the structural engineer and to reduce the amount of work, the hand calculation method is replaced by a tailor-made FE-program “TCD - Tempcalc-Design” developed on a PC in 1985. This software package contains a thermal calculation (Super-Tempcalc), [12], integrated with a structural design calculation (Fire Design), [13].
2. Behaviour model of concrete at high temperatures There exist mainly two constitutive models of concrete for structural analysis at high temperatures which take into account the behaviour under transient conditions: Model 1: Anderberg Y. & Thelandersson S., 1976 [2 & 6] Model 2: Khoury G. et al, 1983, 1985 [4 & 5]. This model became fully developed for structural calculations in 1991 by Terro [14]. 2.1
Model 1
In model 1 the total strain of concrete (silicious) is the sum of four strain components derived on a phenomenogical basis. The constitutive law can be expressed as follows: Htot = Hth(T) + HV (V, T) + Htr (V, V, T) + Hcr (t, T, V)
(1)
where V=
V= Htot(T) = Hth(T) = HV (V, T) = Htr (V, T) = Hcr (t, T, V) =
stress stress history total strain thermal strain instantaneous, stress-related strain based on V-H relationship transient strain creep strain or time dependent strain
Transient strain above 100oC is essentially a function of temperature and not of time. This strain is dominating and much larger than the elastic strain which can be observed in Fig 1. The prediction of total deformation at different load levels as function of temperature is presented in Fig. 2 and the agreement with measurements is excellent. Any structural analysis of heated concrete that ignores transient strain will, therefore, be wholly inappropriate and will yield erroneous results, particularly for columns exposed to fire. This phenomenon is still not fully appreciated by structural engineers and should be incorporated more fully into standards and design codes.
38
Fig. 1 - Relation between different strain Fig. 2 - Deformation upon heating for different components when the model is applied to a levels of relative compressive stress. Full line relative stress of 35% of ultimate stress. curves indicate experiments and dashed line curves prediction with the model. Does concrete have a memory? Is there any influence of load history on stress-strain curves? The answer is yes and can be seen in Fig. 3, illustrating the stress-strain relationship at different temperatures with and without the effect of preloading. The preloading is applied before heating starts and heating continues until a stabilised temperature is attained. After that the load is removed, the stress-strain relationship is measured. If concrete is heated without load, tests consistently show the modulus of elasticity or stiffness to reduce considerably with increase in temperature and even by a larger proportion of the initial value than the compressive strength (Fig. 3a). Both the compressive strength and elastic modulus reduce far less with increase in temperature for the concrete heated under load (Fig. 3b). This evident load history effect is very important and has been observed also for high performance concrete. The accurate prediction of the behaviour compared with measured results for two different fire tests are illustrated in Figs. 4-5. These figures indicate a very good agreement between predictions and measurements where heating curve may have a drop in temperature and a cooling phase (Fig. 4) and the load level (relative stress) is varying during the two tests. In these two examples the account of load history effect in the prediction had a considerable influence and contributed to a successful calculation.
39
Fig. 3a - Stress-strain relationship at different Fig. 3b - Stress-strain relationship at diffetemperatures without any preloading. rent temperatures at 20% preloading.
Fig. 4 - Predicted and measured deformation. The temperature versus time is shown in the lower diagram. Load level is changed after 4 hours from 45 to 67 %.
Fig. 5 - Predicted and measured deformation. The temperature versus time is shown in the lower diagram. Load level is changed after 4 hours from 22.5 to 45 %.
If a concrete specimen is restrained against longitudinal expansion axial restraint forces will develop. Due to the discovery and analytical formulation of the transient strain and the load history effect the prediction of the axial load as function of temperature became possible. In Fig. 6 the predicted and measured restraint force as function of temperature is compared for two heating rates
40
with a very good agreement. The maximum restraint load reaches about 40% at 400 °C and decreases to zero at 800°C.
Fig. 6 - Predicted and measured restraint load (in % of the ultimate load at ambient conditions) as a function of temperature for specimens heated under fully restrained expansion.
Fig. 7 - Calculated stress distributions for an axially loaded cylindrical column under transient thermal exposure. Load level is 40%. Rate of heating: (a) 2, (b) 4 and (c) 8°C/min.
Calculated stress distributions for an axially loaded cylindrical column under at three rates of heating is illustrated in Fig. 7. A characteristic feature is the transition of stresses from the surface to the in the inner part of the specimen after some time.
Fig. 8 - Concrete stress-strain model including unloading and loading in compression as well as in tension. In a concrete structure stresses may change during heating a, compressive stress can be followed by ascending branch and then turn into tensile stress. This feature of behaviour must be modelled, which is fundamentally illustrated in Fig. 8.
41
2.2
Model 2
This constitutive model was developed on a phenomenogical basis by Khoury et al [4 & 5] in 1983 & 1985 based on tests up to 600°C without any refined stress-strain model as illustrated in Fig. 8. This further modelling of stress-strain relationship was included in a computer program for structural analysis in 1991 by Terro [14]. In the original model a new concept was introduced where Load Induced Thermal Strain (LITS) was defined as the sum of three components, the stress-related strain (HV), the transient strain (Htr) and the creep strain (Hcr) as written below LITS = HV (V, T) + Htr (V, T) + Hcr (V, T, t) = Htot - Hth (T)
(2)
The effect of load history is not explicitly defined but shall in some way be integrated in the LITS. A further simplification of LITS is the existence of a “master LITS” for Portland cement based concrete in general for temperatures up to 450oC irrespective of the type of aggregate or cement blend used. 2.3
Models based on Eurocode stress-strain model
There are several examples of structural analysis published in literature where the transient strain and load history effect have been ignored by using only the stress-strain model under compression from Eurocode 2 as presented in Fig. 9 and Table 1. Sometimes it maybe possible to obtain a relevant failure time especially for beams and slabs where the fireexposed zone is in tension without a transient strain effect, because it acts only in compression. The stress and deformation prediction will however not be correct.
H
c1(ș )
fsp,4
Hc1,4
Hcu,4
H
Stress V T
Range
H dH
V
3 H f c ,ș 3 § § H · ·¸ ¨ ¸¸ İ c 1,ș ¨ 2 + ¨¨ © İ c 1,ș ¹ ¸¹ ©
c1,ș
H d H cu,ș
For numerical purposes a descending branch should be adopted. Linear or non-linear models are permitted.
Fig. 9 - Mathematical model for stress-strain relationships of concrete at elevated temperatures. The reason why the prediction of failure time sometimes can be almost correct depends on the fact that very large strains on the descending branch İc1,T and İcu,T has been introduced to compensate for the transient strain. These strains are much larger than those, which have been published in literature [15]. More realistic strain values are indicated within brackets in Table 1 and the difference is very great.
42
Table 1 - Stress-strain values at different temperatures in accordance with Eurocode 2 Part 1.2. Temp
fc,T/fc,k
İc1,T (%)
20 300 600 1000
1,00 0,85 0,45 0,04
0,25 0,70 (0,3) 2,5 (0,5) 2,5
İcu,T % 2,00 2,75 3,5 4,5
(0,35) (0,50) (0.80) (1,10)
As an example Fig. 10 illustrates the predicted and measured deformation behaviour of a reinforced concrete column exposed to ISO 834 fire on three sides This work was carried out in 1984 by Anderberg & Forsén, [16], by using model 1 from 1976. The experimental results on axial as well as the horizontal deformation are predicted very well during the whole fire test and the failure time was very close. If the model based on Eurocode 2:s stress-strain relationships has been used (as explained above) in this structural prediction the result had been quite different from measurements. v- deflection from the fire ' - axial compression Experiment ------ Calculation-
Fig. 10 - Predicted and measured axial and horizontal deformation of a reinforced concrete column fire-exposed (ISO 834) on three sides.
3.
Simplified calculation method – 500 °C isotherm method
3.1
Handcalculation procedure
The “500oC isotherm method or the effective cross-section method is described in Eurocode 2 Annex B [11] under simplified calculation method used for fire design of structural members. A very simple method of analysis based on the hypothesis that the thickness of the damaged siliceous concrete is assumed to equal the average depth of the 500°C isotherm in the compression zone of the cross-section. Damaged concrete (i.e. concrete with temperatures in excess of 500°C) is not expected to contribute to the load-carrying capacity of the member, whilst the residual concrete cross-section is assumed to retain its full initial values of strength and modulus of elasticity. This method is applicable to a reinforced concrete section with respect to axial load, bending moment and their combinations. For this method to apply there should be minimum dimensions of the member depending upon fire resistance time or fire load density as presented in Table 2, [11].
43
Table 2 - Minimum width of cross-section as function of fire resistance (for standard fire exposure) and fire load density (for parametric fire exposure). a) Fire resistance Fire resistance Minimum width of cross-section mm
R 60
R 90
R120
R180
R240
90
120
160
200
280
200
300
400
600
800
100
140
160
200
240
b) Fire load density Fire load density MJ/m2 Minimum width of cross-section mm
When the effective cross-section is determined from i.e diagrams or tables in Eurocode 2, Annex A, [11] the reduced strength with respect to its temperature is assessed. Load-bearing capacity calculation is based on normal temperature design methods.
fcd
x
Ox
As' z' As
Fs = As'fscd,fi(Tm)
Oxbfifcd
dfi
z As1fsd,fi
Mu1
z'
Mu2
Fs = As2fsd,fi(Tm)
bfi b bfi h hfi dfi z z'
original width width of effective cross-section original height height of effective cross-section effective height of effective cross-section lever arm between tension reinforcement and concrete lever arm between tension and compression reinforcement O and x are defined in EN 1992-1
Fig. 11 - Stress distribution at ultimate limit state for a rectangular concrete cross-section with compression reinforcement. A detailed distribution of stresses and forces for an effective cross-section as basis for a general calculation of moment capacity of a beam or a slab is shown in Fig. 11. One note of caution is that the choice of the temperature isotherm will depend upon the type of concrete used and its characteristic strength loss against temperature. For certain concretes, the isotherm temperature may well be below 500oC, or even below 400oC. In Sweden it was found for high strength concrete that the 400 °C was applicable, but all temperature diagrams for 500 °C isotherms could be used by multiplying all results by a reduction coefficient depending on type of structure and number of faces fire-exposed.
44
Another more detailed and cumbersome hand calculation method called the “Zone Method” was proposed by Hertz and is also introduced in Annex B of Eurocode 2, [11].
3.2
Taylor-made software package
A tailor-made FE-software package “TCD - Tempcalc-Design” was developed by Fire Safety Design, Sweden on a PC in 1985 to replace cumbersome hand calculations and to facilitate fire design for the structural engineer. TCD is a finite element application for thermal and structural analysis of members exposed to fire. The software has been validated against a large number of tests since 1985. This software package illustrated in Fig. 12 contains a thermal calculation called Super-Tempcalc [12] integrated with a structural design calculation (Fire Design), [13] for concrete (CBEAM) and steel beams (SBEAM) and composite columns (COMPRES).
Preprocessor with Automatic FE-generator
TCD
Super-TempcalcR
Database
Fire Design CBEAM
SBEAM
Compres
Fig. 12 - Scheme of TCD-software package. 3.2.1 Super-Tempcalc SUPER-TEMPCALC is a thermal, finite element program that solves the two-dimensional, nonlinear, transient, heat transfer differential equation incorporating thermal properties which vary with temperature. The program allows the use of rectangular or triangular finite elements, in cylindrical or rectangular co-ordinates. Heat transferred by convection and radiation at the boundaries can be modelled as a function of time. Structures comprising several materials can be analysed and the heat absorbed by any existing void in the structure is also taken into consideration. A materials properties database is integrated with the main program. Also integrated into the program are pre- and post-processors which allow fast and user-friendly input/output procedures. The pre-processor creates the finite element division automatically and retrieves the relevant information from the database for use in the calculation. Finally, the post-processor presents the results graphically on in a variety of forms including time-temperature curves, isotherms, and temperature gradients. Other characteristics of Super-Tempcalc:
x Used since 1985 on daily basis with continuous improvement x Defined concrete spalling simulated (new geometry automatically updated) x Simulates boards falling off (new geometry automatically updated) 3.2.2 Fire design Fire Design software evaluates moment capacity as function of time of steel- (SBEAM) or reinforced concrete beams and slabs (CBEAM) in normal and fire design. It also assesses axial compression resistance and critical Euler load capacity in fire design for steel, concrete or composite columns (COMPRES).
45
4.
Conclusions
The constitutive model applied for predicting the structural behaviour of concrete members must reflect the true behaviour of concrete at high temperatures. This means that the transient strain (transitional thermal creep or load induced thermal strain) and the load history effect must be considered. It does not help to have the most sophisticated FE-software if the fundamental input is not correct. One may sometimes be lucky to predict the failure time by using the stress-strain relationship from Eurocode 2 but the “real” behaviour (stress distribu-tion and deformation) will never be calculated. The simplified hand calculation method, “500 °C isotherm method” is not quite general and may sometimes be modified to be applied on i.e high strength concrete, where the 400 °C isotherm should be used. The 500 °C isotherm method is applied in a software package called TCD to replace hand calculation methods and to facilitate fire design for the structural engineer.
References [1]
THELANDERSSON S., “Mechanical behaviour of Heated Concrete under Torsional Loading at Transient High Temperature Conditions”, Bulletin No. 46, Lund Institute of Technology, Sweden, 1974.
[2]
ANDERBERG Y. and THELANDERSSON S., “Stress and Deformation Characteristics of Concrete at High Temperatures”, 1. “General Discussion and Critical Review of Literature”, Lund Institute of Technology. Bulletin 34, Lund, 1973. 2. “Experimental Investigation and Material Behaviour Model”, Lund Institute of Technology. Bulletin 54. Lund 1976. SCHNEIDER U., “Zur Kinetik Festigkeitsmindernder Reaktionen in Normalbetonen bei Temperaturen bis 1000 °C“, (Loss of strength due to kinetic reactions of normal concretes up to 1000 °C), PhD Thesis at Technical University Braunschweig, 1973, Germany. KHOURY G.A., “Transient Thermal Creep of Nuclear Reactor Pressure Vessel Type Concretes”, PhD Thesis at Civil Engineering Department, Imperial College of Science and Technology, University of London, London, 1983. KHOURY G.A., SULLIVAN P.J.E., and GRAINGER B.N., “Strain of Concrete During First Heating to 600oC Under Load”, Magazine of Concrete Research, Vol. 37, No. 133, pp. 195215, 1985.
[3]
[4]
[5]
[6] [7]
ANDERBERG Y., “ Fire-exposed Hyperstatic Concrete Structures. An Experimental and Theoretical Study”, Lund Institute of Technology, Bulletin 55, Lund, 1976. BECKER J. and BRESLER B., “FIRES-RC, A Computer Program for the Fire Response of Structures-Reinforced Concrete Frames”, University of California, Berkeley, Fire Research Group, Report No. UCB FRG 74-3, July 1974.
[8]
FORSEN N. E., “A Theoretical Study on the Fire Resistance of Concrete Structures”, Cement and Concrete Research Institute, The Norwegian Institute of Technology, SINTEF Report No: STF65 A82062, Dec.1982
[9]
ANDERBERG Y., “Analytical fire Engineering Design of Reinforced Concrete Structures Based on Real Fire Characteristics”, FIP Congress, London 1978. Proceedings, Part 1, 1 May 1978, pp 112-121.
[10] CEB-FIP Model Code, “Design of Concrete Structures for Fire Resistance”, Bulletin d’Information No 145, January 1982. [11] Eurocode 2, Part 1-2 (EN 1992 1-2), “Design of Concrete Structures, Part 1-2: General rules – Structural fire design”. [12] ANDERBERG Y., “SUPER-TEMPCALC, A Commercial and User friendly Computer Program with Automatic FEM-Generation for Temperature Analysis of Structures Exposed to Fire”, Fire Safety Design AB, Lund,1991.
46
[13] ANDERBERG Y., “Fire Design. A Computer Program for Calculation of the Bending Moment Capacity for Reinforced Concrete Structures and Steel Structures with Thermal Effects”, Institute of Fire Safety Design, Lund (Sweden), 1986. [14] TERRO M., “Computer Modelling of the Effect of Fire on Structures”, Ph.D. Thesis, at Civil Engineering Department, Imperial College of Science and Technology, London University, London (UK), 1991. [15] SCHNEIDER U., RILEM-Committee 44-PHT – “Properties of Materials at High Temperatures- Concrete”, Department of Civil Engineering, University of Kassel, Kassel (Germany), June 1985. [16] ANDERBERG Y. and FORSEN N.E.,” Fire Resistance of Concrete Structures”, Division of Building Fire Safety and Technology, Lund Institute of Technology, Lund (Sweden), 1982, Lutvdg/TVBB 3009. Nordic Concrete Research.
47
Finite – Element Modelling of Concrete Subjected to High Temperature Francesco PESAVENTO Lecturer University of Padua Padua, Italy
Darek GAWIN Associate Professor Technical University of Lodz Lodz, Poland
Carmelo MAJORANA Professor University of Padua Padua, Italy
Bernhard SCHREFLER Professor University of Padua Padua, Italy
Summary The use of mechanistic models to analyse hygrothermal, mechanical and durability time transient phenomena has revealed a strong impact in the solution of many related problems of computational mechanics. In the framework of the European Programme “Competitive and Sustainable Growth”, UPTUN Project GRD1-2001-40739, entitled “Upgrading of existing tunnels” and of FP5 Euratom Programme MAECENAS, entitled “Modelling of ageing in Concrete Nuclear Power Plant Structures” an enhanced, mechanistic model of mass and energy transport in deforming concrete at high temperature has been developed. Keywords:
1.
damage, multiphase, effective stress.
Introduction
In several situations it is necessary to model concrete as a multiphase material [1]-[9], i.e. a material made up of a solid phase and pores which are filled with water (capillary and physically adsorbed), vapour and dry air. Typical cases deal with concrete performance in the high temperature range, e.g. during fire [2]-[4],[7]-[9], with early stages of maturing of massive concrete structures [5], with shotcrete in tunnelling, and with durability. We present here a general model for chemo-hygro-thermo-mechanical analysis of concrete applicable to the above situations using a mechanistic approach. Such a kind of approach leads to governing equations that are usually more complicated formally, but their coefficients have clear physical meaning and often are related to classical material parameters, like for example porosity, intrinsic permeability, diffusivity of vapour in air, etc. When some relations between structure parameters and transport properties are found (e.g. effect of water degree of saturation on relative permeability for water flow), usually they are valid for a class of similar materials, e.g. cellular concrete, ceramic materials, etc. Often models of this group are obtained from microscopic balance equations written for particular constituents of the medium, which are then averaged in space, e.g. by means of Volume Averaging Technique, mixture theory or homogenisation theory. Mass and energy fluxes are usually expressed by means of gradients of thermodynamic potentials causing them, e.g. temperature, capillary pressure, water vapour concentration etc. Phase changes and related to them mass- and energy sources (sinks) are usually taken into account. Moreover, some additional couplings, e.g. effect of material damaging on intrinsic permeability or capillary and vapour pressures (moisture content) on skeleton stresses, can be considered. In “classical” phenomenological approach moisture and heat transport are described by diffusive type differential equations with temperature- and moisture content- dependent coefficients. The model equations are often obtained by means of Irreversible Phenomena Thermodynamics. The model coefficients are determined by inverse problem solution, i.e. using known results of experimental tests, to obtain the best agreement between theoretical prediction and experimental evidence (e.g. in the sense of least square method). Models of such a kind usually give very accurate predictions when applied to phenomena similar to those used to adjust model parameters 49
and often very inaccurate for different situations. In other words, they are very accurate for interpolation and rather poor for extrapolation of the known experimental results. Moreover various physical phenomena are lumped together and model parameters often have not clear physical interpretation. In this approach there is not any distinction between different phases of water, e.g. [10]-[13], which are generally treated as a moisture, hence phases changes cannot be taken into account. In the model presented here concrete is treated as a multiphase system with the voids of the skeleton filled partly with the liquid water and partly with the gas phase. The liquid phase consists of bound water, which is present in the whole range of moisture content, and capillary water, which appears when water content exceeds the so called solid saturation point Sssp, i.e. the upper limit of the hygroscopic region. The gas phase is a mixture of dry air (non-condensable constituent) and water vapour (condensable gas), and is assumed to be an ideal gas. Different physical mechanisms governing the liquid and gas transport in the pores of partially saturated concrete are clearly distinguished, i.e. capillary water and gas flows driven by their pressure gradients, adsorbed water surface diffusion caused by saturation gradients, as well as air and vapour diffusion driven by vapour density gradients. All the important phase changes of water, i.e. adsorption-desorption, condensation-evaporation, and chemical reactions, e.g. hydration-dehydration, as well as the related heat and mass sources (or sinks) are considered. Changes of the material properties caused by temperature and pressure changes, concrete damage or carbonation, fresh concrete hardening, as well as coupling between thermal, hygral, chemical and mechanical phenomena are taken into account. This model further allows to incorporate sorption hysteresis. In particular in this work an application of the aforementioned model to the case of concrete structures exposed to high temperature will be presented.
2.
Numerical model
The model consists of four balance equations: mass conservation of dry air, mass conservation of the water species (both in liquid and gaseous state, taking phase changes, i.e. evaporation/condensation, adsorption/desorption and hydration/ dehydration process, into account), enthalpy conservation of the whole medium (latent heat of phase changes and heat effects of hydration or dehydration processes are considered) and linear momentum of the multiphase system. They are completed by an appropriate set of constitutive and state equations, as well as some thermodynamic relationships (see, [1]-[4],[6]-[9]). The governing equations of the model are expressed in terms of the chosen state variables, [6]: gas pressure pg, capillary pressure pc, temperature T and displacement vector of the solid matrix u. The constitutive laws for the solid skeleton density and water density are based on experimental results, (see [4],[6]) and the density of gas constituents (dry air, water vapour and their mixture) can be calculated with sufficient accuracy, for the numerical simulations, using Clapeyron’s equation, [6]. The governing equations of the model proposed, considering negligible the inertial forces and the convective heat flux related to solid phase and taking into account the Bishop’s stress principle, [1], in their compact numerical form are the following: Cij x
wx K ij x x fi x , wt
(1)
where xT ^ p g , p c , T , u ` and the non-linear matrix coefficients Cij(x), Kij(x) and fi(x) are defined in detail in [1],[4],[9]. The time discretization is accomplished through a fully implicit finite difference scheme (backward difference),
< i x n 1
Cij x n 1
x n 1 x n K ij x n 1 x n 1 fi x n 1 't
0,
(2)
where superscript i (i= g,c,t,u) denotes the state variable, n is the time step number and 't - the time step length. The equation set (2) is solved by means of a monolithic Newton-Raphson type iterative procedure [25],[26]:
50
< i x nk 1
w< i wx
'x nk 1 ,
x nk 11
x nk 1 'x nk 1 ,
(3)
X kn 1
where k is the iteration index and < the Jacobian matrix. For further information about the model, see [1]-[9].
3.
Mechanical and thermo-chemical damaging of concrete
Mechanical damage of concrete is considered following the scalar isotropic model by Mazars [16],[17]. In this model, the damaged material is supposed to behave elastically and to remain isotropic, and it is assumed that its Young modulus at a given temperature, E(T), can be obtained from the relation, [16],[17],
E (T ) Eo (T )
1
d
(4)
where Eo(T) is the Young modulus of mechanically undamaged material at the same temperature. Thermo-chemical effects are also taken into account in multiplicative way, as proposed in [18],[19]. The theory defines a "modified effective stress" and takes into account both the mechanical damage d (0 d d d 1) as a parameter measuring the reduction of resistant area due to cracks, and thermo-chemical damage V (0 d V d 1) as a parameter describing thermo-chemical material degradation at elevated temperatures (mainly due to micro-cracking and cement dehydration) resulting in reduction of the material strength properties,
V
V
1 d 1 V
(5)
The thermo-chemical damage is described in terms of experimentally determined relation of Young’s modulus, E, as a function of temperature E=E(T), [19], V
1
Eo (T ) Eo (Ta )
(6)
where Ta= 20°C is room temperature. As above mentioned, the total effect of the mechanical and thermo-chemical damages acting at the same time is multiplicative, i.e. the total damage D, defined by formula, and not the sum of the thermo-chemical damage, V, and mechanical damage, d. Hence, the stress tensor is as follows: V
/ 0 (1 D ) : H e
/ 0 1 V 1 d : He
(7)
where /0 is the initial stiffness matrix of the material and He is the elastic part of strains. During heating of concrete at high temperature complex physical and chemical processes take place, resulting in changes of inner structure, micro-cracks development and porosity increase, [11][13]. In such conditions concrete, especially high performance and ultra high performance concrete, may be subjected to spalling phenomena which put the integrity of the construction into hazard. Many different forms of spalling exist, but probably the most dangerous is explosive spalling, because it is sudden and capable to result in a general collapse of the structure. Spalling is due to different coexisting coupled processes such as thermal (thermal dilatation), chemical (dehydration of cement paste), hygral (evaporation of the liquid pore water, associated by the vapour pressure increase) and mechanical damage (cracking) processes, [9]. The main factors that influence spalling are the temperature distribution and its variation inside the concrete element, as well as the characteristics of the considered section (size and shape), permeability, mean pore radius, concrete strength,[20]. The vapour pressure can play an important role because of its high values reached during heating which can produce a kind of explosive spalling, especially in high density materials
51
like high and ultra high performance concrete. All these phenomena can lead to a serious loss of load bearing capacity and sometimes to the complete collapse of the concrete structure.
4.
Deformation of concrete at high temperature
Deformations of concrete subjected to high temperature and mechanical loads, and in particular the phenomenon of so called thermal transient creep resulting in load induced thermal strains (LITS), are of great importance for proper evaluation of the performance of concrete structures. In this section we analyze some results of thermo-physical, chemical and mechanical tests of HPC performed within the “HITECO” project (1999), and formulate from them a model and some constitutive relations for concrete deformations at high temperature, including LITS. A strong coupling between processes of concrete deformation and its thermo-chemical deterioration, evident from these results, are taken into account in the proposed constitutive model for the description of the material deformations. This is introduced then in our mathematical model of hygro-thermochemo-mechanical behaviour of concrete at high temperature, [2]-[9] and applied for solution of some numerical examples. An unloaded sample of plain concrete or cement stone, exposed for the first time to heating, exhibits considerable changes of its chemical composition, inner structure of porosity and changes of sample dimensions (irreversible in part). The concrete strains during first heating, called loadfree thermal strains (LFTS), [20], are usually treated as superposition of thermal and shrinkage components, and often are considered as almost inseparable. LFTS are decomposed in three main contributions, see Fig. 1A: • •
Thermal dilatation strains, Shrinkage strains,
•
Thermo-chemical strains
dİ LFTS
dİth dİ sh dİtchem
(8)
For a more detailed description of LTFS see [21]. During first heating, mechanically loaded concrete exhibits greater strains as compared to the load-free material at the same temperature. These additional deformations are referred to as load induced thermal strains (LITS). A part of them originates just from the elastic deformation due to mechanical load, and it increases during heating because of thermo-chemical and mechanical degradation of the material stiffness. The time dependent part of the strains during transient thermal processes due to temperature changes, is generally called thermal creep. Its physical nature is rather complicated and up today not fully understood, thus modelling is usually based on the results of special experimental tests.
1.0E-02
exp. heating total - model
8.0E-03
therm_dilat shrinkage
6.0E-03
thermo-chem.
0 -1
Creep strain [mm/m]
Thermal strain [m/m]
1.2E-02
exp. cooling
4.0E-03 2.0E-03 0.0E+00 -2.0E-03 -4.0E-03
-2 -3 -4
-6 -7 -8
-6.0E-03
-9
-8.0E-03
-10 0
100
200
300
400
500
600
700
800
exp. 45% load 45% load exp. 30% load 30% load exp. 15% load 15% load
-5
0
100
200
300
400
500
600
o
Temperature [oC]
Temperature [ C]
B
A
Fig. 1 - A) decomposition of total strains in heated concrete; B) evolution of thermal creep strain versus temperature (C90 concrete).
52
Typically, they are performed at constant heating rate equal to 2 K/min, for various (but constant during a particular test) levels of material stresses, V=const, ranging from 0% (load-free measurements) to 60% of the compressive strength of material at room temperature, fc(Ta). The results of such transient thermal strain tests performed for the C-90 concrete are presented in Fig. 1B, compared to numerical results. The formulation employed into the model is due to [22] in its original form, here modified using a coefficient Etr (V ) as a function of thermo-chemical damage V (and not constant) and the effective stresses instead of total stresses, coupling in this way the thermo-chemo-mechanical damage model and capillary shrinkage model with thermal creep model.
dİtcreep
Etr (V ) f c (Ta )
Q : ı es dV
(9)
In eq. (9) Q is a fourth order tensor, ı es is the “net” (in the sense of damage mechanics) stress tensor and finally fc is the compressive strength of the material at 20°C. For further details concerning physical-mathematical model and its numerical implementation, see [2]-[9],[21].
5.
Numerical example
This example deals with a comparison between numerical results, obtained using the model described in the previous sections, and experimental results, obtained from compressive tests carried out in United States in the laboratories of NIST [23],[24]. The main goal of this comparison is to show the capability of the code to assess spalling phenomena, in particular occurrence of explosive spalling in concrete structures subjected to elevated temperatures. The specimens, which were cylinders with diameter of 100mm and height of 200mm, have been tested using three test methods, representing the thermo-mechanical loading conditions: stressed test method (specimens were preloaded, with a load equal to 40% of final compressive strength at room temperature, and then heated), unstressed test method (specimens were directly heated until the time of compressive test), residual property test method (the specimens were heated up to the target temperature and kept at this temperature for a certain period; then they were cooled and tested at room temperature). Five target temperatures: 100, 200, 300, 450 and 600°C were reached during the tests by means of furnace heating rate of 5°C/min, in steady state conditions. In this case “steady state” is defined as the temperature state when the temperature at the centre of the specimen is within 10°C of the preselected target temperature T and the difference between the surface and centre temperatures of the concrete specimen is less than 10°C. For further details concerning mix compositions and tests procedures (set-up, instrumentation of the specimens, temperature control), [23],[24]. Our attention was focused on specimens made of concrete type 1, herein indicated as MIX1 in unstressed conditions with a target temperature equal to 450°C. In fact, for unstressed tests, explosive spalling occurred in all MIX1 specimens heated to 450°C. Initial and boundary conditions used in numerical simulation are listed in [21]. Fig. 2A shows the temperature differences between the surface and the centre of the specimens measured during the tests and the corresponding numerical results. The accordance between numerical and experimental results is quite good. The first part of heating shows a strange behaviour with temperature difference between core and surface practically zero for more than one hour. Fig. 2C provides information about damaging of the specimen during heating. Specifically, it shows the history of mechanical damage in three different points (on the surface, in the centre and in the middle of the radius). Fig. 2B shows developments (in three points) of the gas pressure versus temperature compared to the water vapour pressure developments in saturated conditions (red line). The time range between 120 and 150 min seems to be the critical range during which the material achieves a state favourable to spalling occurrence; the specimen experienced explosive spalling right in this range of time. Corresponding to the maximum value of 'T, a sharp increase of mechanical damage parameter d (with a maximum value equal to 80%) may be observed. Similarly to the increase of mechanical damage, the peak of gas pressure corresponds to the maximum value of temperature differences 'T. Moreover, in the same range time there is a peak of “net” stresses, Fig. 2D with a comparison to the tensile strength of the material. The results of numerical simulations presented here, show that both pore pressure and thermally induced strains can be identified as responsible for the spalling occurrence, and that they play a primary or secondary role depending on the particular conditions prevailing.
53
6.
Conclusions
45
1.E+06
40
9.E+05
35
8.E+05
30
GAS PRESSURE [Pa]
TEMPERATURE DIFFERENCE [K]
A numerical model for the analysis of hygro-thermal behaviour of concrete as a multi-phase porous material at high temperatures, including the range above the critical point of water and taking into account material deterioration, has been presented. The so called Load Induced Thermal Strain (LITS), known as thermal creep, accounting for the strain of a concrete element loaded and heated for the first time, is also considered. The results of one numerical example, concerning performance of HPC cylinders, has been described and discussed in detail. It shows complexity of physical phenomena in concrete at high temperature, and in particular, the importance of the LITS, thermochemical degradation and mechanical damage for the global performance of concrete elements at high temperatures. It further demonstrates possibilities and robustness of the proposed method and the developed computer code in the evaluation of spalling occurrence in concrete structures.
simulation experiment
25 20 15 10 5
Satur. Vap. Pres. 2 mm to surf. 2 cm to surf.
7.E+05
Centre
6.E+05 5.E+05 4.E+05 3.E+05 2.E+05 1.E+05
0 0
30
60
90
120
150
180
210
240
270
0.E+00 273.15
300
373.15
TIME [min.]
473.15
573.15
673.15
B 1.4E+07
0.8
0.6 0.5 0.4 0.3 Surface
0.2
1.2E+07
EFFECT. STRESSxx [Pa]
MECH. DAMAGE [-]
0.7
2 cm to surf.
0 273.15
373.15
473.15
573.15
673.15
Tensile strength 2 cm to surf.
1.0E+07
Centre
8.0E+06 6.0E+06 4.0E+06 2.0E+06
Centre
0.1
0.0E+00 273.15
773.15
373.15
473.15
573.15
673.15
TEMPERATURE [K]
TEMPERATURE [K]
773.15
D
C 2.0E+04 1.8E+04
3
ELASTIC ENERGY [J/m ]
0.0E+00
THERM. CREEP STRAIN-yy [-]
773.15
TEMPERATURE [K]
A
-5.0E-04
Surface 2 cm to surf. Centre
-1.0E-03
-1.5E-03
-2.0E-03
1.6E+04 1.4E+04 1.2E+04 1.0E+04 8.0E+03 6.0E+03
Surface
4.0E+03
2 cm to surf.
2.0E+03 -2.5E-03 0
E
30
60
90
120
150
180
210
240
270
300
TIME [min.]
0.0E+00 273.15
Centre
373.15
473.15
573.15
673.15
773.15
TEMPERATURE [K]
F
Fig. 2 - A) Temperature differences history (comparison with experimental results); B) Gas pressure compared to saturated vapour pressure (red line); C) Mechanical damage versus temperature in three different points; D) Effective stresses versus temperature compared to tensile strength; E) thermal creep strain evolution; F) Elastic energy evolution
54
References [1] [2]
[3]
[4] [5]
LEWIS R.W., SCHREFLER B.A., The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media, 2nd ed., Wiley & Sons, Chichester, 1998. GAWIN D., MAJORANA C.E., PESAVENTO F., SCHREFLER B.A., “A fully coupled multiphase F.E. model of hygro-thermo-mechanical behaviour of concrete at high temperature”, Proc. of IV World Congress on Computational Mechanics, Buenos Aires, 1998. GAWIN D., MAJORANA C.E., SCHREFLER B.A., “Numerical analysis of hygro-thermic behaviour and damage of concrete at high temperature”, Mech. Cohes.Frict. Mat., Vol.4, 1999, pp. 37-74. PESAVENTO F., Non-linear modelling of concrete as multiphase porous material in high temperature conditions, Ph.D. thesis, University of Padova, 2000. B.A. SCHREFLER, D. GAWIN, F. PESAVENTO, “Concrete as a multiphase material, with applications to high temperatures, durability and concrete at early ages”, in Ulm F.J., Bazant Z., Wittman F.H. (eds.), Creep, Shrinkage & Durability Mechanics of Concrete and Other Quasi-Brittle Materials, Proc. ‘Concreep-VI’ Conf., MIT, Cambridge (USA), Elsevier, 2001.
[6]
GAWIN D., PESAVENTO F., SCHREFLER B.A., “Modelling of hygro-thermal behaviour and damage of concrete at temperature above the critical point of water”, Int. J. Numer. Anal. Meth. Geomech, Vol.26, 2002, pp 537-562.
[7]
KHOURY G., MAJORANA C.E., PESAVENTO F., SCHREFLER B.A., “Thermo-hydromechanical modelling of high performance concrete at high temperatures”, Magazine of Concrete Research, Vol.54, No2, 2002, pp. 77–101. SCHREFLER B.A., BRUNELLO P., GAWIN D., MAJORANA C.E., PESAVENTO F., “Concrete at high temperature with application to tunnel fire”, Computational Mechanics, Springer Verlag, Berlin, Vol. 29, No 1, 2002, pp.43-51. GAWIN D.. PESAVENTO F., SCHREFLER B.A., “Modelling of hygro-thermal behaviour of concrete at high temperature with thermo-chemical and mechanical material degradation”, Computer Methods in Applied Mechanics and Engineering, Vol. 192, No13-14, pp. 1731– 1771, (2003).
[8]
[9]
[10] BAZANT Z.P., NAJJAR L.J., “Nonlinear Water Diffusion in Nonsaturated Concrete”, Matériaux et Constructions, Vol. 5, 1972, pp. 3-20. [11] BAZANT Z.P., THONGUTHAI W., “Pore Pressure and Drying of Concrete at High Temperature”, J. Engng. Mech. Div. ASCE. Vol. 104, 1978, pp. 1059-1079. [12] BAZANT Z.P., THONGUTHAI W., “Pore Pressure in Heated Concrete Walls: Theoretical Prediction”, Mag. Concr. Res., Vol.31, 1979, pp. 67-76. [13] BAZANT Z.P., KAPLAN M.F., Concrete at High Temperatures: Material Properties and Mathematical Models, Longman, Harlow, 1996. [14] ZIENKIEWICZ O.C., TAYLOR R.L., The Finite Element Method, vol. 1: The Basis, Butterworth-Heinemann, Oxford, 2000. [15] ZIENKIEWICZ O.C., TAYLOR R.L., The Finite Element Method, vol. 2: Solid Mechanics, Butterworth-Heinemann, Oxford, 2000. [16] MAZARS J., Application de la mecanique de l' endommagement au comportament non lineaire et la rupture du beton de structure, (in French). Thesy de Doctorat d' Etat, L.M.T., Universite de Paris, 1984. [17] MAZARS J., PIJAUDIER-CABOT G., “Continuum damage theory - application to concrete”, J. Eng. Mech. ASCE, Vol. 115, No2, 1989, pp. 345-365. [18] GERARD B., PIJAUDIER-CABOT G., LABORDERIE C., “Coupled diffusion-damage modelling and the implications on failure due to strain localisation”, Int. J. Solids Structures, Vol.35, No31-32, 1998, pp. 4107-4120.
55
[19] NECHNECH W., REYNOUARD J.M., MEFTAH F., “On modelling of thermo-mechanical concrete for the finite element analysis of structures submitted to elevated temperatures”, Proc. of Fracture Mechanics of Concrete Structures, R. de Borst, J. Mazars, G. PijaudierCabot , J.G.M. van Mier (eds), Lisse: Swets & Zeitlinger, 2001, pp. 271-278. [20] KHOURY G.A., “Strain components of nuclear-reactor-type concretes during first heating cycle”, Nuclear Engineering and Design, Vol.156, 1995, pp. 313-321. [21] GAWIN D., PESAVENTO F., SCHREFLER B.A., “Modelling of deformations of high strength concrete at elevated temperatures”, Materials and Structures/Concrete Science and Engineering, Vol.37, No268, 2004, pp. 218-236. [22] THELANDERSSON S., “Modelling of combined thermal and mechanical action on concrete”, J. Engng Mech, ASCE, Vol.113, No6, 1987, pp. 893-906. [23] PHAN L.T., LAWSON J.R., DAVIS F.L., “Effects of elevated temperature exposure on heating characteristics, spalling, and residual properties of high performance concrete”, Materials and Structures Vol.34, 2001, pp.83-91. [24] PHAN L.T., CARINO N.J., “Effects of test conditions and mixture proportions on behavior of high-strength concrete exposed to high temperature”, ACI Materials Journal, Vol.99, No1, 2002, pp. 54-66.
56
On Fire Behavior of R/C Sections Subjected to an Eccentric Axial Force Patrick BAMONTE PhD Candidate Dept. of Struc. Engineering Milan University of Technology Milan, Italy
Alberto MEDA Assistant Professor Dept. of Engrg. Technologies University of Bergamo Bergamo, Italy
Summary Three different issues concerning the design of R/C sections are briefly addressed: (a) the use of simplified and realistic laws in ordinary conditions, within the well-known limit-analysis approach; (b) the use of incremental-iterative procedures (“exact” method) and of limit analysis in fire conditions; and (c) the validity of the “effective-section” approach in fire conditions, under the combination of bending and axial force. As expected, in ordinary conditions any realistic law with softening grossly underevaluates the sectional capacity, if it is used within the limit-analysis approach. However, the exact method and limit-analysis (with simplified laws) give very close results in ordinary conditions. In fire conditions, limit analysis applied to the effective - or reduced section and the exact method closely agree in pure bending, but the former approach is too conservative under an eccentric axial force. To improve the performance of limit analysis in fire, the simplified law for concrete in compression should be in some way related to the temperature, in terms of strength and ultimate strain. In this way, limit analysis becomes more computationallycomplex, but still is definitely less complex than the exact approach. Keywords:
1.
R/C sections, interaction envelopes, concrete constitutive laws, moment-curvature diagrams.
Introduction
The ultimate bearing capacity of R/C sections subjected to an eccentric axial force at room temperature is usually checked by means of MRd-NRd interaction diagrams or envelopes. These diagrams can easily be plotted, once concrete and steel constitutive laws are given, by assuming a linear diagram for the strains in the section (as a consequence of the assumption that plane sections remain plane up to failure, Fig. 1), and by enforcing the well-known limits for concrete strain in compression (usually 3.5‰) and steel strain in tension (usually 5 or 10‰). The corresponding values of NRd and MRd are then evaluated by simply integrating the stresses over the section. εcu
εc1
d h
B
C
εsu
A
Fig. 1 - Strain diagrams for the analysis of a section subjected to an axial force and a bending moment: A, B and C are strain limits (A for the reinforcement; B for the concrete in any condition; and C for the concrete in pure compression).
57
This procedure can be used only if the stress-strain law meets a basic requirement: the softening branch, if present, should have a limited extension. This is the case, for example, of the parabolarectangle or the Sargin diagram (Fig. 2a) proposed in EC2 [1], sections 3.1.7 and 3.1.5, for concrete. If the same procedure is used with the stress-strain curve proposed in the EC2-Fire Design [2], section 3.2.2.1 (Fig. 2b), the point corresponding to the attainment of the ultimate strain in the concrete does not correspond - in general - to the failure of the section. In fact, when the ultimate strain is reached in the extreme concrete fiber, a large part of the section is subjected to stress values which are lower than the peak stress fc. In addition, the EC2-Fire Design stress-strain relationship allows larger ultimate strains than the parabola-rectangle diagram and exhibits a softening branch from the peak stress fc to 0. Thus, when the ultimate strain is reached in the top concrete fiber, most of the section has already undergone unloading and the bearing capacity turns out to be lower than in the case of a parabola-rectangle diagram. parabola-rectangle
(a)
(b) prEN1992-1-2 at 20°C
1
σc/fc Sargin 0.5
0 0
-1
-2
εc [‰]
-3
-4
0
-5
-10
εc [‰]
-15
-20
Fig. 2 - Stress-strain diagrams for concrete at room temperature proposed in the Eurocode 2 (a) and in the prEN1992-1-2 (b); note the different scales for the strain Hc. In Fig. 3 three different interaction diagrams referring to the same square section (30 × 30 cm, 616) are plotted by adopting the limit-analysis approach (i.e. by imposing the ultimate strains for steel and concrete, Fig. 1). These envelopes were obtained by using the three afore-mentioned stress-strain relations for concrete. 200
T = 20°C Sargin
160
MRd [kNm]
120
column 30 x 30 6 bars 16 mm
p-r diagram
80
EC2 Fire Design
40
0
-40
-80 -1000
0
1000
2000
3000
4000
NRd [kN]
Fig. 3 - Interaction diagrams for a square section, as obtained by using the classic limit-analysis approach, for three different stress-strain relationships for concrete (p-r = parabola-rectangle). 58
It clearly appears that the results are completely different, and that the bearing capacity of the section is greatly underestimated when using a constitutive laws with a complete softening branch. Although the bearing capacity in pure compression is almost the same in all cases (the slight differences depending on the steel strain), it is worth remarking that the negative part of the dashdotted curve (negative bending moment) is meaningless. Of course, the underevaluation of the sectional capacity is avoided if the EC2-Fire curve is used properly, i.e. by adopting the incremental-iterative analysis. Using this approach, for any given value NRd of the axial force the maximum value MRd of the bending moment is found, on the basis of the moment-curvature diagram of the section. If this calculation is performed for different values of NRd, and these values are plotted together with the corresponding values of MRd, then the interaction diagram is obtained. This procedure was applied with reference to the diagram proposed in [2] and the results are summarized in Fig. 4. 200 N = 1000 kN
MRd [kNm]
160
200
t = 0', T = 20°C
160
N = 500 kN
120
120 N=0
80
80
N = -200 kN
40
40
0
0 0
0.0001
0.0002
0.0003
0.0004
0.0005
k [1/mm]
-1000
0
1000
2000
3000
4000
NRd [kN]
Fig. 4 - MRd-NRd envelopes for a square section, obtained by using the incremental-iterative analyisis with the stress-strain relation for concrete proposed in [2] (full line) and by using the classic limit-analysis approach with the parabola-rectangle constitutive diagram (dashed line). In this case, the combination of an iterative procedure and of a realistic law with strain softening yields numerical results which are in very good agreement with those obtained with limit-analysis and the parabola-rectangle curve. Now the question is: is it possible to extend limit analysis to a fire-damaged section? If yes, proper strain limits should be introduced, and these limit values should be a function of the temperature.
2.
Sectional analysis in fire conditions
The bearing capacity of square sections subjected to fire conditions is usually evaluated in two different ways: (a) by using the “effective section” method ([2], Annex B1), which has to be applied assuming the same parabola-rectangle diagram used for concrete in ordinary conditions; and (b) by using the stress-strain, temperature-dependent diagrams proposed in [2], section 3.2.2.1. Both approaches must be preceded by the thermal analysis of the section in order to work out the temperature distribution in the concrete for different values of the fire duration, as well as the “reference” isothermal line. Since the first approach is based on the parabola-rectangle diagram, it can be used with classic limit analysis based on strain limitations (as it is done at room temperature), making reference to the undamaged part of the concrete section (the “effective section” enveloped by the isothermal line 500°C). On the contrary, the mechanical properties of the steel layers depend on the temperature reached in each bar during the heating process. Although handy and based on reasonable assumptions, this method was originally proposed for sections subjecetd to pure bending [3], where the failure of the section is generally controlled by the attainment of the ultimate strain in the tension reinforcement. The possible extension to members subjected to an eccentric axial force is still under discussion.
59
The second approach, based on a constitutive law for concrete with a softening branch, requires the use of incremental-iterative analysis, as demonstrated in the previous paragraph. To this end, for a given fire duration, the moment-curvature diagrams for different values of the axial force NRd have to be determined and the corresponding maximum moment MRd is evaluated. The envelopes of these points (NRd, MRd) represent the MRd-NRd envelopes of the section. A comparison between these two approaches (Fig. 5a,b) was carried out with reference to the same section considered in the previous section, subjected to a standard ISO834 Fire; the thermal and mechanical properties of the materials, as a function of the temperature, were in accordance with [2]. 200
(a)
200
N = 500 kN
MRd [kNm]
160
(b) t = 0'
160 t = 0'
120
120
t = 60'
80
80
t = 120' t = 180'
40
t = 60'
t = 120'
40 t = 180'
0
0 0
0.0001
0.0002
0.0003
-1000
0
k [1/mm]
1000
2000
3000
4000
NRd [kN]
Fig. 5 - (a) Moment-curvature diagrams of a square section for different fire durations (t = 0’, 60’, 120’ and 180’) and constant value of the axial force (NRd = 500 kN); and (b) corresponding MRdNRd envelopes (full lines), compared with the envelopes obtained by using the “effective section” method (dashed curves). It is worth noting that there is hardly any difference between the two approaches in pure bending (Fig. 5b, NRd = 0): this is nothing new, since, as previously recalled, the “effective section” method was explicitly conceived and validated for sections subjected to pure bending. However, if the axial force is not zero, the “effective section” method becomes conservative and even very conservative at high values of the fire duration (Fig. 6, see also [4]). The area encolsed by the MRd-NRd envelopes and evaluated by using the “effective section” method, is roughly one half of the area obtained with the incremental-iterative analysis. This fact should be kept in mind, even if being conservative puts the analysis on the safe side. 120
MRd [kNm]
t = 60'
80
t = 120'
40
t = 180'
0 -1000
0
1000
2000
NRd [kN]
Fig. 6 - Comparison between the results obtained by using the incremental-iterative analysis (full – lines) and the “effective section” method (dashed lines) for different values of the fire duration. 60
To improve the “effective section” approach in fire in the case of an eccentric axial force, limit analysis may still be used by introducing strain limits in temperature-dependent Vc-Hc curves without softening branch. If this kind of stress-strain curves are given, a method based on limit analysis may be used (Fig. 7, see also [4]). Of course, these diagrams, which do not represent the actual behavior of the material, have to be validated against either the incremental-iterative analysis or appropriate test results, as was originally done with the parabola-rectangle diagram. These curves are not given in the prEN1992-1-2 [2] and thus, designers cannot evaluate the sectional bearing capacity in fire conditions with a limit-analysis approach.
T = 20°C T = 200°C
1
σc/fc
T = 400°C
0.5
T = 450°C T = 500°C 0 0
-4
-8
εc [‰]
-12
-16
Fig. 7 - Temperature-dependent parabola-rectangle diagrams, to be used in the classic limitanalysis approach.
3.
Conclusions
x
The sectional analysis of R/C sections subjected to an eccentric axial force, using the constitutive law for concrete given in prEN1992-1-2, must be carried out in an incrementaliterative way;
x
the classic limit-analysis based on strain limitations is not applicable, if stress-strain diagrams with softening branches are used;
x
the “effective section” method can be applied also in the case of an eccentric axial force, even though it was originally introduced for pure bending, beacuse the results are on the safe side: however, for high values of the fire duration, the method yields a remarkable underestimation of the bearing capacity; the classic limit-analysis may be used in fire conditions if monothonic constitutive laws, with the strength and the ultimate strain formulated as a function of the temperature, are used.
x
References [1] [2]
prEN1992-1-1, “Design of Concrete Structures - Part 1: General rules and rules for buildings”, July 2002, 227 pp. prEN1992-1-2, “Design of Concrete Structures - Part 1.2: General rules – Structural Fire Design”, October 2002, 97 pp.
[3]
ANDERBERG Y., and THELANDERSSON S., “Stress and Deformation Characteristics of Conrete at High Temperatures”, Lund Institute of Technology, Lund (Sweden), 1976, 84 pp.
[4]
MEDA A., GAMBAROVA P., and BONOMI P. : “High-Performance Concrete in FireExposed Reinforced-Concrete Sections”, ACI Structural Journal, V.99, No.3, pp. 277-287.
61
High-Temperature Performance of a HPFRC for Heavy-Duty Road Pavements
Stefano CANGIANO Senior Researcher CTG-Italcementi Bergamo, Italy
Patrick BAMONTE PhD Candidate Milan University of Technology Milan, Italy
Summary A high-performance concrete, containing polymeric fibers and quartzitic aggregates, and characterised by the absence of silica fume has been recently investigated after being exposed to high temperature. The focus was on the evaluation of the mechanical decay and on the microstructural evolution after a thermal cycle. The tests highlighted the beneficial role of the polymeric fibres, that prevent HPFRC from spalling and allow the material to retain a sizeable residual compressive strength after being exposed to high temperature (for instance 600°C for two hours). The results presented in this paper were obtained within a comprehensive research project concerning the use of photocatalytic cementitious materials in heavy-duty road pavements. Keywords:
1.
concrete, electron microscopy, high-strength concrete, high temperature, hybrid fibers, pavements, polypropylene fibers, porosimetry, residual mechanical properties.
Research significance
A high-performance concrete reinforced with polymeric fibers (fc = 120 MPa) is being developed for the construction of heavy-duty road pavements. To this end, a comprehensive research program is in progress at CTG-Italcementi Group Laboratories, and the evaluation of the performance in case of fire is one of the objectives, with specific reference to the residual mechanical properties, after heating to 750°C. The special high-performance concrete studied in this project contains a photocatalytic cement that markedly reduces the NOX concentration in the airborne environment, to the advantage of air quality in heavy-traffic areas [1].
2.
Concrete composition, test specimens and thermal cycles
The composition of the concrete and its mechanical properties at room temperature are given in Tables 1 and 2 respectively (c > 500 kg/m3). Two types of polymeric fibres have been used in order to minimize plastic and hydraulic shrinkage (long and short fibres with vf # 0.6% by volume). The reology of the fresh mix is comparable to that of self-compacting concrete (SCC). A number of cylindrical specimens ( = 36 mm and h = 110 mm) has been slowly heated to 5 “reference” temperatures, and then slowly cooled to room temperature, in accordance with welldefined procedures [2-5], to avoid any sizeable self-stress. The heating and cooling modalities were as follows: x x x
heating (cooling) rate: 30°C/h (-15°C/h) reference temperatures: T = 20, 150, 300, 450, 600 and 750°C rest at the reference temperature (T t 150°C): 't = 2 hours
63
Cement GX – Millenium £
30% by mass of solid mix (*)
Quartzitic aggregates (da = 4.5 mm)
69.71%
Polypropylene fibres:
0.24% 0.05%
macrofibres (L = 20 mm) microfibres (L = 6 mm)
Water/cement ratio
0.31
Acrylic superplasticizer (AXIM AC 2003)
0.58% cement (**)
Mass per unit volume
2300-2350 kg/m3
(*) no water and superplasticizer
(**) dry fraction
Table 1 - Concrete composition.
Age (days)
Compressive strength (cylindrical, MPa)
Tensile strength (in bending, MPa)
Young’s modulus (MPa)
1
59.0
5.5
34000
7
98.0
10.4
40000
28
121.0
15.3
42000
Table 2 - Mechanical properties at room temperature (20r 2°C). After the thermal cycles, each specimen was tested in uniaxial compression and in three-point bending, to evaluate the compressive strength, the elastic modulus (secant, static) and the indirect tensile strength. The plots of fc and Ec are shown in Figs. 1,2. Three tests were carried out for each reference temperature. A limited number of tests was performed in “thermal-shock” conditions, i.e. by introducing the cylinders into the furnace, previously heated to 600°C, and by keeping them at high temperature for 30’. No spalling occurred, but a net of hairlike cracks appeared on the surface of the specimens. On the contrary, two cylinders without fibers exploded 5’-10’ after being put inside the furnace. The explosions broke the cylinders into three pieces, with the cracks localised in the cross sections, because of the combined effects of pore pressure and self-stresses. After being extracted from the furnace, the specimens were left to cool to room temperature and then were tested in uniaxial compression. The residual strength fc* turned out to be very close to that of the specimens slowly heated to 600°C (fc* = 47.5 MPa, see Fig. 1), this fact being totally unexpected, since the mechanical decay appears to be the same for slowly-heated and suddenlyheated specimens. Should it be confirmed by further tests, the conclusion would be that the strength decay depends solely on the maximum temperature reached by the material, and not on the heating rate. All mechanical tests were performed in the laboratory of the Structural Engineering Department of Milan University of Technology.
64
50000
120
Elastic Modulus [MPa]
Compressive strength [MPa]
140
100 80 60 40
40000
30000
20000
10000
20 0
0 20
150
300
450
600
20
750
150
Fig. 1 - Residual compressive strength.
600
750
25 Spec. 20°C Spec. 150°C Spec. 300°C Spec. 450°C Spec. 600°C Spec. 750 °C
80
60
Spec. 20°C Spec. 150°C Spec. 300°C Spec. 450°C Spec. 600°C Spec. 750 °C
20 Relative volume %
Cumulative volume [mm3/g]
450
Fig. 2 - Residual elastic modulus.
100
40
20
15
10
5
0
0 100
101
102
103
104
105
106
100
Pore Radius [nm]
101
102
103
104
105
Pore Radius [nm]
Fig. 3 - Cumulative distribution of pore size.
3.
300
Temperature (Tmax) [°C]
Temperature (Tmax) [°C]
Fig. 4 - Differential distribution of pore size.
Microstructural analyses
The pore-size distribution was investigated by submitting the fragments of the cylinders to mercury intrusion, in order to work out both the cumulative and the differential distributions of pore size (Figs. 3,4). As already observed by other researchers (see for instance [6]), the cumulative porosity increases with the maximum temperature (Fig. 3), and the peak of the differential distribution moves towards larger pore dimensions as the maximum temperature increases (Fig. 4). The physical state of the polymeric fibers was studied by means of electron microscopy. Above 150°C, the fibers disappear, since they melt and vaporize, leaving an evident mark in the form of an oblong cavity (Figs. 5,6). Electron microscopy was used also to investigate the formation and propagation of the microcracks. As shown in Fig.7, discontinuous microcracks appear at 300°C; above this temperature, the microcracks become more numerous and wider (Tmax = 450°C). After the transition of quartz from the D- to the E-crystalline form (T = 573°C), the microcracks exhibit a marked increase in both number and width, and some microcracks start crossing the aggregate particles.
65
Fig. 5 - After heating to 150°C, the fibers are Fig. 6 - After heating to 300°C, only the mark of the fibers is left. still there (melting temp. # 150-170°C).
Tmax = 20 °C
Tmax = 450 °C
Tmax = 150 °C
Tmax = 600 °C
Tmax = 300 °C
Tmax = 750 °C
Fig. 7 - Evolution of the microcracks in the specimens first slowly heated to high temperature and then cooled to room temperature.
66
Optical microscopic observations were also performed on the polished surfaces of thermallydamaged concrete. For increasing values of the maximum temperature, the color of the concrete shifts from grayish to reddish, with the red hue appearing at 300°C (Fig. 8), probably because of the oxidization of the iron minerals contained in the aggregates (limonite, goethite, lepidocrocite and others). All microstructural analyses were performed in the laboratory of CTG-Italcementi of Bergamo.
Tmax = 20°C
Tmax = 300°C
Tmax = 750°C
Fig. 8 - Different hues of the microstructure at various temperatures (optical microscopy).
4.
Concluding remarks
The first results of this research project confirm the good residual mechanical properties of the HPFRC under development, with still 35% of the original compressive strength left after a thermal cycle at 600°C. Both the compressive strength and the elastic modulus tend to decrease linearly with the temperature above 150°C, and the polymeric fibers make the concrete virtually spallingfree. Finally, mercury porosimetry, and electron and optical microscopy give useful information on the damaged microstructure, in terms of crack formation and propagation, and of concrete color, this last point being of great interest for the development of color-based methods to evaluate the maximum temperature locally reached by the material in R/C structures after a real fire.
Acknowledgements The cooperation of MS Candidates A. Locatelli and M. Tamburlini was instrumental in carrying out the tests concerning the mechanical properties. Further tests are in progress with reference to spalling, dynamic elastic modulus, tensile strength and thermal properties.
References [1]
CASSAR L., “Photocatalysis of Cementitious Materials: Clean Building and Clean Air”, MRS Bulletin, 2004.
[2]
RILEM, “Properties of Materials at High Temperatures : Concrete”, Ed. by U. Schneider, Publ. by the Dept. of Civil Engrg. of the University of Kassel (Kassel, Germany), 1985, 131 pp.
[3]
DIEDERICHS U., JUMPPANEN U. M. and PENTTALA V., “Behaviour of High-Strength Concrete at High Temperatures”, Tech. Report 92, Dept. of Struc. Engrg., Helsinki Univ. of Technology, Helsinki (Finland), 1989, 76 pp.
[4]
PHAN L.T. and CARINO N.J., “Review of Mechanical Properties of HSC at Elevated Temperature”, J. of Mat. in Civil Engrg., V.10, No.1, 1998, pp.58-64.
[5]
FELICETTI R. and GAMBAROVA P.G., “Effects of High Temperature on the Residual Compressive Strength of High-Strength Siliceous Concretes”, ACI Materials J., V.95, No.4, 1998, pp.395-406.
[6]
KALIFA P., CHÉNÉ G. and GALLÉ C., “High-Temperature Behaviour of HPC with Polypropylene Fibres from Spalling to Microstructure”, Cement and Concrete Research, V.31, 2001, pp.1487-1499.
67
FRC Bending Behaviour: a Damage Model for High Temperature Matteo COLOMBO PhD Candidate Dept. of Struc. Engineering Milan Univ. of Technology Milan, Italy
Marco DI PRISCO Professor Dept. of Struc. Engineering Milan Univ. of Technology Milan, Italy
Roberto FELICETTI Associate Professor Dept. of Struc. Engineering Milan Univ. of Technology Milan, Italy
Summary Steel fibre-reinforced concrete (SFRC) is increasingly used as an advantageous replacement of diffused reinforcement (like welded steel meshes), especially in thin prismatic members, such as open- and closed-section channel beams. In such cases, fire plays a major role in the design. In a previous research project, the benefits offered by steel fibres to the fire resistance of concrete members subjected to bending were experimentally investigated. The main conclusion was that even in SFRC the mechanical damage due to high temperature depends on the maximum temperature reached during the heating process, rather than on the temperature of the test. Taking advantage of the previous test results, a more complete characterisation of the material exposed to high temperature is proposed in this paper, with the aim of extending the so-called “Crush-Crack” Model to thermally-damaged SFRC. Keywords:
1.
fire resistance, damage model, steel fibre reinforced concrete, uniaxial tension, uniaxial compression, bending behaviour.
Introduction
The main objective of the paper is to summarize the experimental evidence obtained by the authors on steel fibre reinforced concrete when exposed to high temperature in the last few years and to propose a new experimental project on the behaviour of SFRC in fire conditions to calibrate a constitutive model. The reference model is a scalar damage model proposed by di Prisco and Mazars in 1996 [8] that considers damage dependent on the total positive strains according to the same norm used by Mazars (1984; on concrete thermal damage see also [1,2]). The main idea is to univocally correlate irreversible positive strains to damage by means of a tensorial function. Also irreversible compressive strains are introduced, but they are related to a yielding function that depends on only two strain invariants of the negative strains according to a plastic approach. These assumptions involve that uniaxial tension causes damage increase if tensile strain exceeds a certain treshold dependent on the current damage that is defined as an internal variable , while uniaxial compression introduces both damage, controlled by transversal strains, and irreversible compressive strains. Finally another internal variable is introduced to describe the transversal reversible strains associated to Poisson effect. The work is still in a starting phase, and therefore the main assumptions and the experimental programme useful to characterize the material is here presented for discussion.
2.
Mechanical properties of fibre reinforced concrete at high temperature
In this paragraph some experimental results previously obtained on steel fibre reinforced concrete when exposed to high temperature are summarized. The fibre reinforced concrete here considered has a matrix strength equal to 75 MPa and a fibre content of 50 kg/m3; the fibre are low carbon, hooked end, 30 mm long and with an aspect ratio of 45. The results here presented refer to four different types of tests: x Compressive and ultrasonic-wave tests on cubes in residual conditions x Uniaxial tensile tests on notched prisms in residual conditions x Four-point bending tests on prisms either in hot and residual conditions x Tests on slabs loaded with a four point bending scheme and subjected to standard fire
69
Fig. 1 - Residual cubic and cylindrical strength in compression [fcc, fc = cubic and cylindrical compressive strength].
Fig. 2 - Mass loss per unit-volume ('Uc) and ultrasonic-pulse velocity (UPV).
2.1. Compressive strength of SFRC Load-controlled tests in uniaxial compression on cubes exhibited a sizeable thermal decay above 200°C, slightly higher than that generally found in the codes (UNI 9502) for siliceous mixes (Fig. 1) [3]. It is worth noting that, because of the thermal damage in the concrete, the confining action exerted by the platens on the cubic specimens increases with the temperature, to the detriment of the cylindrical strength (the usual value of the ratio fc/Rc = 0.83 in the virgin specimens becomes 0.64 in the specimens heated up to 600°C). As expected, the percent reduction of the mass due to dehydration turned out to be much less marked than the ultrasonic-speed reduction, the latter being measured as the average in two directions at right angles to the casting direction (Fig. 2); it’s important to point out that no difference has been found between the two directions. Moreover, the remarkable analogy between the strength decay in compression and the ultrasonic-velocity reduction makes it possible to calculate a correlation between the thermo-mechanical decay and the ultrasonic speed. 2.2. Uniaxial tensile behaviour of SFRC In order to identify the mechanical constitutive law in uniaxial tension after a thermal cycle, a set of fixed-end tests were carried out (Fig. 3) [4]. The specimens were sawn from an original plate and then introduced into an oven to be subjected to a thermal cycle. Five temperature thresholds were assumed as a reference: 20, 200, 400, 600, 800°C. The heating process was characterised by a rate of 30°C/h up to the reference temperature, a stabilisation phase at constant temperature (2 hours), a controlled cooling process to just 200°C (rate 12°C/h) and finally a natural cooling to room temperature. The specimens were prismatic (Fig. 4), double notched and the tests were displacement controlled. Six LVDTs were adopted to measure crack opening, as shown in Figure 4. The test machine used was a closed-loop electro-mechanical press suitably equipped with four handadjustable ties to keep the press platens parallel. Three nominally identical tests were carried out. The results (Figs. 5, 6) highlight a significant reduction in the peak strength at 400°C and an expected increase of the ductility for high temperature. In fact, pull-out residual strength is less affected by damage with respect to matrix tensile strength. The tests do not give any information on the influence of actual temperature on the residual strength, because the tests were performed at room temperature. This means that the mechanical characterisation is only significant if the damage introduced by high-temperature exposition is related to the maximum temperature reached, indicated as a reference. 70
Fig. 3 - Fixed-platens uniaxial tension test.
Fig. 4 - Specimen geometry and LVDT positions.
Fig. 5 - Average stress vs. crack opening curves Fig. 6 - Tensile strength (fct), cohesive strength at various temperatures. (Vcohes w = 1.5mm) and crack width at max. load. 2.3. Bending behaviour of SFRC When referring to fire design it still has to be fully clarified whether the cohesive strength of cracked steel fibre reinforced concrete, which is governed by the fibre pull-out mechanism at room conditions, switches to other mechanisms at high temperature (e.g. fibre yielding). Another interesting aspect to be checked is if any sizable difference can be recognized by measuring the material response at high temperature (hot behaviour) or after cooling down to room temperature (residual behaviour). Some promising comparisons in direct tension are available in the literature [5], but they are focused on very special concretes with relatively high content of straight steel fibre. In order to answer these questions, an experimental investigation was carried out at Magnetti Building laboratory [6]. Four point bending tests were performed both on hot specimens, just extracted from the oven (as proposed by Pimienta in compressive tests [7]), and after cooling. Considering four different reference temperatures (200, 400, 600 and 800°C), besides the room condition, three nominally identical tests were carried out on prismatic specimens 500 mm long and with a 75 x 60 mm cross section both in hot (H) and in residual (R) condition (Fig. 9). For the residual tests, the cooling process was governed by the natural cooling of the closed furnace. For the hot tests, the specimen was extracted from the hot furnace and placed on the test bench, within an insulating box (Fig. 7). With the same aim of preventing an excessive cooling of the specimen,
71
the test was performed at relatively high displacement rates (1 mm/min and 2 mm/min for the preand the post-peak branches respectively). In order to measure the temperature of the material during the test, two 8 mm diameter holes were drilled into each specimen, as to allow as many thermocouples to be inserted (Figs. 8, 9). Given the difficulties of handling the hot specimen within a short period of time, no other transducers were installed. Hence, the crack opening displacement was evaluated using the two rigid bodies' assumption, based on the displacement ' and on the actual crack position. It is worth noting that only one crack propagates in the critical zone in the whole set of tests.
Fig. 7 - Testing zone and thermal insulating box without frontal panel.
Fig. 8 - Test set-up.
Fig. 9 - Test set-up and specimens dimensions.
Fig. 10 - Average load vs deflection curves at various temperatures with different testing modalities.
In order to evaluate the influence of the fast cooling of the specimen in the hot tests some thermal analyses were performed considering: x Concrete thermal properties governed by the maximum temperature T0 experienced by the material. No heat sources or sinks were taken into account;
72
x
Linear convection and linearized radiation boundary conditions. Hence, the outward thermal flux from the specimen is proportional to the temperature difference between the surface and the surrounding air, through the constant h = hconv + hrad
(a)
(b)
Fig. 12 - Decay of concrete mechanical parameters (a) and V = fct contours 2 min after specimen extraction from the hot furnace (b). By considering the decay of the mechanical properties of this type of concrete [3] and the temperature fields at time t=2min (time to reach bending test peak load), the general trend of the incipient cracking contours can be plotted when thermo-elastic analysis is carried out (Fig. 12). It can be concluded that thermal cracking of the specimen border is likely to occur in this hot-testing f ctT 0 1 technique, especially at a temperature higher than 400°C (see the ratio T 0 ). However, Ec E T0 Tamb the crack penetration does not exceed 10-15% of the beam depth and its influence is expected to vanish as the bending load approaches the peak. Hence, no significant effects are to be expected at the peak load and still more during the fibre pull-out phase. Fig. 10 shows the results of tests performed with high displacement rate by means of the load displacement (') average curves. The most significant results seem to be a good agreement between the residual tests (R) and the hot ones (H); the curves associated to the two ways of testing material show a small difference that gives an idea of the influence of the actual temperature in the specimen on the material behaviour. Focusing on the behaviour at the peak, it is clear that it is not significantly affected by the test procedure for all the materials investigated. In the same way, a good agreement among residual and hot tests can be noticed in the post-peak behaviour, particularly up to 1.5 mm of crack opening displacement. In the final post-peak stage the agreement tends to be lost and this could bring us to conclude that the matrix is less influenced by the testing procedure (its degradation is related only to the maximum temperature reached), whereas the fibres pull-out mechanism, in particular for high crack opening displacement, seems to be more influenced by the instantaneous temperature during the test. It is also important to point-out that the investigated materials are characterized by a high scatter of the results. In order to better weigh the difference between the two testing procedures, it was compared with the maximum difference among the three nominally identical repeated tests performed for in each case. The comparison, shown in Fig. 13, underlines how the difference between the two test procedures is lower than the maximum scatter registered in each homogeneous group of tests for all the temperatures investigated; the only exception is the maximum temperature of 800°C for which the difference is higher than the scatter observed in the hot test.
73
2.4. Structural tests in fire conditions Three plain-concrete and six SFRC slabs were preloaded (3 load levels kept constant during each test) and then exposed to a standard fire up to failure (size l x w x t = 1800 x 600 x 60 mm). Each slab was simply supported along the short sides, and since the downward load was applied along the top surface, the bottom tensile face was exposed to the fire (Fig. 14). The supports consisted of special steel rollers, which rested on the furnace walls. In this way, the boundary restraints were exactly in accordance with the simple-support assumption.
Fig. 13 - Bending test: difference between the maximum and the minimum loads of nominally identical R and H tests and difference between their average loads. The standard fire curve ISO 834 representing a celluloid fire was adopted. The temperature was monitored by means of 2x5 thermocouples placed inside each specimen, at different depths along the thickness (Fig. 14). The thermocouples were fastened to a steel frame, which was embedded in the specimen.
74
In all tests the vertical displacement was measured at 3 points along the longitudinal axis of each slab. Linear potentiometers were used, each having a 150 mm stroke and each provided with an instrumented pirex rod in order to monitor the thermal elongation (3 thermocouples). On the whole, 3 sets of 3 slabs each were subjected to the standard fire. All slabs had the same size (1800 x 600 x 60 mm) and the same concrete.
Fig. 14 - Structural tests: furnace position of the thermocouples inside the slab specimen close to the supports and load set-up. The fitting out of the furnace in order to independently test 3 slabs, by dividing the chamber in 3 compartments, prevented the temperatures of the compartments from having exactly the same time history, though the actual mean temperature-time curve was satisfactorily close to the standard curve (ISO 834). Furthermore, in some cases there was a temporary flame out of the burners due to debris falling from the specimens (Fig. 15). In both cases the interpretation of the test results and their fitting with a theoretical model were no easy matter, and a specific thermal analysis had to be performed on the basis of the actual temperature-time curve of each compartment. The thermal analyses were instrumental also in the evaluation of the mechanical behaviour of the slabs, and in working out the time to failure corresponding to the standard temperature - time curve, starting from the actual time to failure (which was related to the actual temperature-time curve).
75
Fig. 15 - Comparison between the standard time-temperature curve and the actual heating curves within the three furnace compartments. The tests were aimed at quantifying the time length required to failure, for different load levels, but the results were not directly comparable, since the actual temperature-time curves were quite different from the reference curve. As previously mentioned, the reference curve was satisfactorily matched only in the 2nd cell, except during a very brief period (roughly 6 minutes, when the burner flame-out occurred - Fig. 15). The time gap corresponding to the differences between the actual temperature curves and the reference curve had to be evaluated, by superimposing the theoretical temperature profiles across the thickness (as obtained with the standard curve) and those measured during the tests (Fig. 16). The favorable effects that fibres have on fire resistance can be summarized as follows: the fire resistance increases by 9, 3 and 1.33 times at the maximum, intermediate and minimum load levels (at the minimum load, the failure of the SFRC slab was triggered by local spalling) as shown in Tab. 1 which is an amazing performance indeed. Tab. 1 - Collapse time for considered load levels. Material
Collapse time (min) Max. Load Mean load
Min. load
PC
6
16
51
SFRC
36
50
65(°)
(°) Collapse due to partial spalling
Fig. 16 - Theoretical temperature profiles across the thickness of the slabs: these profiles were instrumental in correcting the actual fire duration on the basis of the standard fire.
76
3.
Damage Model: future development
3.1. Crush–crack model: general assumption at room conditions The model here considered [8] represents the inelastic strains by a local tensor if associated with crushing and by a non-local tensor if associated with cracking. The latter represents a non-local measure of the discontinuities in the displacements field at the interface of growing cracks. At the same time, an internal variable controls the transverse reversible strains, described in elasticity by the Poisson's ratio and related to damage accumulated in compression. To describe the concrete mechanical behaviour the assumption that the three different failure modes can be associated to three different mechanical behaviours, each identifiable in the softening branch by means of suitable experimental tests (cube specimen or cylindrical specimens and PIED test) has been made. It's assumed that any fracture is a combination of these three basic failure modes (uniaxial tension, uniaxial and biaxial compression). Each of them involves a different damage evolution law and the damage is controlled only by a function of the principal tensile strains and in particular this function is defined according to a non-local kinematic description of the displacement field. Crushing is taken into account due to the high value of compressive principal strains; it is controlled by an internal variable (s) which can be regarded as a threshold associated to the irreversible volume contraction. An uniaxial compression test shows significant transverse strains of which only a small part is reversible; this reversibility is assumed to be linked to an increasing Poisson's ratio Q whose evolution is described by the introduction of an internal variable G related only to damage in compression. The model remains elastic and isotropic till the yield functions which control the evolution of the three internal variable are not activated. The model considers the two elastic constants E, Q associated with internal variables (D, G) which control their evolution for damage states. The model considers irreversible strains whose modulus is expressed as a function of damage; this choice allows us to simplify the identification of each damage evolution law associated with the three different failure modes. The model considers the damage (D) to be an isotropic, internal and scalar variable, as in Mazar's previous model: this choice is a simplified assumption rather than an accurate description of the behaviour of concrete. Damage represents the reduction in the area capable of transferring stress which decreases with the propagation of microcracking and decreases even more with macrocraks. It is associated to the stiffness controlled by Young's modulus E. The volume also changes as the cracking process develops. The irreversible increase in volume is described by means of irreversible strains strictly related to damage, while the reversible part is associated to the evolution of Q, Poisson's coefficient. The small strain and displacement assumption and isothermal processes are considered. The inelastic strain tensor rate H ijir which may be split into a non-local tensor related to cracking H ijir (x) and the local tensor related to crushing are added, as usually, with elastic strains H ijel :
H ij
H ijel H ijir H ijir
H ij* H ijir
(1)
3.2. Damage model at high temperature: assumption and experimental investigations The experimental investigation previously described on high temperature suggested that damage can be regarded only as a function of the maximum temperature reached from the material during the heating process and not of the instantaneous one. In order to develop the model, some experimental tests will be carried out to characterize the material and to verify if the assumption of the crush-crack model are valid also after the thermal damage has occurred. First of all, two ultra-sonic tests are performed on the specimen respectively before and after the thermal treatment. This test measures the time a ultra-sonic wave takes to propagate through the specimen; the time is linked to the elastic modulus. Performing a test before and after the thermal cycle it is possible to detect the damage induced only by the thermal treatment.
77
150
150
15 0
Fire resistance will be checked by imposing thermal cycles with different maximum temperature (Tmax= 200, 400 and 600°C) characterized by a heating rate of about 30°C/h up to the maximum temperature and by a cooling at about 12°C/h. After the second ultra-sonic test, a four point bending test will be performed on the specimen according to the national recommendation UNI 11039-2 and during the tests some loadingunloading cycles will be planned. Besides four point bending test, two cylindrical specimens 150 mm high and with diameter equal to 75 mm will be cored from the initial prismatic specimen just tested (Figure 17).One of the specimens will be notched and will be tested in a uniaxial tensile test with fixed end platens; during the test several loading-unloading cycles will be performed to detect the damage evolution in tension. The tensile test will be instrumented with four LVDTs to measure crack opening displacement as shown in figure 18. The other cored specimen will be tested in uniaxial compression, always carrying out loading-unloading cycles and according to the set-up shown in figure 19. In this test the circumferential and the axial strains will be measured. For each test batch 3 nominally identical tests will be performed. A first result could be revealed by comparing the thermal damage measured by ultra-sonic tests with those detected by mechanical tests (uniaxial tension, uniaxial compression and bending). Four point bending test Another result of the experimental investigation will be the reliability of the identification process suggested by the authors [9] which aims to determine the tensile behaviour of the material from the bending test, even when the material is thermally damaged. The last and the most important purpose of the experimental investigation is to understand if 600 Cored Cored the damage assumed as a scalar variable, produced in the material by various thermal conditions, I could always be related to the same tensile strain Notch invariant and if, at the same time, positive irreversible strain could be related to damage by Uniaxial compression Fixed-end uniaxial tensile test with stearic acid means of the same tensorial function. V In the compressive test the relationship between the damage (measured by loadingunloading average slope with reference to the axial strain) and the positive irreversible strain (measured in loading-unloading cycles by the w circumferential positive strain) can be directly obtained even after strain localization if short inclined shear planes will occur and the related Fig. 17 - Test set-up crack displacements are smeared in the volume. Regarding the tensile test, the notch of the specimen induces a strong strain localization, and so it is not possible to release the positive irreversible strain to damage; only a relationship between damage and crack opening displacement can be found. In order to detect the strain in tension it is necessary to introduce the characteristic length of the material, that cannot be assumed as a constant with the temperature for a plain concrete as shown by di Prisco et al. [10]. In order to evaluate the thermal strains and to consider the transient thermal creep strains some experimental tests are planned. Two different kinds of compressive test will be performed both on 75 mm diameter cylindrical specimens considering the followings procedures: loading – heating – cooling – unloading (LHCU test) and heating – loading – cooling – unloading (HLCU test). Performing these tests three different loading levels (V = 0,unload, V = 0.15 fc and V = 0.3 fc) and two different maximum temperatures (Tmax = 400°C and Tmax = 600°C) will be considered. In each of this test the axial and radial strain will be measured in order to evaluate the thermal strain coefficient D and the irreversible thermal strains after the cooling process.
78
The final propose is to relate irreversible thermal strains to damage D that could become a function of both an invariant of total positive mechanical strains and maximum temperature. In this wD irr case a suitable relation J between H Tij and wT G ij must be introduced. max By adopting this solution the relation (1) could be enriched by adding two terms: ij Tij
el ij
irr ij +
irr ij -
T T
ij
Tij irr Tij
irr Tij
D T
(2) ,T max
ij
V 120° 1 ° 120
°
LVDT
120
2
2 2
1
1 0°
1
12
12
0°
Extesnometer
Extensometer
2 120°
75 mm
V
Fig. 18 - Uniaxial tensile test set-up.
Fig. 19 - Uniaxal compressive test set-up.
References [1] [2] [3]
[4]
NECHNECH W., MEFTAH F. and REYNOUARD J.M., “An elasto-plastic damage model for plain concrete subjected to high temperatures” Engineering Structures 24, 2002, 597–611. BAKER G, STABLER J., “Computational modelling of thermally induced fracture in concrete” Proc. Euro-C; 1999, 530–45. DI PRISCO M., FELICETTI R., GAMBAROVA P.G and FAILLA C., “On the fire behavior of SFRC and SFRC structures in tension and bending”, “High performance fiber reinforced cement composites HPFRCC4” Proc. 4th Int. RILEM Workshop PRO 30, 2002, 205-220. DI PRISCO M., FELICETTI R. and COLOMBO M., “Fire resistance of SFRC thin plates” Computational Modelling of Concrete Structures EURO-C 2003, 2003.
79
[5]
FELICETTI R., GAMBAROVA P.G., NATALI SORA M.P. and KHOURY G.A, “Mechanical behaviour of HPC and UHPC in direct tension at high temperature and after cooling”, Proc.5th Rilem Symp. on FRC, Lyon (France), September, 2000, 749-758.
[6]
COLOMBO M., FELICETTI R., MANZONI M. and BERGAMINI E., “On the bending behaviour of SFRC exposed to high temperature”, Proc. 6th Rilem Symp. on FRC, Varenna (Italy), 2004, 647 – 658.
[7]
PIMIENTA P., “Évolution des caractéristiques des BHP soumis à des températures élevées: Résistances en compression et modules d'élasticité”, Cahiers du CSTB n. 3353, 2001 14 p.
[8]
DI PRISCO M. and MAZARS J., “Crush-Crack: a Non-local Damage Model for Concrete”. Mechanics of Cohesive-Frictional Materials and Structures, 1996, 1321-347. [9] DI PRISCO M., FERRARA L., COLOMBO M. and MAURI M., “On the identification of SFRC constitutive law in uniaxial tension”, Proc. 6th Rilem Symp. on FRC, Varenna (Italy), 2004, 827-836. [10] DI PRISCO M., FELICETTI R., and GAMBAROVA P.G., “On the evaluation of the characteristic length in high strength concrete”, High Strength Concrete:1999,377-390 ASCE.
80
Mass Transport through Concrete Walls Subjected to High Temperature and Gas Pressure Abdelslam LAGHCHA Researcher INSA de Lyon, URGC Structures Villeurbanne, France
Gérard DEBICKI Associate Professor INSA de Lyon, URGC Structures Villeurbanne, France
Summary This study is focused on the mass transport through a concrete wall, when an increasing temperature from 20°C to 141°C, associated with gas pressure (dry air plus vapour), is applied on one face of the wall, the other face being kept in normal ambient conditions. A uni-dimensional numerical analysis was performed. The THM Model (Non-Saturated Porous Media Thermo-Hydro-Mechanic Model) included in Code_Aster® was used. Two fluid phases were considered in the material: a liquid phase (water) and a gas phase (dry air plus vapour) with the liquid-to-vapour phase change. Because of the progressive saturation of the wall, the shape of the sorption isotherm and the permeability gave an important contribution to the results. The numerical results were in good agreement with the tests in terms of phenomenological evolution and flow rate through the wall of a “reference” uncracked concrete. Keywords:
1.
concrete wall, permeability, sorption isotherm, saturation, leak flow, mass transport.
Introduction
In nuclear power plants, the reactor building is the third and final barrier to the outside environment. In French design practice, the 1300-1450 MWe NPP containments consist of a double concrete wall, which comprises an outer R/C wall to assure protection against external actions, and an unlined inner P/C wall to prevent the leakage of radioactive fission products into the environment in the event of an accident. Furthermore, the space between the two containments is maintained under light depressurisation in order to suck in and filter potential leaks from the inner containment [1]. In accordance with the operational procedures, global air tightness tests must be performed in order to measure the actual leak rate of the containment during the lifetime of the plant (after the construction, after the first refuelling and then every 10 years). The containment is submitted to an internal air pressure corresponding to the design pressure. Nevertheless, it is quite obvious that the pressure tests, are not true representations of accidental conditions, since they are carried out at ambient temperature. While in the actual LOCA conditions (Loss Of Coolant Accident) the pressurising medium is a mixture of air and vapour (including even aerosols), the pressure tests are carried out with air, which represents a significant difference in terms of mass transfer through the wall. In order to have some information about the ratio between the air-leak flow (at ambient temperature) and the leak flow with air + steam (under accidental conditions), the model for non saturated porous media included in Code_Aster® [2] was used to simulate the experimental tests performed on a permeable, uncracked reference concrete: a cylindrical specimen 1.3 m thick was used. Since the pressure is relatively small, the mechanical aspects are not treated in this paper.
2.
Mesh and boundary conditions
Figure 1 shows the mesh used in this study. The mesh density has been increased close to the two faces of the specimen. No flux is considered through the lateral sides of the specimen.
81
EXTRADOS
INTRADOS (heated face) PAIR+VAPOUR = 4.2 bar
P=PATM CONCRETE SPECIMEN = 0.5 m - L=1.3 m
T = 141°C
In the autoclave
T=TAMB
RH = 100%
Constant RH (see Figure 3)
x=0m
24 elements QUA4 / 19.5 cm
x = 1.3 m
28 elements QUA4 / 45.5 cm
Fig. 1 - Mesh of the concrete specimen and boundary conditions of the problem.
4.5
140
4.0
120
3.5
Temperature (°C)
Effective gas pressure (bar)
The input variables can be assigned only by means of their values at the extremities of the domain under study (THM-Code_Aster® model). Consequently, the applied temperature takes into account a superficial surface exchange between the environment and the surface of the concrete, i.e. the temperature applied to the specimen is lower than the ambient temperature in the autoclave. Figure 2 shows the boundary conditions in terms of pressure and temperature applied to the two faces of the concrete specimen; this type of accidental condition includes also the mixture of air and vapour.
3.0 2.5 2.0 1.5
100 80 Film coefficient of heat transfer: 13.4 W/m².°C
60 40
1.0
20
0.5
0
0.0 0
200
400 600 Time (min)
800
1000
0
200
400 600 Time (min)
800
1000
Fig. 2 - Temperature and pressure boundary conditions applied on the heated face.
3.
Concrete characteristics
For the non-saturated case (presence of air and water), the independent variables are the total gas pressure (Pgz = Pvp + Pas), the capillary pressure (Pc = Pgz - Plq) and the temperature of the medium (T).
82
Main symbols (…)s : solid phase - (…)as : dry air - (…)lq : liquid phase - (…)vp : water vapour - (…)gz : gas OT I S OI Ui Ci Kv 3.1
thermal conductivity of constituent i (W/m.°C) porosity (-) liquid saturation (-) hydraulic conductivity of constituent i (m²/Pa.s) , volumic mass of constituent i : Ugz, = Uas + Uvp (kg/m3) concentration of constituent i in the gas : Ci = Pi / Pgz (-) intrinsic permeability (m²) Permeabilities
Furthermore, we have: M gz U gz
(1 C vp )
M vp M as C vp U as U vp
(1)
The mass flux consists of a liquid mass flux, a dry-air mass flux and a water-vapour mass flux: M as O gz grad Pgz U gz F m C vp F grad C vp U as M vp O gz grad Pgz U gz F m (1 C vp ) F grad C vp U vp M lq O lq grad Plq U lq F m U lq
(2) (3) (4)
The hydraulic conductivity OlqH and OgzH have the following expressions: O Hlq
K vlq K rlq
O Hg
µ lq
K v Klink K srg K prg
(5,6)
µ Tg
In order to take into account the dependence of the gas permeability on the pressure flow, the following expression is derived from the Klinkenberg’s definition [3]: Kprgz = (1+ b* / Pgz ) with b* = 9.2.103 Pa in the case of a humid state [4]. Note that we consider distinct intrinsic permeabilities for the gaseous and liquid phases. The experimental measurements obtained for this concrete indicated an intrinsic water permeability, (according to Darcy’s definition) which is roughly twenty times lower than the intrinsic permeability Kv klink determined with the Klinkenberg’s definition. Such observations are in good agreement with Claudot-Loosveldt [5], whose works were about the hydraulic behaviour of a damaged mortar or Cazaux [6] who specified that some non-Darcian flows can occur for small hydraulic gradients ('P< 10 bar). Consequently, in this study the effective hydraulic conductivity for the liquid phase can be formulated as follows: O Hlq
K vKlink K rlq 20 µ lq
83
(7)
The relative permeabilities are determined according to van Genuchten-Mualem approach applied to the isotherm sorption [7], [8], [9], with m = 0.4049: 1S (1S 1/ m ) 2 m
K Srgz
K Srlq
S ( 1 ( 1 S 1/ m ) m ) 2
(8)
From permeability measurements performed on specimens extracted after the tests, the variations of intrinsic permeability Kv klink have been taken into account. Figure 3 shows this evolution versus the distance from the face placed in the autoclave (x):
a b x 1/ c
Kv
(9)
where: x = distance from the face placed in the autoclave (cm), and: a = 1.8174.1013 3.2
b = -1.2197.1011
c = 0.7999
Sorption isotherm
The last equation is the the capillary pressure/liquid saturation relation. In accordance with the problem in question, the following formulation is adopted for the sorption isotherm [4]: (10)
(1 ( a P c ) b ) c
S
where a = 1.41.10-7 (Pa-1)
b = 0.689
c = - 1.145
Intrinsic permeability Kvklink (m²)
5E-16 Measured
4E-16
Fit : equation (19)
3E-16
2E-16
1E-16
1E-17 0
20
40
60
80
100
120
Distance from the face placed in the autoclave (cm)
Fig. 3 - Intrinsic permeability profile. 3.3
Other coefficients
Both the porosity ()) and the concrete volumic mass (Mv) are determined by means of mercury porosimetry: Mv = 2150.0 Kg/m3
) = 0.2
In the first approach, the coefficient Dmacro is constant and was calculated for an average temperature (80°C) and an absolute pressure (1.68 bar), while thecoefficient ) was calculated for an average liquid saturation (0.8), as previously stated.
84
Concerning the thermal conductivity of the solid phase, Eurocode 4 [10] suggests the following law (Os7 = 1 W/m.K for T = 20°C): O Ts
(11)
aTb
where a = -18.58.10-4
b = 1.55
The specific isobaric heat-capacity of the concrete is taken equal to 900 kJ/kg.°C.
4.
Comparison between experimental and simulated results
4.1
Temperature distribution
It can be observed that the experimental results are higher than the calculated results during the transient regime (temperature rate: 1°C/min). One possible explanation is that - because of some heat transfer through the metallic encasement of the apparatus - a radial heating of the cylindrical specimen occurs during the transient phase. However, in spite of the uncertainties concerning the thermal conductivity of the solid phase, the numerical model yields satisfactory results in terms of temperature evolution when the permanent regime is reached. 4.2
Pressure distribution
The measured and predicted pressure distributions qualitatively agree. The marked convexity of the curves comes from the intrinsic permeability profile (Fig. 5). The model describes also very well the decrease of the pressure field in the bottom part of the specimen after 70 hours. This situation corresponds to the gradual termination of the saturation process in the concrete and to the maximum value of the gas flow at the extrados (see next paragraph). 4.3
Liquid and gas flows at the extrados
A good agreement is observed also for the gas leak flow (Fig 4a). After reaching the maximum value at roughly 70 hours, the quantity of humid gas (the numerical results show a proportion of dry air-mass flow about 38.7 times larger than the water-vapour mass flow, while the experimental data give a similar ratio) gradually decreases to reach very low values after 300 hours. As for the liquid flow through the external face, the numerical simulations allow to distinguish the liquid flow due to the applied process from the liquid flow due to some desorption phenomena. For instance, if we consider the temperature at x = 1.3 m measured during the test, the numerical simulation predicts a slight drying in the zone close to the extrados during the transient regime. Thus, by giving this temperature a constant value (20°C), the liquid-flow kinetics yields no desorption at all, and the agreement between the measured and the predicted liquid flow is quite good (Fig. 4b). 3.5E-07
1.8
Calculated
2.5E-07
Liquid flow (g/h.m²)
Gas flow (kg/s.m²)
Qlq calculated with Tx=1.3m measured
1.6
3.0E-07
Measured
2.0E-07 1.5E-07
(a
1.0E-07
1.4 1.2
Qlq measured
1.0 0.8
(b
0.6 0.4
5.0E-08
Qlq calculated with Tx=1.3m constant (20°C)
0.2
0.0E+00
0.0
0
50
100
150 Time (h)
200
250
300
0
50
100
150 Time (h)
Fig. 4 - Gas (a) and liquid (b) leak flow. 85
200
250
4.4
Moisture distribution
The moisture gauges embedded inside the specimen prior to casting make it possible to monitor the initial hydric state of the concrete before the thermal process is started (see 0 h in Fig. 7). We can observe a remarkable drying close to the intrados, confirmed by the intrinsic permeability profile. Indeed, this profile assumes that the sorption isotherm is more convex in this zone. Therefore the liquid saturation becomes rapidly lower than the critic water saturation (i.e. Ksrlq= 0): the darcian water movement and the ensuing water evaporation at the frontiers boundaries (which are the main factors in concrete drying [4], [13]) are slow compared to a concrete presenting conventional sorption isotherms. 1.0 0.9
Liquid saturation (-)
0.8 0.7 0h
0.6
10 h
0.5
20h
0.4
40 h
0.3
100 h 150 h
0.2
246 h
0.1 0.0 0.0
0.2
0.4 0.6 0.8 1.0 Distance from the face placed in the autoclave (m)
1.2
Fig. 5 – Distribution of liquid saturation. These parameters (that are related to the liquid phase) are fundamental in mass transfer, even more when the evolution of the kinetics of the saturated zone under accidental conditions is considered. This evolution (Fig. 5) shows that the wall depth affected by a marked increase in water content (S > 0.96) is about 25 cm. In spite of the extreme sensibility of this evolution to the method chosen to obtain a continuous profile of the intrinsic permeability (Fig. 3), this result satisfactorily matches the measurements obtained with the moisture meters (the last meter which indicates an effective liquid saturation is located at 29 cm from the heated face). Note that if the liquid permeability of this concrete had not been taken into proper account, a liquid leak-flow 250 times larger than that measured would have been obtained with the theoretical model and the progress of the saturated zone would have reached a depth of 82 centimetres. Consequently, the definition of the intrinsic permeability is crucial, and there is no equivalence between Klinkenberg’s and Darcy’s approaches to intrinsic permeability.
5.
Conclusions
The comparison between the experimental and theoretical results shows that the THM Model (Thermo-Hydro-Mechanic of non-saturated porous media) included in Code_Aster® is a reliable tool to simulate the behaviour of a concrete wall under temperature and pressure gradients. The numerical results show a fairly good agreement with the experimental results, especially in terms of leak flow-rates (both for liquids and gases). Therefore, this study contributes to the improvement of the transposition-ratio predictions between the air flow at ambient temperature and the (air-plusvapour-plus-liquid water) flow under accidental conditions, even if a slight underestimation of this ratio obtained with the model seems to be induced by the sorption isotherm, which homogenizes the porous structure. Nevertheless, in addition to the experimental determination of the main transport parameters (permeability profile of the wall, initial hydric state, sorption isotherm) some precautions should be taken concerning the determination of liquid permeability to achieve good numerical results. Moreover, the results indicate that the permeability according to Klinkenberg’s definition is not equivalent to the permeability according to Darcy’s definition: this is certainly a crucial issue. 86
References [1]
GRANGER L., SHEKARCHI M., and TOURET J.P., “Leak Tightness of HPC in Accidental Conditions - EDF Strategy in Terms of R&D”, International Symposium on High Performance Concrete and Reactive Powder Concretes Sherbrooke, Canada, 1998, pp. 227242.
[2]
CHAVANT C., CHARLES P., DUFORESTEL TH., and VOLDOIRE F., “Thermo-Hydromécanique des Milieux Poreux non Saturés dans le Code_Aster®”, EDF, Division Recherche et Développement, HI-74/99/011/A, 1999,51 p.
[3]
KLINKENBERG L. J., “The Permeability of Porous Media to Liquids and Gases”, Drilling and production Practices, American Petroleum Institute, New York, 1941, pp. 200-214.
[4]
BILLARD Y., DEBICKI G., and COUDERT L., “Experimental Performances of a non Cracked Concrete Wall in Air Permeability and in Accidental Conditions”, International Conference on Structural Mechanics in Reactor Technology, SMiRT 17, Prague, 2003.
[5]
CLAUDOT-LOOSVELDT H., “Etude Expérimentale des Comportements Hydraulique et Poromécanique d’un Mortier Sain ou Dégradé Chimiquement”, Thèse, Université des sciences et technologies, Lille, France, 2002, pp. 46-52. [6] CAZAUX D., “Mesure et Contrôle in Situ de la Perméabilité des Matériaux Utilisés dans les Dispositifs d’Étanchéité pour la Protection de l’Environnement”, Thèse, INSA de Lyon, France, 1998, pp. 41-44. [7] MUALEM Y., “A New Model for Predicting the Hydraulic Conductivity of Unsaturated Porous Media”, Water Resourc. Res., 12, 1976, pp. 513-522 [8] PARKER J.C., LENHARD R.J., and KUPPUSAMY T., “A Parametric Model for Constitutive Properties governing Multiphase Flow in Porous Media”, Water Resour. Res., 23(4) , 1987, pp.618-624. [9] SAVAGE B.M., and JANSSEN D. J., “Soil Physics Principles Validated for Use in Predicting Unsaturated Moisture Movement in Portland Cement”, Cement and Concrete Research, Vol. 94, No. 1, 1997, pp.63-70. [10] Eurocode 4, “Calculs des Structures Mixtes Acier et Béton”, Commission des Communautés Européennes, Luxembourg, 1993. [11] COUSSY O., BAROGHEL-BOUNY V., DANGLIA P., and MAINGUY M., “Evaluation de la Perméabilité à l’Eau Liquide des Bétons à partir de Leur Perte de Masse durant le Séchage”, Actes du Séminaire “Transferts 2000”, Paris, 2000, LCPC, pp. 97-108.
87
Microstructure of High-Strength Concrete Subjected to High Temperature Gian Luca GUERRINI Senior Researcher CTG Italcementi Group Bergamo, Italy
Pietro G. GAMBAROVA Professor Milan Univ. of Technology Milan, Italy
Gianpaolo ROSATI Professor Milan Univ. of Technology Milan, Italy
Summary This paper summarizes several recent studies jointly carried out at CTG Laboratories and at Milan University of Technology, on concrete behavior at high temperature. More specifically, some experimental results concerning the microstructural aspects are presented, with reference to different thermally-treated high-strength concrete (HSC) mixes: x HSC containing crushed limestone or dolomitic aggregates and synthetic fibers (PP and PVA) x White HSC containing white cement and marble aggregates x HSC containing quartz aggregates and hybrid fiber reinforcement (PP and micro-steel fibers) The results show that the behavior of concrete, after being exposed to high temperature, depends on concrete mix-design, specimen geometry and thermal history. In some cases, adding polymeric fibers is not necessary, even if the concrete matrix is dense, due to the presence of mineral additions (microsilica, metakaolin). Keywords:
high-strength concrete, concrete microstructure, Mercury-Intrusion Porosimetry, concrete porosity, polypropylene fibers, polyvynilalcohol fibers, residual properties, Scanning Electron Microscopy, spalling, white-cement concrete.
1. Introduction Concrete is generally considered an excellent heat-resistant material, but the increasing use of highstrength concrete (HSC) requires a better understanding of concrete behavior with respect to extreme environmental conditions, to improve designers' confidence in using HSC in such structures as tunnels and underground structures. However, questions arise on whether these types of concrete, with low porosity and permeability, are still effective as a fireproofing material. Several experimental studies – see, for example [1-6] – seem to demonstrate that normalstrength concrete (NSC) loses approximately 25% of its original compressive strength when heated to 300°C, and approximately 75% when exposed to 600°C. Other physical and mechanical properties (e.g. the tensile strength and the elastic modulus) are similarly – or even more severely reduced, due to the microstructure damages resulting from microcrack. However, the thermal properties of concrete at high temperature depend also on aggregate composition and on the relative thermal expansion of the various components [5]. Besides, in the case of HSC, due to the reduced water/binder ratio and to the presence of pozzolanic additions (e.g. microsilica and metakaolin): the ability of moisture to escape from concrete pores in case of fire is so limited that pore pressure builds up in the pores until the stresses in the surrounding matrix become so large that explosive spalling occurs. Even though the choice of the aggregates remains fundamental (because of the influence of their chemo-physical properties on concrete thermal conductivity), the thermal behaviour of the HSC matrix is equally important, in order to guarantee the structural integrity in case of fire. A practical solution to avoid explosive spalling in HSC has been achieved by adding polypropylene (PP) fibers to the mix: the uniformly-distributed fibers melt and vaporize (at 160200°C), leaving pore space inside the concrete and preventing dangerous phenomena of pore pressure build-up [6]. In order to assess the performance of HSC mixes exposed at high temperature, an appropriate approach consists of a combination of mechanical tests, physical analyses and microscopical/petrographical observations [7, 8].
89
In the experimental studies cited in this paper, residual tests were performed after heating the material to 250°C, 500°C and 750°C (Fig. 1). After the thermal cycle, the residual mechanical properties, the porosity and the damaged microstructure were investigated, with reference to the virgin material.
2. High-strength concrete containing polymeric fibers In this investigation, seven HSC mixes (C100/115 MPa) – some of them containing polymeric fibers (PP and PolyVynilAlcohol-PVA fibers) – were tested in order to evaluate their thermal behavior, after being exposed to 750°C [9, 10] and to make comparisons among R/C sections made of different materials [11]. Two different types of aggregates were used: crushed limestone aggregates (Mix 1-4) and dolomitic aggregates (Mix 5-7). The evolution of the porous structure (evaluated as a variation of the porosity) as a function of the temperature was also performed, in order to understand the damage mechanisms of the material with respect to the residual mechanical strength. Even though the right choice of the aggregate may avoid the explosive failure of the material without fibers (as in the case of the limestone aggregates), adding fibers is undoubtedly an effective solution to guarantee material integrity (in the case of dolomitic aggregates).
Temperature (°C)
800
750°C
600 500°C 400 250°C 200 Room temperature 0 0
5
10
15
20
25
30
35
40
45
50
Time (h)
Fig. 1 - Thermal cycles. 140
resistenza, MPa
V MPa
Limestone aggr.
120
120
MIX 1- 4
100
resistenza, MPa
V MPa
Fig. 2 - Specimen explosion at 330°C.
- 0,1376x
y = 198,43e 2 R = 0,9463
80 60 40
Dolomitic aggr.
100
MIX 5-7
80
y = 246,2e 2 R = 0,9513
- 0,1151x
60 40 20
20 0 0
10
20
30
0 0,00
40
Porosity, %
10,00
20,00
30,00
40,00
porosità, % % Porosity,
porosità, %
Fig. 3 - Correlation between the compressive strength and the total porosity. A correlation between the porosity (MIP) and the compressive strength is also proposed, by using a simple exponential model suggested in literature [12]: ae
bP
(1)
where P is the total porosity (%), and a and b are two empirical constants. The plots of Eq.(1) are shown in Fig. 3.
90
3. High-strength white concrete containing metakaolin The high-strength white concrete used in the construction of the “Dives in Misericordia” church in Rome (“God of Mercy” church designed by R. Meier) is here considered. This concrete had enhanced mechanical properties (compressive cubic strength 85MPa), similar to other high-strength concretes, that were prone to spalling at high temperature. The thermally-induced damage in this “architectural concrete”, incorporating metakaolin and crushed marble as aggregate, was evaluated by testing a number of specimens in uniaxial compression and direct tension, and the compressive and tensile strengths were determined as a function of the maximum temperature reached during the thermal cycle [13]. The white concrete exhibits a mechanical decay which is similar to that of other high-strength concretes containing calcareous aggregates and having the same water-binder ratio. The results demonstrate also the good physical-mechanical performance of the white-cement concrete up to 500°C, while the residual properties dramatically decrease at 750°C. A comparison with another HPC containing metakaolin but made with ordinary Portland cement and crushed granite as coarse aggregate is shown in Fig. 4, with the predictions of EC 2. It is evident that up to 400°C the granite ensures a better behavior, but there is very little difference at higher temperatures. However, explosive spalling was not observed in concrete specimens during the thermal treatments, even if fibers were not added to the mix. However, a progressive temperature-triggered microcracking was observed (Fig. 5). Finally, a possible correlation between the residual strength and the total porosity (%) was also proposed. 1.2
Relative residualstrength strength ff c/f c(20°C) Relative residual c/fc(20°C)
1.1 1
1
marble HS-M granite HS-G EC 2 EC 2
0.91
1 0.92
0.8
0.8
0.6
0.48
0.4
0.38 0.2
0.16 0.1
0.16
0 0
200
400
600
800
Temperature (°C) Temperature (°C)
Fig. 4 - A comparison between two types of thermally-treated metakaolin HSC mixes.
Fig. 5 - Crack observation after a thermal cycle at 500°C.
4. Hybrid fibers in HSC A recent study has been dedicated to the evaluation of the residual properties of a HSC mix containing quartz aggregates and hybrid-fibers (PP plus micro-steel fibers) [14, 15]. As a matter of fact, combining polymeric and steel fibers seems to be promising, to increase the ductility and to ensure an adequate fire resistance. The overall behavior in uniaxial compression and bending was considered at first. Particular attention was devoted to the evolution of cracking with the load. Therefore, the tests were monitored with laser interferometry (ESPI) [14]. The development of the damage zone in terms of shape and size was assessed with this highly-accurate nondestructive technique. Fiber hybridization with polypropylene fibers appears not to be particularly effective in enhancing the efficiency of steel fibers. A weakening effect was the results of adding polypropylene fibers to concrete, due to the poor mechanical properties of the fibers and to the additional defects during concrete preparation. Secondly, the porosity and the microstructure were investigated in order to evaluate the deterioration of the different materials, as a function of the temperature [15].
91
No explosive spalling was observed in all types of concrete, during the thermal treatment, most probably because of the very low heating rate. Only a change in color was observed. Besides, internal cracking within the cement paste, cracking around and across the aggregate grains and modifications of the fibers (melting and evaporation of the synthetic fibers, partial melting of the steel fibers) were observed, see Figs. 6 and 7. (a) NT
(b) 250°C steel fibers
PP fibers
air
(c) 500°C
(d) 750°C
steel fiber damaged
Fig. 6 - SEM analysis of a hybrid concrete, at different temperatures. An unexpected behavior of the two mixes containing steel microfibers was also observed: brasscoated steel microfibers were found to lose most of their mechanical properties and to change their color from yellow to brown: fiber oxidation was confirmed (a) by the changes in the morphology of the fibers observed with SEM. And (b) by the chemical changes investigated with EDS and XRD. Naked fibers were also submitted to thermal cycles (leading to the melting during the heating process, followed by solidification-recrystallization after cooling, Fig. 8). The microstructural transformations were confirmed by the analysis carried out on the fibers by means of Differential Scanning Calorimetry (DSC) and the fiber-melting point turned out to be 737°C (normal steel fibers show a melting point at 903°C).
Fig. 7 - SEM analysis of a mix without Fig. 8 - Partial melting of steel fibers, fibers, after 750°C. after 750°C. A partial diffusion of steel-fiber material (Fe) inside the matrix was also observed, as well as the presence of microcracks, due to the thermal treatment (Fig. 5). In the end, hybrid fibers did not improve concrete residual mechanical properties. 92
5. Conclusions The test results presented in this paper, concerning a number of HSC mixes exposed to high temperature show that concrete residual behavior depends on the specific mix-design, on the constituents and on the heat-induced chemo-physical transformations. The addition of polymeric fibers to avoid spalling is not always necessary, even if the concrete matrix is dense, provided that appropriate mineral additions (like microsilica and metakaolin) are added. Porosimetry, colorimetry and petrographical analyses (with possible correlations among the different methods) are very effective tools to assess the thermally-induced damage, and can be – in principle – easily used on drilled concrete cores belonging to real fire-damaged structures. However, further studies are needed to make these methods reliable and to work out the correlations among the different test results.
References [1]
HOFF G. C., BILODEAU A., MALHOTRA V.H., “Elevated Temperature Effects on HSC Residual Strength”, Concrete International, April 2000, pp. 41-47. [2] PHAN L.T., CARINO N.J., “Review of Mechanical Properties of HSC at Elevated Temperature”, J. Materials in Civil Engrg., February1998, pp. 58-64. [3] PHAN L.T., “Fire Performance of High-Strength Concrete: a State-of-the-Art Report”, NISTIR 5934, Dec. 1996, 105 pp. [4] FELICETTI R., GAMBAROVA P.G., “Effects of High Temperature on the Residual Compressive Strength of High-Strength Siliceous Concretes”, ACI – Materials J., V. 95, No. 4, 1998, pp. 395-406. [5] KHOURY, G.A. “Compressive strength of concrete at high temperatures: a reassessment”, Magazine of Concrete Research, 1992, V. 44, No. 161, pp. 291-309. [6] NISHIDA A., YAMAZAKI N., INOUE H., SCHNEIDER U.; DIEDERICHS U., “Study on the Properties of High-Strength Concrete with Short Polypropylene Fibers for Spalling Resistance”, Proc. of Int. Symp. “Concrete under Severe Conditions” – CONSEC 95 (K. Sakai, N. Banthia and O.E. Gjørv Eds.), V. 2, 1995, pp. 1141-1150. [7] ST. JOHN D.A., POOLE, A.B. and SIMS I.S, Concrete Petrography, John Wiley and Sons Editor, New York, U.S.A, pp. 308-316. [8] LARBI J.A., NIJLAND T.J., “Assessment of Fire-Damaged Concrete: Combining Metamorphic Petrology and Concrete Petrography”, Proc. of the 8th Euro-Seminar on Microscopy Applied to Building Materials, Athens, Greece, September 4-7, 2001, pp. 191198. [9] GUERRINI G.L., MICHELETTI V., ACITO M., GAMBAROVA P., “Correlation between Physical and Mechanical Properties of High Strength Concrete with Reference to High Temperatures”, 13th Congress CTE 2000, Pisa, V. 1, pp. 449-458 (in Italian). [10] GUERRINI G.L., MICHELETTI V., “Correlation between Microstructure and Mechanical Strength in High-Strength Concrete Submitted to High Temperatures”, Proc. of EUROMAT 2001, 7th European Conference on Advanced Materials and Processes, Rimini, Italy, June 1014, 2001. [11] MEDA A., GAMBAROVA P.G., BONOMI M., “High-Performance Concrete in Fire-Exposed Reinforced Concrete Structures”, ACI Structural J., V. 99, No. 3, 2002, pp. 277-287. [12] BOUGUERRA A.L., DE BARQUIN F., DHEILLY R.M., QUEDENEC M., “Effect of microstructure on the mechanical and thermal properties of lightweight concrete prepared from clay, cement and wood aggregates”, Cement Concrete Research, V.28, No.8, 1998, pp. 1179-1190.
93
[13] GUERRINI G.L., ROSATI G., “Residual Strength of White Cement Concrete Exposed to High Temperatures”, Proc. of 6th CANMET/ACI Int. Conf. On Durability of Concrete, Thessaloniki, (Greece), 1-7 June 2003, ed. V.M. Malhotra [14] CATTANEO S., ROSATI G., GUERRINI G.L., “Hybrid Polypropylene-Steel Fiber Reinforced Concrete at High Temperatures”, Proc. of RILEM Symposium “Advances in Concrete Through Science and Engineering”, Chicago U.S.A., March 22-24, 2004, 10 pp. [15] BIOLZI L., GUERRINI G.L., BERTOLINI L., “Cementitious Materials with Hybrid Fibers Exposed to High Temperatures”, 6th RILEM Symposium on Fibre-Reinforced Concretes (FRC) – BEFIB 2004, September 20-22, 2004 (Varenna, Italy), RILEM PRO 39, V. 1, pp. 637-648.
94
Mechanical Properties of HPC at High Temperature
Izabela HAGER Civil Engineer Cracow Univ. of Technology Cracow, Poland
Pierre PIMIENTA Materials Engineer CSTB Marne la Vallée, France
Summary This paper presents some recent results of an experimental research on the mechanical properties of High Performance Concrete at high temperature. In order to carry out this study, a new experimental device was developed, enabling the heating and the application of compressive and tensile loads in the “hot” state. The evolution of the compressive strength and elastic modulus with temperature was studied. Some results on the influence of water/cement ratio and test procedure (hot/residual tests) are presented. The evolution of the mechanical properties can be related to the presence of free water inside the material, especially in the range of temperatures up to 300°C. An important part of this study was dedicated to the study of transient thermal strains, both in compression and in tension. Keywords:
high-performance concrete (HPC), compressive strength, direct tensile strength, thermal strains, thermal strains under load (transient creep), hot tests.
1. Introduction The evolution of the mechanical properties of ordinary and high performance concretes (HPC) have been studied by several authors [1-4]. The present research was initiated in France in the frame of the National Project on HPC, BHP 2000 [5-7]. The aim of this project was to better understand the behavior of HPC subjected to high temperatures and to extend the application field of French codes to HPC. This research was then continued in the frame of the PhD of the first co-author [8]. The most common way to study the influence of elevated temperatures on the properties of concrete is to expose the material to high temperature, cool it down to room temperature and then carry out test, both in compression or in tension. This method yields the “post fire” or “post exposure to the high temperature” ( residual) properties of concrete. However, one must consider that the most appropriate procedure to test the mechanical properties at high temperature is to determine the properties of material at elevated temperatures (“hot” tests). In order to carry out this kind of observations, a special high temperature test equipment has been developed. This test device performs compressive tests, but can also be adapted to direct tensile tests in the “hot” state. Moreover the system device allows to measure the thermal strain of concrete during the heating stage under load (transient thermal strain) or without load (free thermal strain). This paper presents some results obtained within this research project, concerning the influence of water/cement ratio and test procedure (hot/residual tests) on the compressive strength and elasticity modulus. An important part of this study was dedicated to the study of transient thermal strains. Examples of results on transient thermal strain in compression are also presented, as well as some results on the phenomenon in tension.
95
2.
Experimental investigation
2.1
Test equipment
A prototype measurement system (Fig. 1) was set up at CSTB (Centre Scientifique et Technique du Bâtiment, France). It consists notably of a 600 °C maximum temperature furnace (a), where a cylindrical 104 mm × 300 mm specimen is placed, an extensometer enabling the measurement of deformations (b) and a testing machine with a maximum load of 5000 kN (c). The 100 kN tensile test machine is shown in the right part of the figure. The specimen is heated by 3 independentlycontrolled heating elements in order to minimize the thermal gradients. The 3 thermocouples devoted to the temperature control are placed on the surface of the specimen. The deformation is measured by an apparatus, made of two rings and 3 displacement transducers, located outside the oven and connected to the test specimen via thin rods. The extensometer system was calibrated using an aluminum specimen with well known thermal and mechanical properties.
a
b
c
Fig. 1 - Test equipment: compression (left) and tension (right). 2.2
Test procedures
Mechanical properties in the “hot” state were determined on the specimens heated at a constant heating rate of 1°C/min. After the test temperature was reached, it was maintained at a constant level for 2 hours at 120°C and 1 hour at 250°C, 400°C and 600°C. The 120°C temperature was mantained for a longer time due to its slower propagation caused by the higher specific heat of concrete at temperatures around 100°C. The strains were measured during the loading process up to failure. The load-increase rate was constant in all tests and equal to 0.6 MPa.s-1. The Young’s modulus of the concrete was determined from the displacements measured by the extensometer. Thermal strains and thermal strains under constant load were measured during transient heating at a constant heating rate of 1°C/min. For the samples heated under mechanical load, two load levels were studied. For compressive load, 20 and 40% of the compressive strength at 20 °C, for direct tensile load, 1 and 2 MPa, were applied during heating from 20 to 600°C. 2.3
Mix compositions and specimens
The experimental studies presented in this paper were carried out on 4 HPC mixes; these four mixes were all derived from the composition of a BHP 2000 100 MPa concrete called M100C. Aggregates
96
are Boulonnais limestone aggregate with an addition of quartz sand of the river Seine. Silica fume is added in excess of 10% of the cement mass. The water/cement ratio varies from 0.33 to 0.5%. The mix named M100C f = 0.9 is made with fibrillated Fibermesh fibers 19 mm long, in quantities of 0.9 kg/m3. Precise information on the studied mixes are given in [7-9]. The research was conducted on 104 mm × 300 mm cylindrical specimens. The tensile test specimens were 600 mm long. The higher size of the specimens for the tensile tests was used in order to fix the specimen between the testing machine platens. The specimens were removed from the moulds after 24 hours, stored in plastic bags for the subsequent 7 days and then placed in climatic chamber at T = 20°C, 50% RH prior to testing.
3.
Experimental results and discussion
3.1
Uniaxial compressive strength - Influence of the w/c ratio
In this paragraph the results of an investigation on the influence of the water/cement ratio on the “hot” compressive strength and modulus of elasticity are presented. Three concretes were cast on the basis of the composition of a M100C concrete by adding different quantities of water, respectively 124, 150 and 189 l/m3. The only difference was their w/c ratio: 0.33, 0.4 and 0.5 respectively. The plots in Fig. 2 (top) show the changes in compressive strength and relative compressive strength for the three concretes. The relative compressive strength of the 3 mixes does not exhibit significant differences except at 120°C. The evolution of strength with temperature can be divided in three phases. The compressive strength decreases during the first stage of heating, reaching a local minimum at a temperature of around 120°C: this first phase was related by different authors to the presence of water [3]. The more significant decrease observed in the case of w/c = 0.5 may be explained by its more important water content. During the second stage, between about 120 and 300°C, the strength is partially recovered. The strength increases below 250°C for w/c = 0.4 and 0.5 and 400°C for w/c = 0.3. This can be explained by the migration of water from the material. The lower water permeability of the w/c = 0.3 concrete can explain its delayed strength increase. Further heating causes a continuous, quasi-linear strength decrease. The elastic modulus decreases linearly with temperature (Fig. 3, bottom) and the relative decay seems to be independent of the water/cement ratio. No significant differences between those three concretes are observed. 3.2
Compression tests - “Hot” versus residual tests
“Hot” and residual tests were carried out on the same concrete specimens and in the same oven in order to study the influence of the test procedure. The only difference between the 2 tests was that, for the residual tests, the specimens were cooled in the oven prior to application of the load. Tests were carried out on a 100 MPa concrete containing 0.9 kg/m3 polypropylene fibers. Fig. 3 shows the changes in the relative compressive strength and the relative elastic modulus for both types of test. Hot tests lead to lower values of the relative compressive strength when T = 120 °C, which can be related to the influence of the hot water mentioned above. At 250 °C and beyond the residual relative strength becomes lower; this can be explained by the additional damage during the cooling phase. A similar behavior is observed when comparing the evolution of the different elastic moduli. 3.3
Thermal strains under compressive load
An important study was carried out on free thermal strains and thermal strains in compression [8, 10, 11]. The values of the thermal strains under load values are considered as the superposition of free thermal strains and transient thermal strains. Transient thermal strains is a unique feature of concrete heated under a mechanical load, and are largely more important than the strains due to basic creep and elastic deformation [4]. In this study the thermal strains and thermal strains under 20 and 40% of the ultimate compressive load were studied. The thermal strain of concretes appears to depend on the nature of the aggregates used: limestone or gravel (siliceous). On the opposite, the transient thermal strain appears to be independent on the nature of aggregates up to 300°C, temperature at which cracking develops. The absolute value of transient thermal strain, combination 97
of free thermal strain and transient thermal strain under load is lower. The actual practice, that generally does not take into account the transient thermal strain, is thus on the safe side. In this paper, some results on the transient thermal strain phenomena under compressive load obtained on HPC and HP cement paste are presented, as well as some results of the study on the phenomena in tension. fcT/fc20°C [%]
fc [MPa]
E/C=0.3 E/C=0.4 E/C=0.5
106.4
100
E/C=0.3 E/C=0.4 E/C=0.5
100
88.6 83.9
78.6
80
81.5
80
68.8 64.8
62.5
60
60 55.8
48.5
40
44.2
45.4
41.9
40 33.2 28.8
20
20
0
0 0
100
200
300
400
500
T [°C]
600
0
100
200
300
400
500
600
T [°C]
ET/E20°C[MPa] E [MPa]
40
100
E/C=0.3 E/C=0.4 E/C=0.5
51.9
50
39.6 32.1
30
31.1
28.8
24.0
24.7 21.0
20
E/C=0.3 E/C=0.4 E/C=0.5
80
39.4
60 22.0
40
18.9 11.1
12.5
10
20
7.8 6.7
0
0 0
100
200
300
400
600 T [°C]
500
0
100
200
300
400
500
600 T [°C]
Fig. 2 - Effect of the water cement ratio on compressive strength and relative compressive strength of concretes (top); effect on the modulus of elasticity and relative modulus of elasticity (bottom). ET/E20°C [%]
fcT/fc20°C[%]
hot
hot
100
100
residual
residual 80
80
60
60
40
40
20
20
0
0 0
200
400
600 T [°C]
0
200
400
600 T [°C]
Fig. 3 - Effect of temperature on the “hot tested” and residual values of compressive strength and modulus of elasticity of concrete. Plots of the free thermal strain and the thermal strain in compression are presented in Fig. 4a. The transient thermal strain values are obtained subtracting the free thermal strain from the thermal strain under load. Additionally, as was already mentioned by other authors [4], the transient thermal strain phenomenon does not appear during the cooling stage (Fig. 4a). Fig. 4b presents the thermal strains and thermal strains under load determined on high performance cement paste samples. It is worth noting that the transient thermal strain appears in the
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pure cement paste between 100 °C and 200°C. Strain values are as high as 6 mm/m: this behavior is largely dependent on the thermal story of the concrete, as already mentioned by Khoury et al. [4]. These observations lead us to distinguish two phases in the evolution of the concrete transient thermal strains: the first phase (from 20°C to almost 400°C) is attributed to the paste and is related to water content; the second phase, beyond 400°C, is related to the crack development in concrete. 15000
a) HPC concrete
10000
b) HP cement paste
4000 Thermal strain
Thermal strain
Strain [µm/m]
2000
Strain [µm/m]
5000 Thermal strain under load 20%
0 0
200
400
600
T[°C]
0 0
50
100
150
-2000
200
250
300 T[°C]
Thermal strain under load
-5000 -4000
-10000
Transitional thermal strains
-15000
Transient thermal strain
-6000
-20000
Fig. 4 - Thermal strain, thermal strains under compressive load of 20% fc, and transient thermal strain of: a) HPC concrete and b) HP cement paste.
3.4
Thermal strain under tensile load
10000
Thermal strains under 1 and 2 MPa tensile loads were measured on 4 samples. Fig. 5 shows plots of the thermal strain versus temperature. These diagrams are compared with the free thermal strain. We can observe that thermal strains in tension are superimposed on the free thermal strain curve. Transient thermal strain in tension appears then to be either non detectable or non existent. The first case (non detectable) could be related to the very weak load (1 and 2 MPa) that can be applied without exceeding the failure load.
Thermal strain l Thermal strain under load 1 MPa 1 MPa 2 MPa 2 MPa
Strain [µm/m]
8000
6000
4000
2000
0 0
200
400
600 T [°C]
Fig. 5 - Transient thermal strains under tensile load.
4.
Conclusions
The relative compressive strength decay of 3 concretes with different water/cement ratios does not exhibit significant differences except at 120 °C. At this temperature, higher water/cement ratio induces lower relative strength which could be explained by the more important water content. We propose to distinguish three phases in the evolution of the compressive strength with temperature: a decrease at a temperature about 100-150°C, an increase between about 120 and 300°C and a continuous, quasi-linear strength decrease above 300°C. Comparing hot and residual test leads to the conclusion that relative compressive strength at T = 120 °C is lower when considering hot tests. This can be related to the influence of the hot water mentioned above. At 250 °C and higher temperatures residual relative strength becomes lower. This can be explained by the additional damage during the cooling phase. A similar behavior is observed when comparing the modulus of elasticity evolution. Thermal strains and thermal strains under load were determined on HPC and cement paste specimens. We can observe that transient thermal strain appears in pure cement paste between 100 °C and 200°C. We propose to distinguish two phases in the evolution of the concrete transient thermal strains.
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Transient thermal strain under tensile load appears to be either non detectable or either non existent. First case could be related to the weak load than can be applied without exceeding the rupture load.
References [1]
SCHNEIDER U., “Behaviour of Concrete under Thermal Steady State and non-Steady State Conditions”, Fire and Materials, 1976, 1, pp. 103-115
[2]
DIEDERICHS U., JUMPPANEN U. M. ET PENTALLA V., “Behavior of High Strength Concrete at Elevated Temperatures”, Espoo 1989. Helsinki University of Technology, Department of structural Engineering, 1992, Report 92, p 72.
[3]
KHOURY G.A., “Compressive Strength of Concrete at High Temperatures: a Reassessment”, Magazine of Concrete Research, 1992, 44, n° 161, pp 291-309.
[4]
KHOURY G.A., GRAINGER B.N. and SULLIVAN G.P.E., “Transient Thermal Strain of Concrete: Literature Review, Conditions within Specimen and Behaviour of Individual Constituents”, Magazine of concrete research, 1985, Vol 37, No 132, pp 131-144.
[5]
PIMIENTA, P., “Propriétés des BHP à Haute Température – Etude Bibliographique”, Cahiers du CSTB, July-August 2001, n° 3352, Livraison 421.
[6]
PIMIENTA, P., “Evolution des Caractéristiques des BHP soumis à des Températures Élevées - Résistances en Compression et Modules d'Élasticité”, Cahiers du CSTB, July-August 2001, n° 3353, Livraison 421.
[7]
PIMIENTA P., and HAGER I., “Mechanical Behavior of HPC at High Temperature”, Proceedings of 6th International Symposium on Utilization of High Strength/High Performance Concrete. Leipzig, June 2002, pp 1291-1298.
[8]
GAWESKA HAGER I., “Propriétés Mécaniques des Bétons à Haute Performance à Haute Température – Évolution des Principales Propriétés Mécaniques”, Thèse de Doctorat, Ecole Nationale des Ponts et Chaussées, November 2004, 172 pp.
[9]
HAGER I., and PIMIENTA P. “Impact of the Polypropylene Fibers on the Mechanical Properties of HPC Concrete”, Proceedings of Sixth Rilem Symposium on Fibre Reinforced Concrete (FRC), BEFIB 2004, 20-22 September 2004, Varenna, Italy.
[10] HAGER I., PIMIENTA P. “Etude de la Déformation Thermique Transitoire des Bétons à Haute Performance (BHP)”, XXIIèmes Rencontres AUGC – Ville & Génie Civil, 3-4 June 2004, Marne la Vallée. [11] HAGER I., PIMIENTA P. “Thermal Strains of High Performance Concretes”, (in polish), Proceedings of II Conference DNI BETONU 2004, 11-13 October 2004, Wisáa, Poland.
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Measurement of Concrete Thermal Properties at High Temperature
Robert JANSSON MSc, Project Manager, Fire Resistance Swedish Nat. Testing and Res. Institute Fire Technology, Sweden
Summary A method for the determination of concrete thermal properties at high temperature is examined in this paper. The so-called TPS Method (Transient Plane Source) makes it possible to simultaneously evaluate the thermal conductivity, the thermal diffusivity and the specific heat from 30 to 1000 °C. The standard technique is briefly described, and some measurements carried out on selfcompacting concrete reinforced with polypropylene fibres are presented. The theoretical results based on the values of the thermal properties measured in the tests turn out to be in satisfactory agreement with the measurements concerning a full-scale fire test. Finally, a comparison is made between the results obtained with TPS and those obtained with MDSC (Modulated Differential Scanning Calorimetry). Keywords:
self-compacting concrete, thermal properties.
1.
Background
1.1
Introduction
The heat propagation in a material governs the chemical and structural degradation processes in a fire situation. Therefore the thermal properties of concrete are of fundamental interest when theoretical predictions of the behaviour in fire are done. In this short paper the use of a transient method for simultaneously determination of the thermal conductivity, thermal diffusivity and specific heat in self-compacting concrete is investigated. When using the Transient Plane Source (TPS) method a specimen in thermal equilibrium is exposed to a heat pulse and by using the recorded transient thermal response of the material and the geometrical data for the sensor a calculation of the thermal properties can be done.
1.2
Previous studies
Determination of the thermal properties of concrete at high temperature is not a new issue. As an example Ödeen and Nordström [1] performed measurements on concrete at temperatures from room temperature up to 1000 oC. The measurements at high temperature were performed with the Stålhane-Pyk method (thermal conductivity) and a Dynatech calorimeter (specific heat). The thermal conductivity measurements show the typical decay at high temperatures. When the material is cooling after an exposure at high temperature the thermal conductivity is approximately constant, see Fig. 1.
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Fig. 1 - The temperature dependent thermal conductivity for concrete with w/c = 0.7 (Ödeen and Nordström 1972). The cooling phase is included in the diagram. In the literature there exist several good compilations of data of the thermal properties for different qualities of concrete at high temperature [2,3,4]. One example, which shows the specific heat, is shown in Fig. 2.
Fig. 2 - Effect of temperature on measured specific heat of various concretes. Compilation made by Bažant and Kaplan [4]. (1) granite aggregate concrete (Ödeen [5]); (2) limestone aggregate concrete (Collet and Tavernier [6]); (3) lime stone aggregate concrete (Harmathy and Allen [7]); (4) siliceous aggregate concrete (Harmathy and Allen [7]); (5) limestone aggregate concrete (Hildebrand, et al. [8]); (6) siliceous aggregate concrete (Hildebrand, et al. [8]). The prescribed values in the Eurocode 2 part 1-2 [9] are shown in Fig. 3. The thermal conductivity is described by an upper and lower limit.
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Fig. 3 - The thermal conductivity (3a) and specific heat(3b) of concrete according to Eurocode 2 part 1-2 [9].
2.
Experimental procedure
2.1
Test method
The basic idea behind the TPS method is to apply a constant heating effect and measure the temperature response in the same sensor. When a measurement according to the TPS method is performed a flat round hot disc sensor is placed between two pieces of material, see Fig. 4. The sensor consists of a thin nickel foil spiral, 10 µm, which is sandwiched between two sheets of electrical insulation material. When the temperature is below 500 K the insulation material is Kapton with a thickness of 25 µm and in the 500 – 1000 K range Mica with the thickness of 60 µm is used. The reason for using Nickel as the conducting material in the sensor is because of its large temperature coefficient of resistivity over a big temperature range.
Fig. 4 - The test setup for a measurement according to the TPS method [11]. The hot disc sensor in Fig. 4 acts as a constant effect generator and a resistance thermometer at the same time. The time dependant resistance rise is recorded and converted with the temperature coefficient of resistivity for Nickel to a temperature response curve. When a constant electrical effect is applied the temperature in the censor rises and heat starts to flow to the tested material. The temperature rise in the sensor is then a direct response of the thermal properties of the tested material. Depending of the thermal properties a proper applied effect, size of sensor and measurement time must be chosen, i.e. it is an iterative process if the properties of the tested material are totally unknown. The effect selection is direct connected to the desired temperature rise in the test specimen. For metals a suitable temperature rise is < 1 oC and for insulation materials between approximately 1 and 5 oC. There is a characteristic time for every measurement when the thermal conductivity, thermal diffusivity and the specific heat can be determined from one
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measurement. This is when the heat profile in the test specimen can be approximated as a mix of the mathematical solutions from a semi-infinite slab and a point source. If the measurement time is to short only the thermal effusivity can be calculated because the mathematical solution approaches the semi-infinite slab case. If the measurement time on the other hand is to long the mathematic solution is more like an infinite solid heated by a constant point source and only the thermal conductivity can be calculated [11,12]. A more detailed mathematical description of the solution strategy used in the software Gustafsson [12] gives. When measurements are made with the TPS method the test specimen must have a uniform internal temperature distribution. A temperature drift recording that is the start-up for every measurement checks this. If the temperature recording show a systematic drift in any direction there is a possibility to compensate for that in the software but the accuracy of the measurement can be suffering and therefore it is not recommended. The measurements at high temperatures in this project have been performed inside a muffle furnace. All the measurements presented in this article are a result of at least three repeated measurements with the same experimental setup. This is done to assure that no time dependant processes in the material are going on, and to detect if any external random errors occur. 2.2
Tested material
One quality of self-compacting concrete with polypropylene fibres has been studied. This type of concrete does not require vibrating when it is cast in a mould. To the concrete recipe a small amount of polypropylene fibres were added with the purpose to avoid or reduce the possibility of spalling when the concrete is exposed to fire. The recipe for the concrete is shown in Table 1. All the thermal property measurements on concrete described in this article were done on dried material. Table 1 - Concrete mixture [13]. Dry materials (kg/m3) Cement Slite (CEM I) Limestone filler Limus 25 Fine gravel 0-8 Sätertorp Coarse gravel 8-16 Sätertorp Plasticizer* CemFlux Prefab Plasticizer (% of C+F) Fibres Fibrin 18µm Water/moisture (kg/m3) Water Dilution water Moisture in material w/c-ratio
380.76 119.24 899.96 721.90 5.73 1.15% 1.0 149.69 10.02 37.54 0.518
* Plasticizers are given as weight in diluted form, as delivered. The moisture is included in ”Moisture in material” in the table.
3.
Test results
The temperature sequence for the test on concrete was chosen to be 20, 90, 110, 200, 500, 600, 500, 200 and 20 oC. The decrease of the temperature from 600 to 20 oC was done to see if the thermal conductivity was to remain constant during cooling as reported in the literature [1]. At every temperature level the measurement was performed when the test sample had a uniform temperature distribution. In Fig. 5, the thermal conductivity from the measurements is presented and in Fig. 6 the thermal diffusivity is shown. As explained earlier the thermal conductivity, thermal diffusivity and the specific heat are determined simultaneously i.e. in the same measurement.
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2
Ȝ [ W/mK ]
1,6 1,2 0,8
TPS measurement
0,4 0 0
100
200
300
400
500
600
700
Temperature [ oC ]
Fig. 5 - The thermal conductivity for the tested concrete at different temperatures and place in the heating cycle. The heating cycle starts at the highest conductivity value at 20 oC.
Į [ mm2/s ]
1.2
0.8
0.4 TPS measurement 0 0
100
200
300
400
500
600
700
Temperature [ oC]
Fig. 6 - The thermal diffusivity for the tested concrete at different temperatures and place in the heating cycle. The heating cycle starts at the highest diffusivity value at 20 oC. 2
C [ KJ/kgK ]
1,6
1,2 TPS measurement 0,8
MDSC measurement (A) MDSC measurement (B)
0,4
0 0
100
200
300
400
500
600
700
o
Temperature [ C ]
Fig. 7 - The specific heat of the investigated concrete. The volumetric values from the TPS measurements are converted to the right unity with the temperature dependant density taken from the Eurocode 2 part 1-2 [9].
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To get some kind of accuracy check on the measurements done with the TPS equipment a supplementary test on the concrete was done with a MDSC (Modulated Differential Scanning Calorimeter) to determine the specific heat. In Fig. 7 the specific heat results from the TPS test and two scanning tests are shown.
4.
Discussion
Concrete is a mixture of aggregate and cement paste. The thermal conductivity in the aggregate is normally higher than in the paste so it is important to use a sensor of a suitable size to get a representative picture of the material. This was checked by MDSC (Modulated Differential Scanning Calorimeter) measurements on pulverized material. From this measurement a representative value of the specific heat can be achieved. The specific heat measurements done with the TPS agreed well with MDSC, see Fig. 7. A fire test on self-compacting concrete slabs made with the same recipe as the concrete tested with the TPS equipment was performed with an ISO 834 exposure. The dimensions of the specimen were 200 x 1200 x 1800 mm (thickness x width x length) [13]. Inside the specimen the temperature was recorded at the depths 10, 25, 50, 100 mm from the fire-exposed surface. The measured temperature at the depth 10 mm, Tm(10 mm), was then used as boundary condition in an onedimensional finite element calculation. The finite element code TASEF [14] was used for the calculation and the thermal properties from the TPS measurements were used as input. The thermal data from the TPS measurements on dried concrete shown in Fig. 5 and 7 were completed with data for the latent heat corresponding to the moisture content measurements that were done prior to the fire test on the concrete plates. The moisture content in the concrete was 4,8 % and both the amount of energy that was needed for heating the water up to 100 oC and latent heat was added in the simulation model. The effect of latent heat of evaporation was spread out between 100 and 150 oC.
700 Tm(10 mm) Tm(25 mm) 500
Tm(50 mm)
o
temperature [ C]
600
Tc(25 mm)
400
Tc(50 mm) 300 200 100 0 0
10
20
30
40
50
60
time [min]
Fig. 8 - Temperature curves from the measurement, Tm = temperature measurement, Tc = temperature calculation. The calculated temperature response, Tc, shown in Fig. 8 shows a good agreement with temperature measurements Tm. The only significant difference is in the 100 oC region which is probably caused by moisture movements or/and pressure dependant boiling points.
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5.
Conclusions
With the TPS (Transient Plane Source) method the thermal conductivity, thermal diffusivity and the specific heat can be determined at the same time. The thermal data at elevated temperatures from the TPS (Transient Plane Source) measurements on self-compacting concrete correspond well with data from specific heat measurements done with MDSC (Modulated Differential Scanning Calorimeter). A good correlation in a practical case has been shown between a finite difference calculation based on TPS data and temperature measurements on a full-scale fire test object.
References [1] [2] [3]
[4] [5] [6]
[7] [8]
[9]
ÖDEEN K., and NORDSTRÖM Å., Termiska egenskaper hos betong vid höga temperaturer Statens Provningsanstalt, Brandtekniska Laboratoriet, 1972:1. Properties of Materials at High Temperatures Concrete RILEM Committee 44-PHT June 1985, Edited by U. Schneider. FLYNN D.R., Response of High Performance Concrete to Fire Conditions: Review of Thermal Property Data and Measurement Techniques Metsys Report No. 98-01-101 December 1998, NIST. BAZANT Z.P., and KAPLAN M.F. Concrete at High Temperatures: Material Properties and Mathematical Models Longman (Addison-Wesley), London, 1996. ÖDEEN K., Fire Resistance of Prestressed Concrete Double T Units, National Swedish Institute of Material Testing, 1968. COLLET Y., and TAVERNIER E., Etude des properties du beton soumis a des temperatures elevees, Comportement du Materiaux Beton en Fonction de la Temperature, Groupe de Travail, Brussels, November 1976. HARMATHY T.Z., and ALLEN L.W., “Thermal properties of selected masonry unit concretes”, ACI Journal, 70(2), pp. 132-42, 1973. HILDEBRAND G., PEEKS M., SKOKAN A. and REIMANN M., Untersuchung der Wechselwirkung von Kernshmelze und Reaktorbeton Research Paper BMFT RS 154, May 1978, Erlangen. Eurocode 2: Design of concrete structures - Part 1-2: General rules - Structural fire design, prEN 1992-1-2, final draft, December 2003.
[10] Instruction Manual, Hot Disk Constants Analyser, Version 5. [11] GUSTAFSSON S.E. and LONG T., “Transient Plane Source (TPS) Technique for Measuring Thermal Properties of Building Materials”, Fire and Material, Vol. 19, 1995, pp. 43-49. [12] GUSTAFSSON S.E., “Transient Plane Source (TPS) Technique for Thermal Conductivity and Thermal Diffusivity Measurements of Solid Materials”, Rev. Sci. Instrum, 62(3),1991, pp 797804. [13] BOSTRÖM L, Innovative self-compacting concrete-Development of test methodology for determination of fore spalling, SP report 2004:06, Sweden 2004. [14] WICKSTRÖM U., TASEF User’s Manual, Swedish National Testing and Research Institute, Sweden 1989.
107
Experimental Investigation on Concrete Spalling in Fire Robert JANSSON MSc, Project Manager, Fire Resistance Swedish Nat. Testing and Res. Institute Fire Technology, Sweden
Lars BOSTRÖM PhD, Manager, Fire Resistance Swedish Nat. Testing and Res. Institute Fire Technology, Sweden
Summary Some results from two test series aimed to study the probability of spalling and the amount of spalling of different concrete mixes are presented in this paper. A self-compacting concrete mix, as well as ordinary concrete mixes for tunnel linings were investigated. The tests were carried out on large and small specimens, in order to identify a reliable, cost-effective small-scale test, suitable for the assessment of the probability of spalling, for any given concrete mix. To this end, relativelysmall concrete slabs (600 u 500 u 200 mm), having one face exposed to the fire and the other subjected to the loads, look like a promising tool to evaluate the spalling tendency. Keywords:
1.
fire resistance; spalling; self-compacting concrete; tunnel concrete; test methods.
Introduction
The increased use of denser concrete qualities like self-compacting concrete and high performance concrete requires a deeper understanding of the fire behaviour of these materials. Especially the rather complex phenomena fire spalling, which makes the elsewhere more easy foreseeable behaviour of concrete at high temperatures more uncertain. The aim of the studies [1] presented in this article was to develop a suitable small-scale test method to determine the probability of spalling for different concrete qualities and boundary conditions as well as a large-scale test for verification. The purpose of the small-scale test method is to get a cost effective technique to pinpoint critical cases. Of practical reasons the test method has to be a typical furnace method and the geometry of the small-scale specimens has to be designed in a way to be able to be scaled up and tested in more realistic sizes as a reference. Therefore the simplest possible shape was chosen, the flat plate i.e. a semi-infinite slab case. The fire-exposed surface of the small slab in this test setup is 450 x 360 mm2 and the loading of the specimen can be introduced by an external loading system. Inside the specimens thermocouples at different depths monitors the thermal response of the material and can be used as a rough indication of the spalling velocity. During the development of the small size method a medium size test method has been tried out. Medium size in this notation is a building element, full size a structure and small size a part of an element. The medium size tests were performed on specimens with a fire exposed surface area of 1500 x 1200 mm2. Two different ways of applying the load were examined, with pre stressing wires or by internal steel bars. Different fire scenarios were also tested. Along with the ISO 834 curve also a specially designed time-temperature curve for the City tunnel in Malmö was used [2], called X2000 in table 1. Recently we have also start to perform tests with the RWS-curve in the horizontal furnace (3 x 5 m). The amount of spalling was evaluated in two ways during this test series. By weighing or/and by actual measurement of the amount off scaled off material. Weighing is the simplest and fastest way of evaluating the amount of spalling but the accuracy will suffer if the specimens are big and by the fact that it is hard to make an accurate compensation of the water loss from the specimen. A geometrical measurement on the other hand are more time consuming but gives a more correct picture of the amount of spalling. The geometrical measurements were performed with a sliding calliper. A steel frame acted as a grid and reference for the measurements.
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2.
Experimental study
2.1
Materials
The materials used in the experimental studies were four different self-compacting concretes and six different tunnel concretes. The self-compacting concretes was manufactured with three different water-powder ratios, i.e. the ratio between the mass of water and the total mass of powder (cement plus filler), w/p=0.30, 0.40, 0.55. The concrete with w/p=0.40 was manufactured with and without an addition of 1 kg/m3 polypropylene fibres with the diameter 18 µm. The mean compressive strength of the manufactured concretes varied between 37 and 78 MPa when the fire test was performed and the moisture content was near 5%. The six tunnel concretes were all done with water cement ratio w/c = 0.38. Three qualities were used and each quality was manufactured with and without addition of 2 kg/m3 polypropylene fibres of the same kind as used in the self-compacting concretes. The difference between the three concrete qualities was the addition of fillers. Specimen A and B were without filler, C and D contained 25 kg/m3 silica and specimen E and F were manufactured with 100 kg/m3 limestone filler. The compressive strengths of the concretes were from 88 to 107 MPa and the moisture content from 3.7 to 4.9 %. 2.2
Test results
Tables 1-3 show the obtained test results. It should be noted that the values given for weight loss have been fitted so the specimens without any visible spalling reached zero weight loss. This was done to make a rough estimation and compensation of the loss of water in the specimens. The tables show the initial stress levels applied on the specimens during testing. Table 1 - Test results obtained with large slabs. Code
LS3001 LS4001 LS4011 LS5501 LB4001 LB4011
A1 A2 B1 B2 C1 C2 D1 D2 E1 E2 F1 F2
Max Charact Weight Mean Stress Fire level curve spalling spalling spalling loss (%) (mm) (mm) (mm) (MPa) (kg/m3) Self-compacting concrete - Slabs 1800 x 1200 x 200 mm3 0.30 0 Pre-stress, comp 8.8 Std 45 65 57 15.8 0.40 0 Pre-stress, comp 8.8 Std 45 67 56 18.7 0.40 1 Pre-stress, comp 8.8 Std 0 0 0 0.0 0.55 0 Pre-stress, comp 8.8 Std 48 68 62 15.3 Self-compacting concrete - Beams 3600 x 600 x 200 mm3 0.40 0 External 7.7 Std 8 40 21 3.1 bending 0.40 1 External 7.7 Std 0 0 0 0.0 bending Tunnel concrete without filler - Slabs 1800 x 1200 x 400 mm3 0.38 0 Pre-stress, comp 2.1 X2000 162 314 273 21.8 0.38 0 Pre-stress, comp 2.1 X2000 127 227 213 16.9 0.38 2 Pre-stress, comp 2.1 X2000 23 37 35 4.0 0.38 2 Pre-stress, comp 2.1 X2000 8 38 28 1.8 Tunnel concrete with silica - Slabs 1800 x 1200 x 400 mm3 0.40 0 Pre-stress, comp 2.1 X2000 56 80 85 8.3 0.40 0 Pre-stress, comp 2.1 X2000 61 76 78 9.7 0.40 2 Pre-stress, comp 2.1 X2000 0 32 3 0.6 0.40 2 Pre-stress, comp 2.1 X2000 0 7 2 0.0 Tunnel concrete with limestone filler - Slabs 1800 x 1200 x 400 mm3 0.31 0 Pre-stress, comp 2.1 X2000 182 359 306 23.9 0.31 0 Pre-stress, comp 2.1 X2000 84 130 116 12.5 0.32 2 Pre-stress, comp 2.1 X2000 40 67 56 6.7 0.32 2 Pre-stress, comp 2.1 X2000 33 57 54 5.0 w/p
Fibres
Stress type
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Table 2 - Test results obtained with small slabs. Code
SS3001 SS3002 SS3003 SS3004 SS4001 SS4002 SS4003 SS4004 SS4011 SS4012 SS4013 SS4014 SS5501 SS5502 SS5503 SS5504 A23 B23 C23 D22 D23 E22 E23 F22 F23
Charact Max Mean Stress Fire level curve spalling spalling spalling (mm) (mm) (mm) (MPa) (kg/m3) Self-compacting concrete - Slabs 600 x 500 x 200 mm3 0.30 0 Non 0 Std 37 51 50 0.30 0 Non 0 Std 31 52 48 0.30 0 External comp 2.5 Std 69 94 105 0.30 0 External comp 2.5 Std 102 175 186 0.40 0 Non 0 Std 29 45 49 0.40 0 Non 0 Std 26 36 38 0.40 0 External comp 2.5 Std 93 167 170 0.40 0 External comp 2.5 Std 111 180 193 0.40 1 Non 0 Std 0 0 0 0.40 1 Non 0 Std 0 0 0 0.40 1 External comp 2.5 Std 0 0 0 0.40 1 External comp 2.5 Std 0 0 0 0.55 0 Non 0 Std 15 30 30 0.55 0 Non 0 Std 20 34 34 0.55 0 External comp 2.5 Std 76 125 132 0.55 0 External comp 2.5 Std 57 113 117 Tunnel concrete without filler - Slabs 400 x 400 x 100 mm3 0.38 0 External comp 2.5 Std 18 35 27 0.38 2 External comp 2.5 Std 0 0 0 Tunnel concrete with silica - Slabs 400 x 400 x 100 mm3 0.40 0 External comp 2.5 Std 13 23 19 0.40 2 External comp 2.5 Std 0 0 0 0.40 2 External comp 2.5 Std 0 0 0 Tunnel concrete with limestone filler - Slabs 400 x 400 x 100 mm3 0.31 0 External comp 2.5 Std 29 48 44 0.31 0 External comp 2.5 Std 19 32 29 0.32 2 External comp 2.5 Std 0 0 0 0.32 2 External comp 2.5 Std 0 0 0 w/p
Fibres
Stress type
Weight loss (%) 10.6 9.5 19.0 32.1 9.1 7.9 27.5 32.5 0.1 0.1 0.0 0.1 4.7 5.2 26.9 16.6 12.5 0.2 9.4 2.3 0.3 18.9 14.4 0.6 0.0
Table 3 - Test results obtained with long cylinders. Code
w/p
LC3001 LC3002 LC3003 LC3004 LC4001 LC4002 LC4003 LC4004 LC4011 LC4012 LC4013 LC4014 LC5501 LC5502 LC5503 LC5504
0.30 0.30 0.30 0.30 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.55 0.55 0.55 0.55
Fibres (kg/m3) 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0
Stress type Non Non External comp External comp Non Non External comp External comp Non Non External comp External comp Non Non External comp External comp
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Stress level (MPa) 0 0 5.3 5.3 0 0 5.3 5.3 0 0 5.3 5.3 0 0 5.3 5.3
Fire curve Std Std Std Std Std Std Std Std Std Std Std Std Std Std Std Std
Weight loss (%) 1.6 2.2 17.8 19.4 2.1 4.8 23.4 21.4 1.6 2.0 0.0 0.3 1.6 4.0 19.3 14.7
When comparing the spalling between large and small slabs of tunnel concrete the weight loss was in most cases comparable. Although, the spalling depth was much smaller for the small slabs compared with the large slabs. This may also be due to boundary effects. The thickness of the small slabs was only 100 mm compared to the 400 mm thickness of the large slabs. Hence, it is more easy for the water/vapour to escape the small slabs which decreases the probability and amount of spalling. When comparing the amount of spalling of the small and large slabs of self-compacting concrete, the small specimens spalled much more. This was not expected since the large slabs had a stress level three times higher than that of the small slabs. Furthermore the amount of spalling of the large slabs did not differ between the different concrete qualities (expect the concrete with polypropylene fibres). An explanation is that the loading of the large slabs was done through prestressed wires placed relatively close to the fire exposed surface. Due to spalling the wires were heated to high temperatures after a short time and the compressive stress in the specimens were lost. After the compressive stress was lost the spalling terminated. Thus there were no difference in the amount of spalling between the different concrete recipes, and the amount of spalling of the large slabs was lower than the one for the small slabs.
Fig. 1 - Large slab after test (A1). Surface area 1800 x 1200 mm2.
Fig. 2 - Beam loaded in bending after (LB4001). Surface area 3600 x 600 mm2.
Fig. 3 - Cylinders after test (LC 3001-3004). Length 450 mm, diameter 150 mm.
3.
test
Fig. 4 - Small slab after test (SS3004). Surface area 600 x 500 mm2.
Conclusions
All concrete qualities included in the tests without protection in the form of polypropylene fibres spalled severely. The moisture content in the tested concretes was relatively high, but not higher than can be expected in many tunnel linings. According to Holt [3] tests have been carried out in Netherlands showing average moisture content of the concrete 10 years after construction at approximately 6-7 %. By using fibres of polypropylene the amount of spalling can be reduced.
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The loading is important for the probability as well as the amount of spalling. The probability for spalling is much greater if the structure is compressed. The amount of spalling is best measured as the depth of the spalling. Since it is more difficult to measure the spalling depth on a circular specimen, it is preferable to use specimens with a flat surface. An alternative method is to measure the spalling by the weight loss. The weight loss is, however, not recommended since it is difficult to compensate the measured weights for the loss of water during the test. Tests on externally loaded, one-sided fire exposed, slabs with the dimension 600 x 500 x 200 mm3 looks like a promising way of perform small-scale tests in orienting purpose. But some verification test in bigger scale may still be necessary.
References [1] [2] [3]
BOSTRÖM L., “Innovative Self-Compacting Concrete - Development of Test Methodology for Determination of Fire Spalling”, SP Report 2004:06, Sweden, 2004, 224 pp. INGASON H., “Time-Temperature Curves for X2000 and the Öresund Trains”, Report P003814, Borås, 2000 (in Swedish). HOLT I.R., “Is your Tunnel Protected against Fire?”, International Fire Protection, No. 16, November 2003.
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Fire Tests on Fibre-Modified Concrete
Sven J. SEIRER Assistant Head of Research & Development Hagerbach Test Gallery Ltd. Sargans, Switzerland
Summary Fires in tunnel installations often have serious consequences for both the tunnel users and the structure itself [1]. Therefore, increased attention needs to be paid to structural safety in fire conditions. The Hagerbach Test Gallery (VSH) has a long and well-known tradition in carrying out fire tests on both materials and structures [2,3]. Recently, extensive fire tests have been performed on behalf of Alp Transit Gotthard AG, in order to verify the effectiveness of various PP fibres to be used as a constructional fire-protection precaution. Two initial mixtures containing various aggregates and different cements were prepared; these mixtures had five different types of PP fibres. Three test prisms for each fibre type were cast: two for the fire tests and one for further laboratory investigations. Four small specimens at a time were cast into a single large slab, making it possible to test four different mixtures in each fire test. Keywords:
1.
explosive spalling, fireload, fire protection, fire-resistant concrete, fire tests, furnace (for fire tests), polypropylene fibres, safety in tunnels, temperature-time curves.
Introduction
Fire-protection precautions in constructions are being implemented in the Gotthard Base Tunnel (GBT) to deal with the case of a fire involving passenger and freight trains. In February 2004, Hagerbach Test Gallery Ltd was asked to carry out the first phase of several fire tests in order to verify the effectiveness of various PP fibres to be used as a constructional fire-precaution. The fire tests were carried out in March and April 2004. The aim of the tests was to answer as many questions as possible regarding the addition of PP fibres to cast-in-situ concrete mixtures. One point of special interest was the influence of the PP fibres on explosive spalling; other aims were to verify the temperature calculations for the sealing system and to answer questions about the workability of fibre-modified concrete.
2.
Description of the tests
2.1
Prisms
After the preparation of the concrete, the fresh concrete properties were checked, and two hours later the test prisms, measuring 600 x 600 x 300 mm, were cast. In these two hours the concrete was kept moving inside a drum mixer. Two types of excavated materials were used for the aggregates. For all mixtures, the fibre content was 2 kg/m3 (roughly vf = 0.2% by volume). With a mobile concrete pump (POMPUNO 606-L), the concrete was pumped at a distance of 50 m into the wooden formwork. For each mix, three prisms were cast, two for the fire tests and one for further investigations in the laboratory. The prisms were stored at 14 °C, 85% R.H.
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Fig. 1 - Casting of three prisms for each mix design.
Table 1 - Mix-design of the reference mixtures (no fibres).
Mix 1 Mix 2
2.2
cement type [kg/m3] CEM I 42.5 N 375 CEM I 52.5 R 410
aggregates 0/22 0/22
plast. admixture [%] 1.2 1
w/c 0.48 0.52
Specimens
Four small specimens at a time were cast together to create a single slab measuring 1800 x 1600 x 400 mm, since this is the normal size of the specimens to be tested in the furnace of Hagerbach Test Gallery. On the back side of each specimen a thermocouple was installed. By adequately sealing the sides of the slab, the real situation in the tunnel could be simulated. The test slabs were cast on February 27th and March 3rd, 2004; then they were stored in the same conditions already mentioned for the prisms.
Fig. 2 - Assembling of the test slabs – Each slab consists of four small specimens.
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2.3
Fire tests
The furnace used for the fire tests at the Hagerbach Test Gallery consists of a two-layer wall structure with a fire-resistant inner lining, provided with an oil burner. The size of the fire chamber is about 1100 x 1100 x 1100 mm; therefore the exposed surface during each test is 1100 x 1100 mm. The temperature-time curve was specified by the customer. During the entire test, the temperature in the concrete was recorded by means of embedded thermo-elements (type “K”).
test slab
110 cm
110 cm
burner
fire resistant inner lining concrete elements
Fig. 3 - The furnace of the Hagerbach Test Gallery.
3.
Temperature curve
1200
1200
1000
1000
Temperature [°C]
Temperature [°C]
The temperature in the furnace was measured in the centroid of the slab, at 100 mm from the exposed surface. The shape of the curve was given by the customer and consisted of two phases: Phase 1: from 0 to 240 minutes - the furnace is on; Phase 2: from 240 to 480 minutes - the furnace is off.
800 600 400 200
phase 2: colling-down period
800 600 400 phase 1: furnace "on"
200 0
0 0
60
120
180
240
0
60
120
180
240
300
360
420
480
Time [min]
Time [min]
Fig. 4 - Left side: theoretical temperature-time curve as specified by the customer; right side: temperature diagram as measured during the tests.
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4.
PP Fibres
The different types of PP fibres were delivered by the manufacturer and were used in accordance with the technical specifications. The fibres have different length (6 to 19 mm), diameter (16 to 45 Pm), and shape (one was tubular).
Fig. 5 - Four of the five types of PP fibres used in this study.
5. Tests Extensive laboratory tests were carried out beside the fire tests. Before and after the fire tests, drilled cores were taken from the prisms in order to evaluate the compressive strength. Whenever explosive spalling occurred, the volume of the concrete fragments was accurately measured, and the permeability of all prisms was evaluated. All the drilled cores were visually examined to assess the effects of the temperature. 70.0 before fire test
63.7
after fire test_1
60.4
60.0
57.3
50.4 45.9
45.1
[N/mm2]
51.2
50.4
50.0 41.5
after fire test_2
54.3
54.2 51.2
47.2 44.8
43.9
41.8
40.7
40.5
40.3 38.0 38.6
40.0
37.2 35.6
35.3
30.0
20.0
10.0
0.0 A1
A2
A3
B1
B2
B3
B4
Fig. 6 - Compressive strength before and after the fire tests.
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B5
6.
Results
The tests described in this paper are preliminary tests (1st series) aimed at a first classification of the materials, but not sufficient to formulate final conclusions. The results are as follows: All the mixtures were processed without any problems, with a fibre content of 2 kg/m3; The compressive-strength reduction after the fire tests was close to 20 - 30 %; In the fibre-modified mixtures, the initial value of the compressive strength was roughly 20 % lower than for the "zero mixtures" (plain concrete, reference mixtures); The visually-assessed limit of fire effects was between 40 and 70 mm from the heated surface. However, the term "damage limit" can hardly be used here, since neither the temperature nor the strength were measured in the damaged zone; The various fibre types were not equally effective in improving concrete fire resistance, with respect to the reference concretes, and one type was totally ineffective.; The fibrous reinforcement showed a positive influence in limiting the progression of the explosive spalling; No differences were observed between mix 1 (CEM I 42.5 N) and mix 2 (CEM I 52.5 R).
7. Outlook Over the last few years several severe fires in tunnels have occurred, causing extensive losses in terms of human lives and severe damages to the infrastructures. The tests described in this paper are a first step to develop a reliable fire resistant-concrete for the Gotthard Base Tunnel. In order to reproduce the actual tunnel conditions as closely as possible, the future tests will include also the loads acting on selected structural members (2nd series of tests), and the temperature will be monitored in a much greater number of points.
References [1] [2] [3]
WETZIG V., “Destruction Mechanism of Concrete in Event of Fire and Protective Systems”, Tunnel 7/2000, Official Journal of the STUVA, Cologne, 2000. AMBERG F., and WETZIG V., “The Fire Resistance of Various Types of Shotcrete”, Spritzbetontechnologie / Concrete Technology, Alpbach, Austria, January 2002. SEIRER S., and WETZIG V., “Sequence of Fire Tests for the Ventilation Control Center of the Reppisch Valley” (Zürich Western Bypass), Hagerbach Test Gallery Ltd., 2003.
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Constitutive Aspects of High-Temperature Material Models Kaspar WILLAM Professor CEAE Univ. Colorado at Boulder Boulder – Co, USA
Holger D. BASCHE Professor CEAE Univ. Colorado at Boulder Boulder – Co, USA
Yunping XI Professor CEAE Univ. Colorado at Boulder Boulder – Co, USA
Summary In this article we examine the performance of total (hyper) and incremental (hypo) material models to account for high temperature effects under transient conditions. Specifically we focus on thermal effects on the elastic stiffness and strength properties within the framework of thermo – hyper - and -hypo-elasticity. For definiteness we consider a thermal cycle when an axial member is heated up to 1220°C and cooled back to room temperature with and without end restraints. In the subsequent discussion the highly idealized temperature dependence of reinforcing steel in the elementary model problem is extended to realistic properties of concrete materials subjected to heating up to T=800°C. In the final part of the paper the uniaxial constitutive relations are generalized to triaxial conditions in order to study coupling effects between the thermal and mechanical properties when we start from Gibbs potential to develop thermo-mechanical constitutive relations. Expansion of the Gibbs free energy potential exhibits surprising volumetric-deviatoric interaction effects when constitutive nonlinearities are considered in stress, temperature, and relative humidity. Keywords: temperature effects, stiffness; strength, thermal expansion, cyclic temperature history of fire test, thermo-hyper-elasticity, thermo-hypo-elasticity, continuum thermodynamics.
1. Introduction Traditionally, thermal sensitivities of stiffness, strength, and the coefficient of thermal expansion are determined from 'isothermal' laboratory experiments under constant temperature and stress conditions. Thermal and mechanical transients raise a number of issues which are central to the formulation of consistent constitutive models. For an appreciation of these questions we explore the uniaxial response of a restrained and an unrestrained test article which are subjected to a severe thermal cycle resembling a fire scenario in analogy to the tests reported in [1] and some of the damage simulations [2,3].
2.
Constitutive setting
There are two points of departure to formulate thermo-elastic constitutive relations. One is referred to as the total format of thermo-hyper-elasticity, while the other is the incremental format of thermo-hypo-elasticity. The fundamental difference between the two formulations is apparent if we compare the additive decomposition of total strain into instantaneous elastic and thermal components. For the sake of illustration we consider uniaxial conditions, where the total format reads as follows: (a) Hyper-elastic Thermal Stress: (1) Differentiation leads to the rate form to be used for transient fire analysis within the framework of thermo-hyper-elasticity:
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(2) In contrast to the rate form in Eq. (2) the incremental format of thermo-hypo-elasticity starts from the decomposition of the strain rate into incremental elastic and thermal components as follows (b) Hypo-elastic Thermal Stress: (3) Note that the last two terms on the rhs of Eq.(2) are missing in Eq.(3) which account for the change of the elastic modulus and the thermal expansion. In small excursion thermal stress analysis the difference between the two formulations can be neglected as long as the temperature sensitivity is sufficiently small. However in large excursion transient fire analysis the temperature dependence may lead to very large differences.
3. Uniaxial Model Problem To illustrate the underlying issues let us consider the response of two thought experiments when the axial member in Fig. 1 is subjected to the extreme thermal heating-cooling cycle shown in Fig. 2. The ensuing 'relaxation' and 'creep' response histories with and without end restraints exhibit a number of features which are puzzling at first, and which deserve scrutiny. For definiteness let us consider the temperature history of the model fire in Fig. 2. During heating the temperature increases from room temperature 20°C to 1220°C within 300 s and decreases back to room temperature after a hold time of 1600 s. For the sake of argument let us assume a highly idealized material behavior of steel exhibiting a linear increase of the coefficient of thermal expansion from D=110-5 K-1 at room temperature to D=510-5 K-1 at 1220°C, and a linear decrease of the elastic stiffness from E=200 GPa at room temperature to zero stiffness at 1220°C as shown in Fig. 3a,b.
Fig. 1 - Axial force member.
Fig. 2 - Temperature history.
a) Coeff. of thermal expansion
b) Modulus of elasticity
Fig. 3 - Highly idealized temperature-dependent properties of steel.
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The resulting hyper- and hypo-thermo-elastic response histories exhibit the curious behavior illustrated in Fig. 4a when the axial thermal stress is considered. In case of hyper-elastic behavior, the minimum value of thermal stress can be obtained from eq. (2) considering that the change of stress with respect to the temperature must vanish. Letting Hx=0 we obtain the condition for thermal stress reversal in terms of the zero time derivative, (4) Note that the compressive axial thermal stress reaches a minimum value when the temperature is equal to 778.25°C,
Subsequent heating leads to a full reversal of thermal stress down to zero when the elastic stiffness diminishes to zero at the assumed melting temperature of 1220°C. In the cooling phase we note a similar reversal of the initial thermal expansion followed by subsequent shrinkage. This puzzling behavior is the hallmark of thermo-hyper-elasticity which exhibits path-independence and full reversibility under the thermal cycle. In contrast, the thermo-hypo-elastic format does not exhibit this reversal, in fact the incremental format yields a residual thermal stress at melting when E(T=1220)=0.
Fig. 4a: thermo-elastic Vx.
Fig. 4b: strains in heating phase.
The strain response histories shown in Fig. 4b also exhibit a very significant difference between hyper- and hypo-elastic behavior for the unrestrained 'creep'-test during heating under constant stress of Vx=-120 MPa. In contrast to the usual thermal expansion of the hypo-type response behavior, the hyper-type response shows a full reversal of axial deformation from thermal swelling in the initial phase to full contraction in the final high temperature phase when the modulus of elasticity approaches zero. In contrast to the thermo-elastic stress histories, the plastic response of the thermo-hyperelastoplastic model exhibits totally different behavior which is shown in Fig. 5a, 5b, and 5c. In this case the plastic yield strength controls entirely the stress history which was assumed to degrade linearly from Vy=240 MPa at room temperature to zero strength at 1220°C. In this case the concomitant thermal stresses are delimited by the yield condition which is rapidly reached during the heating phase at t=23 s with Vy(T)=-221.6 MPa. This response is followed by a linear reduction of stress to the level of zero strength when the temperature reaches 1220°C. The path-dependence and irreversibility is clearly apparent during the cooling cycle when
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a) pressure history
b)Vx –history
c) Plastic strain Hp(t)
Fig. 5 : Results for temperature-dependent yield strength Vy=Vy(T). thermal shrinkage dominates the response leading to a residual axial stress state in tension corresponding to the level of the yield strength Vy=240 MPa at room temperature. We observe that the uniaxial stress response is governed by the temperature dependence of the yield strength irrespective of the thermo-elastic format and the coefficient of thermal expansion. Although this study was carried out incrementally with the aid of 3-d finite elements, simple 1-d elastoplastic analysis results in the following yield constraint for the axial stress history, (5) Fig. 5 illustrates thermoplastic response histories of pressure, axial stress and plastic strain for the entire heating-cooling cycle. In other terms, the thermal softening of strength during heating reduces the thermal stress history to zero irrespective of hyper- or hypo-elastic stiffness models being used.
4.
Heating of Concrete under constant strain and constant stress
In this section, the model problem above for steel is extended to concrete with realistic material parameters. Recently, the temperature variation of the modulus of elasticity is specified in eq. (6) for concrete under sustained load during heating which is illustrated in Fig. 6b. (6)
4 describes the dimensionless temperature with T0=20°C as room temperature. (7) The free thermal strain follows a logarithmic function until 4=6 and remains constant for temperatures 4>6. The corresponding coefficient of thermal expansion D is described by eq.(8) for 4d6 (8) The formulation of D manifests the principal difference between the total and the incremental format: While for the total format D needs to be constant as illustrated in Fig. 6a for temperatures 4>6 (to match experimental results showing a temperature-independent free thermal strain), the thermal coefficient must be zero for the incremental hypo-type formulation.
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a) Coeff. of thermal expansion
b) Modulus of elasticity
Fig. 6:Temperature-dependent properties of concrete. Load Induced Thermal Strain (LITS) [5] describes a transitional thermal strain component which only occurs under heating and sustained compressive stresses in concrete. An analytical model for the uniaxial thermo-mechanical strain was presented in [4] which describes load induced thermal strain by an expression which is proportional to the normalized value of axial compression, and which grows parabolically with increasing temperature. (9) A,B, and C are dimensionless constants which are: A=0.0005, B=0.00125, and C=0.0085, [5], and Young's modulus is E0=20000 MPa.
a) strain-components
b) hypo- vs. hyper-elastic formulation
Fig. 7: Thermal strains under sustained constant load with LITS during heating phase. The large differences of hypo-and hyper-elastic results shown in Fig. 7a, 7b are mainly due to the great increase of the coefficient of thermal expansion with temperature which is about 600% higher than its value at room temperature. Hence, the hyper- term involving the derivative of T dD is of the same order of magnitude as the thermal strain term D dT . Note, due to the negative value of stress induced thermal strains, the total strains including LITS show a reversal from swelling to shrinkage strains at high temperatures. The decomposition of thermal stresses for the ‘relaxation’-test in Fig. 8a shows two compressive terms and one tensile term. The tensile stresses result from the degradation of the modulus of elasticity while the compressive terms originate from the change of temperature and the coefficient of thermal expansion. Again, the latter term has a great influence leading to the large difference between the hypo- and hyper-elastic formulations. Note, the effects of LITS were not included in this study. Consideration of load induced thermal strains would lead to a drastic reduction of compressive stresses.
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a) stress components
b) hypo- vs. hyper-elastic formulation
Fig. 8: Thermal stresses in ‘relaxation’ test under constant total strain during heating phase (without LITS).
5.
Coupling of Hyper-Thermal-Elastic Constitutive Model
Let us now consider some of the fundamentals of temperature dependent constitutive relations with a triaxial rather than uniaxial setting. To this end we focus on the results of representation theorems for isotropic hyper-elastic solids subjected to mild nonlinearities due to mechanical, thermal and excursions of the relative humidity from an unstressed and undeformed reference state. For the sake of argument we confine our attention to load regimes in closed systems in which phase transformations and mass transfer can be neglected from the discussion. Starting point is the Gibbs potential and its expansion into an isotropic scalar function of the stress, absolute temperature and relative humidity, (10) Considering this three field format, the rate of change of the potential leads to, (11) where the partial derivatives yield the expressions for the strain tensor, the entropy, and the thermodynamic force conjugate to relative humidity, (12) Here the subscripts indicate that e.g. the strain is evaluated at constant temperature and humidity and so on. Differentiating the strain-temperature-humidity relationship leads to the tangential compliance relation which extends the constitutive relationship to transient stress, temperature, and humidity conditions. (13) Starting from a complete quadratic expansion of the primal variables V, T, h, we recover the traditional format of the strain-stress-temperature-humidity relation, (14) Here 1 is the second order unit tensor, with I1=1:V denoting the first invariant of stress, and s is the deviatoric stress tensor with J1=1:s=0. K and G are the elastic bulk and shear moduli while D and E designate the linear coefficients of thermal expansion and shrinkage. The corresponding 126
tangential relationship results in the well-known expression, (15) Here I designates the symmetric fourth order unit tensor and the symbol
signifies the dyadic product of two second order tensors. In this case of linear isotropic behavior only four material moduli fully characterize the triaxial response. Note, there is no interaction between stress induced deformations and the environmental temperature and hygral strains which are purely volumetric in this case. Let us now extend the linear strain-stress-temperature-humidity relationship into the nonlinear regime. Neglecting arguments of convexity of the underlying free energy function let us expand the Gibbs potential into a complete cubic polynomial in the primal variables V, T, h, whereby the stress is represented in terms of the three trace invariants, (16) Considering all possible combinations of monomials I1,J2,J3,T,T2,T3 and h,h2,h3 we start with 25 terms in extension of the four material moduli in the linear constitutive format above. The gradient of the Gibbs potential with regard to stress renders the strain expression in terms of three irreducible tensors, (17) and the conjugate scalar-valued response functions, (18) (19) We recognize the interaction between the thermal and hygral terms in the volumetric G1 as well as in the deviatoric response functions G2 and G3. In fact, it is the effect of the cubic terms in the Gibbs potential which introduces extensive coupling between the volumetric and deviatoric components in the mechanical as well as in the thermal and hygral components. These interaction effects are more visible if we consider the tangential relationship, (20) The elastic compliance tensor has the following constitutive structure, (21) whereby the last term involves the symmetrized format of the dyadic product along the line of the unit fourth order tensor. The extension of the bulk compliance involves, (22) and the shear compliance (23)
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In the nonlinear case the thermal expansion exhibits volumetric-deviatoric coupling between the mechanical, thermal, and hygral components, (24) In analogy the hygral shrinkage tensor exhibits volumetric-deviatoric coupling between the mechanical, thermal, and hygral components, (25) Note, that the two last expressions define the tensors of thermal expansion and hygral shrinkage both of which exhibit coupling through their dependence on stress, temperature and humidity. In fact, we note that the two second order tensors exhibit both volumetric as well as deviatoric components through their dependence of the state of stress. It is this stress dependence which has been at the heart of load induced thermal strains or transitional thermal strains as they are also called in the concrete literature [5]. They introduce a very pronounced strain reversal from expansion to contraction under the first cycle of heating as shown in the concrete creep example in Section 4. For illustration of the different levels of coupling let us assume there is no volumetricdeviatoric interaction. In this case the influence of the third invariant must vanish, i.e. a6 = 0, and also a5 = 0 must hold in order to decouple the shear from volumetric effects. Consequently, the constitutive model looks quite familiar and has essentially the same structure as the linear isotropic format in eq. (15), except for the hygral and thermal effect in the bulk and shear moduli, and the stress induced terms in the tensors of thermal expansion and the hygral shrinkage. (26) The expression of the bulk compliance reduces to, (27) and the shear compliance simplifies to, (28) Note, if we were to insist that the tensors of thermal expansion and hygral shrinkage remain purely spherical, then b6 = 0 and c6= 0 must also hold. In this case the level of hygro-thermomechanical coupling would reduce to (29) which still exhibits stress induced thermal strains and (30) strains. However at the same time this simplification would remove altogether the effect of temperature and moisture from the shear modulus in eq.(28).
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6.
Conclusions
The brief exposition showed the subtle effects of temperature dependent material properties when transient fire cycles were considered during heating and cooling. For definiteness the axial stress and strain histories where explored for two limiting cases: (a) unconstrained ‘creep test’ with and without pre-loading, and (b) constrained ‘relaxation’ test of varying thermal stresses during heating and cooling. Section 3 did illustrate the full reversal of thermal stresses back to zero level at melting temperature when a hyper-elastic constitutive format was used as opposed to a hypo-elastic one. Further, the temperature dependence of the plastic yield condition did delimit the magnitude of the thermal stresses to the value of temperature dependent yield capacity irrespective of the elastic response. These observations lead to the conclusion that the stress history is primarily governed by the temperature dependence of the axial strength. In contrast the deformation behavior of an unconstrained test article depends critically on the amount of preloading in compression and on the temperature sensitivity of the coefficient of thermal expansion. Section 4 explored the effect of load induced thermal strain for realistic concrete properties. The unrestrained creep test showed the large reversal of thermal swelling followed by shrinkage under an initial cycle of heating under compression. The restrained relaxation test did exhibit large differences of thermal stresses when the hyper-elastic results were compared with the hypo-elastic ones. In this case the effect of load induced thermal strains was not considered although these transitional strain effects would have considerably reduced the thermal stress. The exploratory constitutive study in Section 5 did illustrate the extensive coupling of the volumetric-deviatoric material response with the thermal and hygral components when a nonlinear hyper-elastic model was considered in the form of a third order polynomial expansion of the Gibbs potential. Thereby, the thermal and hygral strain tensors did exhibit deviatoric effects in addition to the traditional volumetric thermal swelling and hygral shrinkage response of linear strain-stress-temperature-humidity relationships.
Acknowledgements The authors wish to acknowledge partial support of this research by the US National Science Foundation under grant CMS-0409747 on "High Temperature Effects on Concrete Materials: A Multiscale Approach". Opinions expressed in this paper are those of the authors and do not necessarily reflect those of the sponsor.
References [1]
ANDERBERG Y. and THELANDERSSON J., Stress and Deformation Characteristics of Concrete at High Temperatures, Bull. 54, Div. of Struct. Mech. Concrete Const., Lund Institute of Techn., Lund, Sweden. 1976
[2]
WILLAM K., RHEE I. and XI Y., Thermal Degradation in Heterogeneous Concrete Materials, Journal of Materials in Civil Engineering, ASCE. 2005
[3]
WILLAM K., RHEE I. and SHING B., Interface Damage Model for Thermomechanical Degradation of Heterogeneous Materials, Comp. Methods Appl. Mech. Eng., Vol. 193, pp. 3327-3350. 2004
[4]
NIELSEN C.V, PEARCE C.J, BICANIC N., Improved phenomenological modelling of transient thermal strains for concrete at high temperatures, Computers and Concrete, Vol. 1, No.2 (2004), pp.189-209
[5]
OZBOLT J., KOZAR I., ELIGEHAUSEN R., PERISKIC G.: Transient thermal 3D FE Analysis of headed stud anchors exposed to fire, Workshop fib Task Group 4.3.2, Fire Design of Concrete Structures, Politecnico di Milano, Italy, Dec.2-4, 2004 KHOURY G.A., SULLIVAN P.J.E., and GRAINGER B.N., Transient thermal strain of concrete: literature review, conditions within specimen and individual constituent behavior, Magazine of Concrete Research, Vol. 37, pp. 131-144. 1985
[6]
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Session 3 Structural Behavior and Plastic Analysis
Plastic Analysis of Concrete Structures Subjected to Fire Jean-Marc Franssen* Nonlinear and Plastic Analysis of Reinforced-Concrete Beams Paolo Riva* Structural Behavior and Failure Modes of R/C at High Temperature R/C Sections and 2-D Membersi Patrick Bamonte, Roberto Felicetti, Pietro G. Gambarova and Alberto Meda Plastic-Fracturing Model for the Analysis of Reinforced-Concrete Structures in Fire Jan Cervenka, Jiri Surovec and Vladimir Cervenka
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Page 133 147
159 175
Plastic Analysis of Concrete Structures Subjected to Fire
Jean-Marc FRANSSEN Research Director NFSR University of Liège Liège, Belgium
Summary This paper discusses the question whether load redistributions among the different sections of a structural member in bending can be accepted in case of fire, taking for granted that the sectional behaviour is generally inelastic. Accepting load redistributions seems to be possible, since a (limited) number of examples show that the ductility of a section tends to increase during a fire. Consequently, a plasticity-based approach can be adopted in the analysis. In so doing, a theoretical validation is given to the assumption that several effects leading to self-equilibrated stress distributions can be neglected in nonlinear analysis. This is the case of shrinkage, creep, construction phases and thermal loads (occurring before the fire). Finally, some considerations are made on why transient creep has not been directly introduced in the concrete model adopted by the Eurocode, and why the original “stiffer” model contained in the ENV version of the Eurocode has been made “softer” in the final version. Keywords:
concrete, fire resistance, fire, plastic analysis, analysis.
1.
Conditions and consequences of a plastic analysis
1.1
Plasticity in the analysis of the section
When the plastic analysis is introduced to students who have been so far familiar only with the world of elasticity, the question of the behaviour of the cross section is first treated. It is demonstrated that, because of the non linear behaviour of the material, the ultimate resistance in bending of a cross section is higher than the one based on the yielding of the first fibre in the section. For steel constructions based on H sections bending around the strong axis, the difference between the plastic bending moment and the elastic plastic moment is in the order of magnitude of only 15% if steel is assumed to have an elastic perfectly plastic stress strain relationship. It thus still makes sense to analyse a steel cross section on the base of the elastic theory because the approximation is not so big. For a concrete section on the other hand, the non linear behaviour of concrete in compression for stress level lower than the compressive strength, and the even higher non linearity existing at the transition between compression and tension has lead to the consequence that the verification of cross sections on the base of elasticity has been abandoned for many years. This is true at room temperature and should be even more so in the fire situation. Fig. 1a, for example, shows the normalised stress-strain relationship of cold worked steel at room temperature and at elevated temperatures (two curves are drawn for the cold Eurocode, EN 1992-1-1, depending on the hypothesis made for the slope of the plastic branch). This figure shows clearly that the domain of proportionality is shorter at elevated temperatures than at room temperature and a verification of the stress distribution in the section based on the hypothesis of elasticity would be even less correct in the fire situation than at room temperature. Fig. 1b shows the stress-strain relationship in siliceous concrete at room temperature (one curve for the analysis of sections by a simple model and one curve for non linear analyses) and at elevated temperatures.
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Stress / Effective yield strength [-]
1.2
1.0
0.8 EN 1992-1-1 EN 1992-1-1 0.6
T = 200°C T = 400°C T = 600°C
0.4
T = 800°C 0.2
0.0 0.000
0.005
0.010
0.015
0.020
0.025
0.030
Stress-related strain [-]
Fig. 1a - Normalised stress-strain relationship in steel. The fact that the analysis of the section must be based on non linear stress strain relationship in the fire situation is thus clearly demonstrated. 35 EN 1992-1-2
30
EN 1992-1-2 T = 20°C
Stress [N/mm²]
25
T = 200°C T = 400°C T = 600°C
20
T = 800°C 15
10
5
0 0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045
Stress Related Strain [-]
Fig. 1b - Stress-Strain relationship in concrete. 1.2
Plasticity in the structural analysis
The question that is addressed in this paper is the plastic analysis of the structure, i.e. the determination of the effects of actions, namely bending moments and shear forces, in the fire situation. It has been demonstrated for steel sections that the moment-curvature relationship can be approximated as rigid perfectly plastic, which leads to the notion of plastic hinges and to moment redistribution. One of the key condition for this theory to be valid is the ductility of the section, i.e. the capacity of the section to keep on supporting the plastic bending moment when the curvature increases to very high values. In reinforced concrete sections at room temperatures, the ductility is assumed to be present provided that the depth of the compression zone xu is not higher than a defined percentage of the depth of the section d. For a C30 concrete, for example, the ratio xu/d should not exceed 0.288 if the
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plastic bending moment after redistribution is reduced to 80 % of the elastically determined bending moment. This limit of 80% of redistribution is linked to the concept of limited redistribution. If the ratio xu/d is less then 0.25, the rotation capacity requirement is deemed to be satisfied and full redistribution is allowed, provided that class B or class C re-bars are used and that the ratio between bending moments on the supports and in the spans is comprised between 0.5 and 2.0. These requirements on the depth of the compression zone in fact ensure that the re-bars in tension will indeed reach yielding, which produces a failure mode more ductile than the one obtained from an excess of compression capacity in the concrete. For example, a compression zone that extends into 25% of the depth of the section will lead, with the upper fibber of the section at a strain of 0.35%, to a tensile strain of 1.05 % in the steel re-bars. What is the situation at elevated temperatures? Is the ductility increased or decreased compared to the ambient temperature condition? This question will be discussed here through a simple application case. Let us consider a rectangular section of 160x400 mm² in size, with 2 hypothetical re-bars of 256 mm² (As/Ac = 0.8%) with an axis distance of 40 mm to the edges of the section. Fig. 2 shows how this section will be discretized for the subsequent numerical analyses. The steel is S500 grade and concrete is C30. Diamond 2004 for SAFIR 60x400 mm² FILE: span_section NODES: 720 ELEMENTS: 663 SOLIDS PLOT
SILCONCEC2 STEELEC2
Y X
Z
Fig. 2 - Rectangular section discretised. At room temperature, the design strength of the materials are fc,d = fc,k / Jc = 30 / 1.5 = 20 N/mm² fy,d = fy,k / Js = 500 / 1.15 = 435 N/mm² If a rectangular stress block is considered in the compression zone, the extend of the compression zone, the maximum curvature as well as the plastic moment are easily determined. Tensile force Depth of the compressive block Depth of the compression zone
Ft = As fy,d = 512 x 435 = 227 720 N = Compressive force xu,V = Ft / ( fc,d b ) = 227 720 / ( 20 x 160 ) = 69.6 mm xu = xu,V / 0.8 = 69.6 / 0.8 = 87 mm xu / d = 87 / 360 = 0.24
135
F = Hcu3 / xu = 0.0035 / 0.087 = 0.040 m-1
Maximum curvature Plastic moment
Md = Ft z = 227.72 x ( 360 – 69.6 / 2 ) = 74.05 kNm
In the fire situation, at time t = 0, if the same stress-strain relationship are considered as in the cold situation, the fact that the partial safety factors on the materials Jc = 1.5 and Js = 1.15 are replaced by Jm,fi = 1.0 reduces the compressive zone to 66.7 mm, i.e. xu / d = 0.185, and increases the maximum curvature to 0.053. This is in fact an increase of (Jc - Js ) / Js = 30%. The plastic moment is also increased to MRd;fi = 85 kNm. Also in the fire situation, at time t = 0, if the stress-strain relationship of concrete from ENV1992-1-2 is used and the curvature is progressively increased numerically (the discretisation shown on Fig. 2 is used), the plastic moment of 85 kNm is found, exactly the same as the one found by the simple calculation method. The ductility is in fact slightly higher, with the exact value depending on the assumption made for the descending branch. The maximum curvature is found to be 0.062 for a non linear descending branch and 0.056 for a linear descending branch, see Fig. 3. 35 EN 1992-1-1
30
EN 1992-1-2 Non linear
Stress [N/mm²]
25
EN 1992-1-2 Linear
20
15
10
5
0 0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
0.020
Stress Related Strain [-]
Fig. 3 - Different hypotheses for the descending branch.
The moment-curvature relationships in the section have been computed in the rectangular section at different moments in the fire. The section is heated by the ISO fire on 4 sides. Fig. 4, for example, shows the isotherms in the section after 60 minutes of fire. The results are presented on Fig. 5 which clearly shows that the ductility increases significantly as the temperature in the section is increased. Each curve has been computed for both hypotheses about the descending branch, see Fig. 3, either linear, noted L on the figure, or non linear, noted NL on the figure. The ductility is somewhat smaller with the hypothesis of a linear descending branch, but the difference with the hypothesis of non linear descending branch is not significant. The same exercise has been made for a 140 mm thick concrete slab that has a hypothetical layer of steel bars with a section of 1120 mm² (As / Ac = 0.8 % ) located at an axis distance of 27.5 mm from the lower side of the slab, i.e. with a cover of 25 mm on the bars. This section represents a slab in positive bending heated from underneath. The bars in tension have their temperature increased by the fire, whereas the concrete in the compression zone remains at a relatively low temperature. The result is shown on Fig. 6 which shows that the ductility is also increased by the elevation of temperature, but to a lesser extend than for the rectangular section.
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Diamond 2004 for SAFIR 160 x 400 mm² FILE: section4 NODES: 720 ELEMENTS: 663 CONTOUR PLOT TEMPERATURE PLOT TIME: 3600 sec >Tmax 1000.00 900.00 800.00 700.00 600.00 500.00 400.00 300.00 200.00 100.00
2(1 e 2 ) cos T (2e 1) 4(1 e 2 ) cos2 T 5e 2 4e
@
1 2
In the above equations ([ , U ,T ) are Heigh-Vestergaard coordinates, f c and ft is compressive strength and tensile strength respectively. Parameter e 0.5,10 . defines the roundness of the failure surface. The failure surface has sharp corners if e 0.5 , and is fully circular around the hydrostatic . . The surface evolves during the yielding/crushing process by the laws denoted in axis if e 10 Fig. 3. Special iterative algorithm is developed [1] to solve the plastic and fracture models such that the final stress tensor in both models are identical. This algorithm is schematically shown in twodimensions in Fig. 4.
Fig. 2 - Shape of the 3D Menetréy-Willam failure criterion [5] for concrete in three-dimansional space of principal stresses.
f'c
f’c0=f'c 2/3 p
Heq Hc=f'c/E
Fig. 3 - Compression hardening/softening laws.
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Fig. 4 - Schematic description of the algorithm for the combination of fracture-plastic models.
3.
Material model for reinforcement
Finite element modelling of reinforced concrete structures requires special tools for modelling of all types of reinforcement. Most of these models are illustrated in Fig. 5 for three-dimensional solids. Concrete is modeled by solid elements. Concrete to concrete, or concrete to other material interfaces can model the frictional type of interaction between structural elements. The mesh type of reinforcement can be represented as smeared reinforcement. In this element, the individual bars are not considered, while reinforcement is considered as a component of the composite material. Individual bars can be modelled by truss elements embedded in concrete elements with axial stiffness only. In this technique the mesh is generated first for concrete. Then the bar elements are embedded in this mesh. The bar element can be considered as any other element but its nodes are made kinematically dependent on concrete nodes. Thus the reinforcing is not affecting the mesh generation. The described family of finite elements make it possible a to cover most practical cases of reinforced concrete structures.
Fig. 5 - Three-dimensional elements of reinforced concrete.
4.
Temperature dependent material properties
The used material models for concrete as well as reinforcement are formulated in a purely incremental manner, and the selected material parameters are temperature dependent. The
177
temperature dependent evolution laws of these parameters are shown in Fig. 6. They have been derived based on Eurocode formulas [6] and the experimental results [7]. Analogical dependence is used also for the stress-strain law for reinforcement, where this law is scalled based on the maximally reached temperature at each reinforcement element based on the Eurocode formulas for reinforcement yield strength temperature dependance [6]. Fc 1,00
0,90
0,90
0,80
0,80
Relative value of Fc
Relative value of E
E 1,00
0,70 0,60 0,50 0,40 0,30 0,20
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900 1000 1100 1200
100
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900 1000 1100 1200
Ft
2,00
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Relative value of Ft
Relative value of Gf
600
Temperature
Temperature
1,60 1,50 1,40 1,30 1,20 1,10
0,80 0,70 0,60 0,50 0,40 0,30 0,20
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Temperature
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Temperature
eps_cp
wd
6,00
3,75 3,25
Relative value of wd
Relative value of eps_cp
3,50 5,00 4,00 3,00 2,00 1,00
3,00 2,75 2,50 2,25 2,00 1,75 1,50 1,25 1,00
0,00
0,75 0
100
200
300
400
500
600
700
800
Temperature
0
100
200
300
400
500
600
700
800
Temperature
Fig. 6 - Evolution laws for temperature dependence parameters.
5.
Examples
Several examples are presented to demonstrate the behavior of the proposed model in simple uniaxial tests as well as on a more complicated example of a tunnel suspended ceiling subjected to fire.
5.1
Uniaxial tests
The tests consisted of standard compression and tension test simulation, where the specimen was loaded to collapse during uniform temperature field distribution. The temperatures chosen were in range 100°C to 800 °C with a step of 100 °C. The results show the behaviour of material model during different temperatures and are depicted in Fig. 7 and Fig. 8.
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40 35 100
Stress [MPa]
30
200
25
300 400
20
500
15
600 700
10
800 5 0 0,0000
0,0010
0,0020
0,0030
0,0040
0,0050
0,0060
0,0070
Strain
Fig. 7 - Uniaxial comression test at different temperatures. 2,25 2,00 1,75
Stress [MPa]
1,50 100 200 300 400 500 600 700 800
1,25 1,00 0,75 0,50 0,25 0,00 0,0000
0,0005
0,0010
0,0015
0,0020
Strain
Fig. 8 - Uniaxial tension test at different temperatures.
5.2
Suspended ceiling simulation
The structure consists of a reinforced concrete suspended ceiling slab with total span of 8.0 m, suspended in the mid-span by pair of hangers. The geometry corresponds to a specimen, which will be tested during a european research project UPTUN. The presented results are part of a pre-test simulation program. At both ends the slab is simply supported with possibility of rising. The thickness of the slab is 200 mm, width is 2.0 m. The symmetry of structure was employed in the analysis, so the model (Fig. 9) consists of one quarter of the structure. The structure was exposed with bottom size to Modified HC fire scenario. For the upper surface condition the constant ambient temperature of 20 °C. No thermal shielding was considered. The structure was initially loaded with assumed self weight of 5 kN/m2 and live load of 3.5 kN/m2. First transient thermal analysis was performed with temperature dependent material properties was performed the obtained thermal fields were used in subsequent incremental stress analysis, in which the models described in Sections 2,3, and 4 were utilized.
179
(a)
(b) Fig. 9 - (a) Typical tunnel design with suspended ceiling (figure taken from UPTUN report) (b) Geometrical model for the suspended ceiling simulation. The deformed shape and calculated crack pattern after 3 hours of modified hydrocarbon fire is shown in Fig. 10. The structure suffered an extensive damaged, but full collapse was not reached in the investigated time period.
6.
Discussion, Conclusions and Acknowledgements
The paper describes modification to combined fracture-plastic model [1] to extend its applicability for the simulation of reinforced concrete structures subjected to fire. Several examples are presented ranging from simple uniaxial tests up to more complicated problem of a full three-dimensional analysis of a tunnel suspended ceiling. The presented work is part of a european research project UPTUN GRID-CT-2002-00766. The financial support from the european community is greatly appreciated.
180
Extensive cracking on the top surface due to lifting from supports.
Separation of bottom concrete layer
Lifting at supports
Fig. 10 - Deformed shape and crack pattern after 3 hours of modified HCM fire.
References [1]
CERVENKA J., CERVENKA V. and ELIGEHAUSEN R., “Fracture-Plastic Material Model for Concrete, Application to Analysis of Powder Actuated Anchors”, Proc. FRAMCOS 3, 1998, pp 1107-1116.
[2]
BAŽANT Z.P. and OH B.H., “Crack Band Theory for Fracture of Concrete”, Materials and Structures, 16 (1983), 155-177.York, 1984, 360 pp.
[3]
HILLERBORG A., MODÉER M. and PETERSON P.E., “Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements”, Cement and Concrete Research, 6, 1976, pp. 773-782.
[4]
HORDIJK D.A., Local Approach to Fatigue of Concrete, Ph.D. Thesis, Delft University of Technology, The Netherlands, 1991.
[5]
MENETREY P. and WILLAM K.J., “Triaxial Failure Criterion for Concrete and its Generalization”, ACI, Structural Journal, Vol. 92, No. 3, 1995, pp. 311-318.
[6]
EUROCODE 2, “Design of Concrete Structures, Part 1.2. General Rules - Structural Fire Design”, Draft prENV 1992-1-2
[7]
CASTILLO C. and DURANI A.J. “Effect of Transient High Temperature on High-Strength Concrete”, ACI Materials Journal, Vol. 87, No. 1, 1990, pp. 47-53.
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Session 4
Detailing and Connections
Transient Thermal 3D FE Analysis of Headed Stud Anchors Exposed to Fire Josko Ožbolt*, Rolf Eligehausen, Ivica Kožar and Goran Periskic Preliminary Pull-out Tests on Post-Installed Mechanical Fasteners Embedded in Thermally-Damaged Concrete Patrick Bamonte, Pietro G. Gambarova, Lorenzo D’Agostino and Alessandro Genoni
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Page 185
199
Transient Thermal 3D FE Analysis of Headed Stud Anchors Exposed to Fire Josko OŽBOLT Associate Professor Institute for Construction Materials Stuttgart, Germany
Ivica KOŽAR Professor University of Rijeka Rijeka, Croatia
Rolf ELIGEHAUSEN Professor Institute for Construction Materials Stuttgart, Germany
Goran PERISKIC Civil Engineer Institute for Construction Materials Stuttgart, Germany
Summary In the present paper a transient three-dimensional thermo-mechanical model for concrete is presented. For a given boundary conditions, temperature distribution is calculated by employing a three-dimensional transient thermal finite element analysis. The thermal properties of concrete are assumed to be constant and independent of the stress-strain distribution. In the thermo-mechanical model for concrete the total strain tensor is decomposed into pure mechanical strain, free thermal strain and load induced thermal strain. The mechanical strain is calculated by using temperature dependent microplane model for concrete [1]. The dependency between the macroscopic concrete properties (Young’s modulus, tensile & compressive strength and fracture energy) and the temperature is based on the available experimental data base. The free thermal strain, which is stress independent, is calculated according to the proposal of Nielsen et al. [2]. The load induced thermal strain is obtained by employing the bi-parabolic model recently proposed by Nielsen et al. [3]. It is assumed that the total load induced thermal strain is irrecoverable i.e. creep component is neglected. The model is implemented into a three-dimensional FE code. The performance of headed stud anchors exposed to fire was studied. For a given geometry of a concrete member and for a constant concrete properties three-dimensional transient thermal FE analysis was carried out for three embedment depths and for four thermal load histories. The analysis shows that the resistance of anchors can be significantly reduced if they are exposed to fire. The largest reduction of the load capacity was obtained for anchors with relatively small embedment depth. The numerical results agree well with the available experiments. Keywords:
concrete, high temperature, 3D finite element analysis, microplane model, thermomechanical model, headed studs.
1. Introduction Concrete does not burn, however, when its temperature increases for a couple of hundred of degrees Celsius its behavior changes significantly. The concrete mechanical properties, such as strength, elasticity modulus and fracture energy, are at high temperatures rather different than for the concrete at normal temperature. At high temperature large temperature gradients lead in concrete structures to temperature induced stresses which cause damage. Furthermore, creep and relaxation of concrete that is due to high temperature plays also important role. The main reason for the complexity of the behavior of concrete at high temperature is due to the fact that concrete contains water, which at high temperature changes its aggregate state. Moreover, at high temperature the aggregate can change its structure or it can loose its weight through the emission of CO2, such as calcium based stones. Although the behavior of concrete at high temperature is in the literature well documented [4][5][6][7][8] further tests are needed to clarify the tensile post-peak behavior of concrete, which has significant influence on the response of concrete structures. The main problem
185
in the experimental investigations is due to the fact that such experiments are rather demanding i.e. one has to perform loading and measurement at extremely high temperatures. Furthermore, such experiments can be carried out only on relatively small structures. To better understand behavior of concrete structures, as an alternative to the experiments one can employ numerical analysis. However, one needs models, which can realistically predict behavior of concrete at high temperature. There are principally two groups of models: (i) Thermo-mechanical models and (ii) Thermohydro-mechanical models [9][10][11][12]. The first group of the models are phenomenological. In these models the mechanical properties of concrete are temperature (humidity) dependent whereas the temperature (humidity) distribution is independent of the mechanical properties of concrete. The second group of the models are from the physical point of view more realistic. Namely, in these models the physical processes that take place at concrete micro structural level are coupled i.e. the interaction between mechanical properties, temperature, humidity, pore pressure, hydration is accounted for. These models are interesting from the theoretical point of view. They are rather complex and therefore for practical engineering applications one has to employ the first group of the models. In the present paper a three-dimensional (3D) model that is based on the thermo-mechanical coupling between mechanical properties of concrete and temperature is discussed. The microplane model is used as a isothermal constitutive law for concrete whose model parameters are made temperature dependent. The model is implemented into a three-dimensional finite element code and its performance is first compared with the experimental results known from the literature. Subsequently, the influence of high temperature on the pullout concrete cone resistance of a headed stud anchors is investigated. The finite element analysis is performed in two steps. For a given temperature boundary conditions (air temperature and, or, concrete surface temperature) it is first calculated distribution of temperature. In the second step the required load history is applied with taking into account the influence of temperature on the concrete mechanical properties.
2. Transient thermal Analysis As the first step of coupling between mechanical properties of concrete and temperature, for a given thermal boundary conditions at time t it has to be calculated temperature distribution over a solid structure of volume :. In each point of continuum, which is defined by the Cartesian coordinates (x,y,z), the conservation of energy has to be full field. This can be expressed by the following differential equation:
O ' T ( x, y , z , t ) W ( x, y , z , t , T ) c U
wT ( x, y , z , t ) 0 wt
(1)
where T = temperature, O = conductivity, c = heat capacity, U = mass density, W = internal source of heating and ' = Laplace-Operator. The surface boundary conditions that has to be satisfied reads:
O
wT wn
D (TM T )
(2)
where n = normal to the boundary surface *, D = transfer or radiation coefficient and TM = temperature of the media in which surface * of the solid : is exposed to (for instance temperature of air). To solve the problem by the finite element method the above differential equations (1)(2) has to be written in the weak (integral) form that reads [13]:
§ wv wT
wv wT
wv wT · § wT · ¸ d : ³ v ¨ cU ¸d : ³ vD T TM d * wz ¹ wt ¹ : © *
³ O ¨© wx wx wy wy wz :
0
(3)
where v is trial function. After introducing the condition that the functional is stationary one obtains the following system of linear equations (Voigt notation):
186
>C@^T ` > K @ > H @ ^T` ^R`
(4a)
with
>C@ ³ c U > N @T > N @ d : ; > K @ ³ > B@T >O @> B@ d : ; ȍ
ȍ
T
> H @ ³ D > N @ > N @ d * ; > R @ ³ > N @T D TM d * ī
(4b)
ī
where [N] is the column matrix of shape functions that relates temperature field and nodal temperatures and [B] relates the field of temperature gradients and nodal temperatures. Equation (4a) is solved using direct method based on the following assumption for the solution in the (n+1)th time step
^T`n1 ^T`n 't 1 E T n ET n1
(5)
Parameter E has been set to E = 0.5 what yields to the unconditionally stable Crank-Nicolson method that reads [14]:
§ 1 · ¨ > C@ E > K @ > H @ ¸ ^T`n 1 t ' © ¹ § 1 · ¨ > C@ 1 E > K @ > H @ ¸ ^T`n 1 E ^R`n E ^R`n 1 © 't ¹
(6)
The above equation has been programmed for 3D solid finite elements.
3. Decomposition of strain In the present model the total strain tensor Hij (indicial notation) for stressed concrete exposed to high temperature can be decomposed as [5][6][8]:
H ij
H ijm (T , V kl ) H ijft (T ) H ijtm (T , V kl ) H ijc (T , V kl )
(7)
where Hijm = mechanical strain tensor, Hijft = free thermal train tensor, Hijtm = thermo-mechanical strain tensor and Hijc are strains that are due to the temperature dependent creep of concrete. In general, the mechanical strain component can be decomposed into elastic, plastic and damage part. In the present model these strain components are obtained from the constitutive law. The free thermal strain is stress independent and it is experimentally obtained by measurements on the load-free specimen. In such experiments it is not possible to isolate shrinkage of concrete, therefore, the temperature dependent shrinkage is contained in the free thermal strain. The thermomechanical strain is stress and temperature dependent. It appears only during the first heating and not during the subsequent cooling and heating cycles [5]. This strain is irrecoverable and lead in concrete structures to severe tensile stresses during cooling. The temperature dependent creep stain is of the same nature as the thermo-mechanical strain except that it is partly recoverable. In the experiment is not possible to isolate it. For low temperature rates, what is normal case in the experiments, this strain component compared to the thermo-mechanical strain is small. Therefore, temperature dependent creep stain is in the present model neglected.
4. Mechanical strain The mechanical strain components are obtained from the constitutive law of concrete. In the present model for the temperature independent (isothermal) constitutive law the microplane model is used [1]. The temperature dependency is adopted such that the macroscopic properties of concrete (Young’s modulus, compressive and tensile strength and fracture energy) are made time dependent.
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4.1
Isothermal constitutive law for concrete – microplane model
In the microplane model the material is characterized by a relation between the stress and strain components on planes of various orientations. These planes may be imagined to represent the damage planes or weak planes in the microstructure, such as those that exist at the contact between aggregate and the cement matrix. In the model the tensorial invariance restrictions need not be directly enforced. Superimposing in a suitable manner the responses from all the microplanes automatically satisfies them. The basic concept behind the microplane model was advanced in 1938 by G.I. Taylor [15] and developed in detail for plasticity by Batdorf and Budianski in 1949 under the name "slip theory of plasticity" [16]. The model was later extended by Bažant and co-workers for modelling of quasi-brittle materials that exhibit softening [17][18][19]. a)
b)
z
z
D
integration point
T
y
T,K
microplane V
ni
T,M
microplane
y
x
x Fig 1 - The concept of the microplane model: a) discretization of the unit volume sphere for each finite element integration point (21 microplane directions – integration points) and b) microplane strain components layout The microplane model used in the present paper was recently proposed by Ožbolt et al. [1]. The model is based on the so-called relaxed kinematic constraint concept and it is a modification of the M2 microplane model proposed by Bažant and Pratt [17]. Let ignore for the moment the effect of temperature and assume that the total strain tensor is identical to the mechanical strain tensor i.e. Hijm = Hij. In the model the microplane (see Fig. 1) is defined by its unit normal vector of components ni. Microplane strains are assumed to be the projections of Hij (kinematic constraint). Normal and shear stress and strain components (VN, VTr, HN, HTr) are considered on each plane. Based on the virtual work approach (weak form of equilibrium), the macroscopic stress tensor is obtained as an integral over all possible, in advance defined, microplane orientations (S denotes the surface of the unit sphere):
V ij
3 2S
3
³ V N ni n j dS 2S ³ S
V Tr 2
S
( ni G rj n j G ri ) dS
(8)
To realistically model concrete, the normal microplane stress and strain components have to be decomposed into volumetric and deviatoric parts (VN=VV+VD, HN=HV+HD; see Fig. 1), which lead to the following expression for the macroscopic stress tensor:
V ij
V V G ij
3 2S
3
³ V D ni n j dS 2S ³ S
S
V Tr 2
( ni G rj n j G ri ) dS
(9)
For each microplane component, the uniaxial stress-strain relations read:
VV
FV (H V ) ;
VD
FD (H D , eff ) ;
188
V Tr
FTr (H Tr , eff , H V )
(10)
where FV, FD and FTr are the uniaxial stress-strain relationships for volumetric, deviatoric and shear components, respectively. For the deviatoric and shear microplane strain components in (10) only effective parts of microplane strains are used to calculate microplane stresses. Finally, the macroscopic stress tensor is obtained from (9). The integration over all microplane directions (21 directions, symmetric part of the sphere) is performed numerically. To model concrete cracking for any load history realistically, the effective microplane strains are introduced in (10). They are calculated as:
H m , eff
H m\ m (H m , V I )
(11)
where the subscript m denotes the corresponding microplane components (V, D, Tr), Hm is the microplane strain obtained from the projection of the total strain tensor (kinematic constraint) and \ is the so-called discontinuity function, which depends on the microplane strain components and maximum principal stress VI. On the individual microplanes this function accounts for discontinuity of the macroscopic strain field (cracking). It is calculated such that for dominant tensile load the ratio between the positive volumetric and deviatoric strain components remains constant for the entire load history. The function "relaxes" the kinematic constraint, which is in the case of strong localization of strains physically unrealistic. Consequently, in the smeared fracture type of the analysis the discontinuity function \ enables localization of strains not only for tensile fracture, but also for dominant compressive type of failure. Detailed discussion of the features, development and problems related to various versions of the microplane models are beyond the scope of the present paper. For more detail refer to the above cited literature.
4.2
Thermo-mechanical coupling
To account for the effect of temperature the macroscopic mechanical properties of concrete need to be temperature dependent. The nonlinear finite element analysis is incremental and the load increment is defined by the time step ǻt in which the load, the boundary conditions, the temperature, etc. change. In the present model it is assumed that during load increment the temperature is constant. Consequently, the material parameters that are temperature dependent are during the load step constant as well. 4.2.1 Young’s modulus The experiments show that with the increase of temperature Young’s modulus decreases [20]. It is assumed that at relatively low temperatures decrease of E is caused by the loss of capillary water (vaporisation). However, at higher temperatures decrease of E is due to the decomposition of individual concrete components (cement paste and aggregate). In the present model the temperature dependent Young’s modulus follows the proposal of Stabler [11] i.e. E is assumed to be a scalar function of temperature that reads:
E (T ) (1 max(Zt , E )) E0 for 0 d T d 10 for
T ! 10
Zt , E
0.2T 0.01T 2
(12)
Zt , E 1
where E0 = Young’s modulus at temperature T0 = 20°C and T = (T-T0)/1000C is the relative temperature. The dependency (12) is plotted in Figure 2. As can be seen it shows good agreement with the experimental evidence. Note that max(Zt,E) corresponds to the maximal temperature reached so far i.e. by cooling Young’s modulus does not increases.
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1
1.2
Relative Young's Modulus E
Relative compressive strength fC
Experimental data, Sandstone, Schneider (1986) Experimental data, Basalt, Schneider (1986) Model prediction
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1
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Experimental data, Abrams (1971) Experimental data, Bicanic & Zhang (2002) Model prediction
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0
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Fig. 2 - The dependency of modulus on the temperature
100
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Temperature [°C]
the Young’s Fig. 2 - The influence of the temperature on the concrete compressive strength
4.2.2 Compressive strength of concrete According to the experimental evidence [6][21][22], at temperatures up to 300°C the concrete compressive strength slightly increases with increase of temperature. However, with further increase of temperature, the concrete strength decreases almost linearly. Namely, at lower temperatures hydration of cement paste is more advanced. Moreover, due to the thermal strains the frictional and aggregate locking phenomena are even stronger than for the concrete at normal temperature. Due to these effects the compressive strength does not decrease. At extremely large temperature microcracks, vaporisation and decomposition of cement paste and aggregate cause decrease of the concrete compressive strength. In the present model it is assumed that up to T = 300°C the cylinder compressive strength fc is temperature independent and for higher temperature it decreases as a linear function of temperature: f c (T )
max(Zt , fc ) f c ,0
for 0 d T d 2.80 Zt , fc
1.0
for T ! 2.80
1.43 1.53T
Zt , f
c
(13)
where fc,0 = uniaxial compressive strength at T = 20°C. The adopted dependency is plotted in Figure 3 and compared with experimental results. As can be seen the comparison shows good agreement. 4.2.3 Tensile strength of concrete The experimental evidence indicates that the tensile strength of concrete decreases almost linearly with increase of temperature [6][22]. At lower temperatures thermal strains leads to micro cracking and damage of the aggregate-cement paste interface what, in contrary to the effects on the compressive strength, reduces tensile strength of concrete. With increase of temperature the microcracks, vaporisation and decomposition of cement paste and aggregate also lead to decrease of the concrete tensile strength. In the present model the following dependency of tensile strength on the temperature is adopted:
ft (T )
max(Zt , ft ) f t ,0
Zt , f
t
1 0.131T
(14)
where ft,0 = uniaxial compressive strength at T = 20°C. The plot of (14) is shown and compared with the test data in Figure 4.
190
1
2
Relative fracture energy GF
Relative tensile strength ft
Experimental data, Bicanic & Zhang (2002) Model prediction 0.8
0.6
0.4
0.2
Experimental data, Schneider (1986) Experimental data, Bicanic & Zhang (2002) Model prediction
0
1.6
1.2
0.8
0.4
0 0
100
200
300
400
500
600
0
Temperature [°C]
100
200
300
400
500
600
Temperature [°C]
Figure 4. The relative tensile strength as a Figure 5. The relative concrete fracture function of temperature energy as a function of temperature 4.2.4 Concrete fracture energy A recent experimental investigation [22] show that with the increase of temperature up to approximately 300°C the concrete fracture energy increases for approximately 60%. However, with further increase of temperature it starts to decrease and at approximately 600°C reaches about 90% of its initial value. This can be explained by the fact that at temperatures lower than approximately 300°C the hydration of cement paste is more advanced than at normal room temperature. Moreover, at this stage temperature strains contribute to the frictional effects and aggregate interlock what increases ductility. At higher temperatures the microcracks, vaporisation and decomposition of cement paste and aggregate cause decrease of concrete ductility. In the present model, the dependency of the concrete fracture energy GF on the temperature is obtained by fitting of test data of Biüaniü & Zhang [22]. The adopted dependency reads:
GF (T )
max(Zt ,GF )GF ,0
for 0 d T d 2.80 Zt ,GF for T ! 2.80
Z t ,G
F
0.917 0.467T 0.0833T 2 1 0.407T 0.0727T
(15)
2
where GF,0 = concrete fracture energy at T = 20°C. The dependency is plotted in Figure 5 and compared with experimental results. As can be seen, the comparison shows good agreement.
5. Thermal strain As mentioned before, the total thermal strain generated as a consequence of heating of concrete can be decomposed into strains that are stress independent (free thermal strains) and strains, which are stress dependant (stress induced thermal strains).
5.1
Free thermal strain
The experimental evidence [6] indicates that the free thermal strains in concrete specimen mainly depend on the type and amount of the aggregate. As can be seen from Figure 6, the relationship between the free thermal strain and temperature is highly non-linear and dependent on the thermal stability of the aggregate. Although the experiments indicate that the free thermal strain depends on the rate of the temperature, in the present model is assumed that this strain depends only on the temperature. Moreover, it is assumed that in the case of a stress free specimen, the thermal strains in all three mutually perpendicular directions are the same (isotropic thermal strains). In the present model the rate of the free thermal strain is calculated as (indicial notation):
191
Hijft D T G ij 6.0 105 7.0 T 0
for 0 d T d 6 D for T ! 6
D
(16)
where Gij is Kronecker delta. The above curve is plotted in Figure 6. In the same figure are also shown the experimental results for concrete made of three different aggregate types [6]. It can be seen that the free thermal strain very much depends on the aggregate tape. Up to approximately 600°C the free thermal strain increases with increase of temperature, however, further increase of temperatures cause no further increase of thermal strain. The reason for this is that beyond 600°C the change of the crystalline structure of the aggregate takes place [4]. The relationship (16) is chosen such that only the main trend is covered and not the exact development of free thermal strains for particular concrete type.
5.2
Stress induced thermal strain – creep
When a concrete specimen is first loaded and than exposed to high temperature, the resulting thermal strain is different than for the case when the specimen is not loaded [8][23][24][25][26]. The difference can be obtained if the free thermal strain is subtracted from the resulting thermal strain. This difference is in the literature known as stress induced thermal strain. As already mentioned above, the stress induced thermal strain consists of two parts – irrecoverable part and partly recoverable part (temperature dependent creep). Since the partly recoverable part has only theoretical meaning and is much smaller than the irrecoverable part, in the present model it is neglected i.e. the total stress dependent thermal strain is assumed to be irrecoverable. Based on the experimental evidence, in the present model the bi-parabolic thermo-mechanical strain model is used [3]. The uniaxial (scalar) rate form of this model reads:
Htm (T , V )
V f cT0
E T
°2 A T B 0.01 ® * * ¯°2 C (T T ) 2 A T B
E
for for
0 dT dT*
T !T*
(17)
4.5½° ¾ ¿°
where T* is a dimensionless transition temperature between the two expressions (470°C). The above two expressions are introduced to account for abrupt change in behavior detected in the experiments. A, B and C are experimentally obtained constants that are in the present model set as: A = 0.0005, B = 0.00125 and C = 0.0085. 18
0
Free Thermal Strain [x103]
14
Load Induced Thermal Strain [x103]
Exp. Data, Quartzite, Schneider (1986) Exp. Data, Quartzite, Schneider (1986) Exp. Data, Bazalt, Schneider (1986) Model prediction
16
12 10 8 6 4 2 0
-2 -4 -6 -8 -10 -12 -14 -16
Dissipation of experimental data Model prediction
-18 0
100
200
300
400
500
600
700
800
Temperature [°C]
0
100
200
300
400
500
600
700
Temperature [°C]
Fig. 6 - The
relative concrete fracture Fig. 7 - Stress induced thermal strain as a energy as a function of temperature function of temperature [6]
192
All experimental investigations for stress induced thermal strain are performed for sustained compressive load and there is no test available for sustained tensile load. Because of this and because of the fact that the tensile stress is limited by the relative small tensile strength of concrete, it is assumed that (20) applies only on compressive stress. Furthermore, it is assumed that the Poisson’s ratio, which relates axial and lateral stress induced thermal strains, is a material constant equal to the Poisson’s ratio of undamaged (initial elastic) concrete. Based on these assumptions the three-dimensional form of (17) in indicial notation reads:
Hijtm (T , V ij )
E f cT0
(1 Q )V
ij
QV kk G ij T (Tmax )
(18)
T (Tmax ) T for T t Tmax ; T (Tmax ) 0 for T Tmax where ‘–‘ indicates compressive stress i.e. tensile stress components of the stress tensor are set to zero. Tmax is the maximal temperature reached so far and it is introduced in (18) to recognize the irreversible nature of thermo-mechanical strain.
6. Numerical studies The above presented thermo-mechanical model for concrete is implemented into the 3D finite element (FE) code. The implementation is first verified on two examples from the literature. Subsequently, the influence of the high temperature on the performance of the headed stud anchor that is pulled out from a concrete block is studied.
6.1
Verification
In the first example, transient test data reported by Thelandersson [8] are reproduced using the presented model. The concrete cylinder was loaded by different levels of sustained compressive loads and heated by constant heating rate. The specimen geometry (cylinder) was discretized by eight node solid finite elements. The results of the numerical analysis are shown in Figure 8. As can be seen, the numerical prediction fits the experimental data for all load histories very well. In the second example a concrete specimen with in-plane fully restrained ends and with only two restrained ends, respectively, were exposed to the constant heating rate [27]. The numerical analysis for both boundary conditions was performed by the use of the eight node solid finite elements. The results of the analysis are shown in Figure 9. The comparison between numerical and experimental results shows again good agreement. 1
16 Experimental data, Thelandersson (1987) Model prediction
14
V=0
Experimental data, biaxial loading, Ehm (1986) Experimental data, uniaxial loading, Ehm (1986) Model prediction, biaxial loading Model prediction, uniaxial loading
0.9
12
0.8
Relative stress (VT/fc0)
10
Strain [x103]
8 6
V=-0.225fc0
4 2 0
V=-0.45fc0
-2
V=-0.675fc0
-4 -6
0.7 0.6 0.5 0.4 0.3 0.2
-8
0.1
-10 -12
0 0
100
200
300
400
500
600
700
800
0
Temperature [°C]
Fig. 8 - Total strains versus temperature
100
200
300
400
500
600
700
800
900
Temperature [°C]
Fig. 9 - Thermal induced stresses versus temperature
6.2 Pull-out of the headed stud anchor from a concrete block The performance of the headed stud anchors exposed to high temperature is numerically investigated. A concrete block with a single headed anchor (see Fig. 10) was exposed to fire at its upper side (anchor side). The analysis consists of two parts. In the first part 3D transient thermal FE analysis was carried out. The resulting thermal distribution is then used in the second part of the analysis in which is the above presented thermo-mechanical model is applied. 193
a)
b) 185
185
172.5
172.5 dA
dS=370 hef t=160
dH
Z Y
X
Fig. 10 - (a) Geometry of the specimen and (b) typical finite element discretization of the concrete specimen
The investigated geometry was the same as the geometry tested by Reick [28]. However, in the experiment the concrete block was relatively large. Therefore, to save computer time only a concrete member of a diameter dS = 370 mm with the thickness t = 160 mm ( see Figure 10a), the same as in the experiment, was analysed. The typical finite element discretization, using four node solid elements, is shown in Figure 10b. One fourth of the geometry was discretized i.e. double symmetry was utilized. To approximately meet experimental boundary conditions, two outer vertical rows of the finite elements around the concrete block were taken as linear elastic. The upper (heated) side of the specimen was supported in vertical direction. The diameter of the supporting ring was 345 mm. The thermal and mechanical properties of concrete used in the analysis are summarized in Table 1. To prevent anchor failure, the behavior of steel is taken as linear elastic. Tab. 1 - Mechanical and thermal properties of steel and concrete used in the FE analysis Young’s modulus E [MPa] Poisson’s ratio Q Tensile strength ft [MPa] Uniaxial compressive strength fc [MPa] Fracture energy GF [Nmm/mm2] Conductivity Ȝ [W/(mK)] Heat capacity c [J/(kgK)] Weight density ȡ [kg/m3] Transfer coefficient Į [W/(m2K)]
Concrete 28000 0.18 2.5 21.25 0.07 2.0 900 2300 8.0
Steel 200000 0.34 L.E. L.E. 53.0 470 7850 99.0
The FE analysis was carried out for three different embedment depths hef = 25 mm (dA = 8 & dH = 13 mm – see Fig. 10a), hef = 50 mm (dA = 10 & dH = 20 mm) and hef = 100 mm (dA = 10 & dH = 20 mm). The first was applied design load assuming a room temperature of 20°C. In the next step the fire at the anchor side of the specimen was simulated. The air heating temperature at the upper specimen side was taken according to ISO 833 (equivalent to DIN 4102 part 2) that reads:
TAir (t ) TAir (t0 ) 345 log (8t 1)
(19)
where TAir(t0) is the air starting temperature (in our case room temperature of 20°C) and t is time in minutes measured from the start of the fire. In the case of cooling, it was assumed that the air temperature is linearly decreasing from the start of cooling back to the room temperature of 20°C (see Fig. 11a). The bottom specimen surface temperature was assumed to be constant during the entire load history and equal to 20°C.
194
a)
b) 1000 900.
800.
Temperature [°C]
800
700.
600
600.
500.
400
400.
300.
200
200.
Heating Cooling
100.
Z
0 Y
0
10
20
30
40
50
60
70
80
X
0.
90
Time [min]
Fig. 11 - (a) Assumed temperature increase of air as a function of time; (b) Calculated temperature distribution in °C after t = 90 min
Figures 11 b shows calculated distribution of temperature in the concrete specimen (hef = 50 mm), 90 minutes after start of fire. As one would expect, due to the relatively high conductivity of steel, the temperature of concrete around the anchor is higher than in the rest of the specimen. It was obtained that after cooling of the upper concrete surface almost down to the room temperature, in the mid of the concrete specimen the temperature is still around 300°C. Calculated load-displacement curves for all three embedment depths and for four thermal loading histories are plotted in Figure 12. The relative resistance is obtained as a ratio between the calculated resistance and the pull-out resistance of unheated concrete. In Figure 13 is for all three embedment depths and for all loading histories plotted the relative anchor resistance as a function of the embedment depth (Fig. 13a) and the relative anchor resistance as a function of time (Fig. 13b). In Figure 13a are also for third loading history shown the available test data [28]. It can be seen that the numerical results fit very good the experimental results. a)
b) 100
10
8
FU=5.8 kN
6
4
FU>88.4 kN
80
Load [kN]
Load [kN]
FU=88.4 kN
Embedment depth hef=25 mm Load history: i ii iii iv
FU=8.7 kN
FU=3.3 kN
60 FU=42.5 kN
FU=39.6 kN 40
Embedment depth hef=100 mm Load history: i ii iii iv
20
2 FU=1.5 kN
0
0 0
0.5
1
1.5
2
2.5
3
3.5
0
4
5
10
15
20
25
30
Displacement [mm]
Displacement [mm]
Fig. 12 - Calculated typical load-displacement curves for all four load histories with embedment depths: (a) hef = 25 mm and (b) hef = 100 mm
To investigate the pull-out resistance of the anchor, the anchor was pulled out from the concrete block for the following load histories: (i) before heating (ii) 30 minutes after start of heating, (iii) 90 minutes after start of heating and (iv) after 90 minutes of heating followed by 90 minutes of cooling back to the air temperature of 20°C. In all four cases the anchors were pre-loaded by design load (hef = 25 mm, PD = 1.5 kN; . hef = 50 mm, PD = 5.7 kN; hef = 100 mm, PD = 16.2 kN). As expected, due to damage caused by thermal loading history the pull-out resistance of the headed stud anchors is significantly reduced. It can be seen that with increase of temperature the peak load and stiffness of the anchors decrease. Moreover, displacement at peak load significantly increases if the concrete member was exposed to fire. Compared to the initial resistance at t = 0 and TAir = 20°C, the largest reduction of the ultimate load is obtained for the smallest embedment depth (hef = 25 mm) and for the forth thermal loading history (90 min. heating followed by 90 min.
195
cooling). However, this does not hold for all embedment depths. As can be seen from Figure 13, the pull-out behavior of anchors with hef = 100 mm shows somewhat different behavior than that of smaller anchors. Namely, for second and third load history (heating) there is strong reduction of the pull-out capacity, however, in case of cooling the relative pull-out resistance of the anchor with hef = 100 mm is even greater than one i.e. there is no reduction. a)
b) 1
>1
Load history: (ii) : (iii) : (iv) Experimental data, Reick (2001)
0.8
Relative resistance PU/PU (t=0)
Relative resistance PU/PU,t=0
1
0.6
0.4
0.2
0
Heating
Cooling
0.8
0.6
0.4
hef=25 hef=50 hef=100 Experimental data, Reick (2001)
0.2
0 0
20
40
60
80
100
120
0
Embedment depth [mm]
30
60
90
120
150
180
Time [min]
Fig. 13 - Relative pull-out resistance: (a) as a function of embedment depth and (b) as a
function of temperature For relatively small embedment depths the anchor lies over the entire length in the zone of very high temperature in which the concrete is almost completely destroyed. Extreme cases are observed for embedment depths hef = 25 and 50 mm and for the forth loading history. For these cases the ultimate pull-out capacity is smaller then the initially applied design load (see Figs. 13 a,b) i.e. the anchors failed during cooling. The reasons is the existence of large thermal strains, which are partly irreversible, and which in restrained concrete member generated tensile stresses and damage. This damage together with degradation of concrete mechanical properties due to high temperature cause stronger reduction of the pull-out resistance. When the embedment depth is relatively to the thickness of the concrete member large, than the head of the stud lies in the zone of lower temperature in which the concrete is less damaged. Moreover, due to the restraining conditions and large thermal strains it is possible that the head comes into the zone in which the stresses perpendicular to the axis of the stud are compressive. Such a situation contributes to lower reduction of the pull-out resistance or even, as in the present case, to the relative resistance larger than one. a)
b)
0.01
0.00833
0.00667
0.005
0.00333
0.00167
0. Z Y
Z X
Y
X
Fig. 14 - Typical crack patterns for hef = 50 mm: (a) unheated specimen; (b) specimen exposed 90 min. to fire (loading history (iii)) - concrete cone
In Figure 14a is shown a typical crack pattern (maximal principal strains of the mechanical strain tensor) for unheated concrete member (hef = 50 mm). Figure 14b shows a typical failure cone (hef = 50 mm) pulled out from the heated concrete member (third loading history). As can be seen,
196
for unheated specimen a typical concrete cone forms. The crack starts from the head of the stud and propagates under an average angle of 35°, measured to the horizontal line. On the contrary, for the heated specimen the angle of the crack propagation close to the anchor head is rather steep. As it approaches the concrete surface, where the concrete is completely destroyed, the crack becomes almost horizontal. This observation is in very good agreement with the experimental evidence.
7. Conclusions In the present paper a transient three-dimensional thermo-mechanical model for concrete is presented. For a given boundary conditions, the temperature distribution is calculated by the threedimensional transient thermal finite element analysis using direct integration method. The thermal properties of concrete are assumed to be constant and independent of the stress-strain distribution. In the thermo-mechanical model the total strain is decomposed into pure mechanical strain, free thermal strain and load induced thermal strain. The mechanical strain components are calculated based on the temperature dependent microplane model for concrete [1]. The dependency between the macroscopic concrete properties (Young’s modulus, tensile & compressive strength and fracture energy) is taken from the available experimental data base. The free thermal strain, which is stress independent, is calculated following the proposal of Nielsen et al. [2]. The bi-parabolic model proposed by Nielsen et al. [3] is used for the prediction of the load induced thermal strain. It is assumed that the total load induced thermal strain is irrecoverable i.e. creep component is neglected. The model is implemented into a three-dimensional FE code. To check the model and its implementation two examples taken from the literature were analyzed. In the first the load independent and the load dependent thermal strains were predicted. In the second example the thermal induced stresses were calculated. In both cases the model prediction agrees well with the experimental data. Subsequently, the performance of headed stud anchors under fire was investigated. For a given geometry of the concrete member and for a constant concrete properties three-dimensional transient thermal FE analysis was carried out for three embedment depths and for four thermal load histories. The analysis shows that the resistance of anchors can be significantly reduced if they are exposed to fire. The largest reduction of the load capacity is obtained for anchors with relatively small embedment depth. This is especially thru if the concrete member is first exposed to fire and than cooled down. In such a case for small embedment depth the anchor resistance is even smaller than design load. These results agree well with the experiments. Anchors with larger embedment depth behave somewhat differently. By the heating of concrete the resistance is generally decreasing, however, when the concrete member is heated and than cooled down, than the resistance can increase and it can even be larger than the resistance of the anchor in unheated concrete. Up to which embedment depth this will be the case in usual fire conditions is very much dependent on the thickness of the concrete member. Moreover, the behavior of anchors under fire conditions depends also on the material and geometrical properties of concrete and steel. Obviously, further studies are needed to investigate the problem in more detail. Finally, it can be concluded that the presented, relatively simple, model is a powerful numerical tool which can be used to clarify the behavior of a number of structures and structural details exposed to fire.
8. References [1] [2] [3] [4] [5]
OŽBOLT J., LI Y.-J., and KOŽAR I., “Microplane model for concrete with relaxed kinematic constraint”, International Journal of Solids and Structures, Vol. 38, 2001, pp. 2683-2711. NIELSEN C.V., PEARCE C.J., and BIûANIû N., “Theoretical model of high temperature effects on uniaxial concrete member under elastic restraint”, Magazine of Concrete and Research, Vol. 54, No. 4, 2001. NIELSEN C.V., PEARCE C.J., and BIûANIû N., “Constitutive model of transient thermal strains for concrete at high temperatures”, Submitted to Journal of Engineering Mechanic, 2002. BAŽANT Z.P., and KAPLAN M.F., Concrete at High Temperatures: Material Properties and Mathematical Models, Harlow, Longman, 1996. KHOURY G.A., GRAINGER B.N., and SULLIVAN P.J.E., “Transient thermal strain of concrete: literature review, conditions within specimens and behaviour of individual constituents”, Magazine of concrete research, Vol. 37, No. 132, 1985a.
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[6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]
SCHNEIDER U., Properties of Materials at High Temperatures, Concrete, 2nd. Edition, Kassel, RILEM Technical Comitee 44-PHT, Technical University of Kassel, 1986. SCHNEIDER U., “Concrete at High Temperatures – A General Review”, Fire Safety Journal, Vol. 13, 1988. THELANDERSSON S., “Modelling of combined thermal and mechanical action in concrete”, Journal of Engineered Mechanics, Vol. 113, No. 6, 1987. GAWIN D., MAJORANA C.E., and SCHREFLER B.A., „Numerical Analisys of hygrothermal behaviour and damage of concrete at high temperatures”, Mech. Cohes.-Frict. Mater., Vol. 4, 1999. PEARCE C.J., BIûANIû N., and NIELSEN C.V., “A transient thermal creep model for concrete”, Computational Modeling of Concrete Structures, Lisse, Sweets & Zeitlinger, 2003. STABLER J., Computational modelling of thermomechanical damage and plasticity in concrete, PhD thesis, Brisbane, The University of Queensland, 2000. TERRO M.J., “Numerical modelling of the behaviour of concrete structures in fire”, ACI Structures Journal, Vol. 95, No. 2, 1998. BELYTSCHKO T., LIU W.K., and MORAN B., Nonlinear Finite Elements for Continua and Structures, John Wiley & Sons Ltd, 2001. COOK R.D., MALKUS D.S., PLESHA M.E., and WITT R.J., Concepts and Applications of Finite Element Analysis, 4th edition, John Wiley & Sons Inc, 2002. TAYLOR G.I., “Plastic strain in metals”, Journal of the Institute of Metals, Vol. 62, 1938, pp. 307-324. BATDORF S.B., and BUDIANSKI B., “A mathematical theory of plasticity based on the concept of slip”, Technical Note No. 1871, Washington D.C., National Advisory Committee for Aeronautics, 1949. BAŽANT Z.P., and PRAT P.C., “Microplane model for brittle-plastic material - parts I and II”, Journal of Engineering Mechanics, Vol. 114, 1988, pp. 1672-1702. BAŽANT Z.P., and OŽBOLT J., “Nonlocal microplane model for fracture, damage and size effect in structures”, Journal of Engineering Mechanics 116(11), 1990, pp. 2485-2504. BAŽANT Z.P., CAROL I., and JIRÁSEK M., “A thermodynamically consistent approach to microplane theory: Part I - Free energy and consistent microplane stress”, International Journal of Solids and Structures, Vol. 38, 2001, pp. 2921-2931. THELANDERSSON S., “On the multiaxial behaviour of concrete exposed to high temperature”, Nuclear Engineering and Design, Vol. 75, 1982. ABRAMS M.S., “Compressive strength of concrete at temperatures to 1600F”, ACI SP 25, Temperature and Concrete, Detroit, American Concrete Institute, 1971. BIûANIû N., and ZHANG B., “Residual Fracture Toughness of Normal- and High-Strength Gravel Concrete after Heating to 600°C”, ACI Materials Journal, Vol. 99, No 3, 2002. BAŽANT Z.P., and CHERN J.C., “Stress-induced thermal and shrinkage strains in Concrete”, Journal of Engineering Mechanics, Vol. 113, No. 10, 1987. KHOURY G.A., GRAINGER B.N., and SULLIVAN P.J.E., “Strain of concrete during first heating to 600°C under load”, Magazine of concrete research, Vol. 37, No. 133, 1985b. THIENEL K.-C., Festigkeit und Verformung von Beton bei hoher Temperatur und biaxialer Beanspruchung – Versuche und Modellbildung, PhD thesis, Band 10, Braunschweig, IBMB, TU Braunschweig, 1993. THIENEL K.-C., and ROSTASSY F.S., “Transient creep of concrete under biaxial stress and high temperature”, Cement and Concrete Research, Vol. 26, No. 9, 1996. EHM C., Versuche zur Festigkeit und Verformung von Beton unter zweiaxialer Beanspruchung und hohen Temperaturen, PhD thesis, Band 71, Braunschweig, IBMB, TU Braunschweig, 1986. REICK M., Brandverhalten von Befestigungen mit großem Randabstand in Beton bei zentrischer Zugbeanspruchung, Mitteilungen des Institut für Werkstoffe im Bauwesen, Band 2001/4, Stuttgart, IWB, Universität Stuttgart, 2001.
198
Preliminary Pull-Out Tests on Post-Installed Mechanical Fasteners Embedded in Thermally-Damaged Concrete Patrick BAMONTE PhD Candidate Dept. of Struc. Engineering Milan Univ. of Technology Milan, Italy
Pietro G. GAMBAROVA Professor Dept. of Struc. Engineering Milan Univ. of Technology Milan, Italy
Lorenzo D’AGOSTINO MS Engineer Milan Univ. of Technology Milan, Italy
Alessandro GENONI MS Engineer Milan Univ. of Technology Milan, Italy
Summary Metallic, post-installed, undercut fasteners of medium capacity are experimentally investigated in this research project, in order to have badly-needed information on their behavior after being installed in thermally-damaged concrete. The project aims also (a) to work out relatively-simple limit-analysis models for the description of fastener failure due to concrete fracture; and (b) to formulate a viable experimental procedure to simulate the high thermal gradients ensuing from the standard fire, by means of the much lower gradients obtained in electric furnaces. Twenty fasteners of a single diameter (nominal stem diameter 10 mm) were fixed to as many thermally-damaged concrete blocks, simulating 5 values of the fire duration, and the ultimate capacity turned out to be a linearly-decreasing function of the temperature reached underneath the head of the fasteners. So far, an ordinary high-grade concrete has been used (fc = 50-55 MPa), but further tests are in progress with a low-grade concrete (fc = 25 MPa) and a high-performance concrete (fc = 75 MPa). Keywords:
1.
concrete, undercut fasteners, high temperature, residual behavior, Concrete-Cone method.
Introduction and research significance
The ever-increasing use of structural unions based on metallic fasteners anchored to concrete members nowadays characterizes not only building engineering, whenever prefabricated members have to be assembled, but also industrial engineering, whenever pipes, fittings, lighting devices, blowers, machines and electrical equipments have to be fixed to a concrete wall. Two groups of metallic fasteners are commonly acknowledged: pre- and post-installed fasteners, depending on whether they are installed before or after concreting. Among the latter, there is a further subdivision in four types: adhesive, grouted, expansion and undercut (CEB, 1994 and 1997; ACI, 2001 [1-3]). Pre-installed fasteners are extensively used in prefabrication and their technology is close to that of ordinary reinforcing bars. On the contrary, post-installed fasteners require some specific working, since a hole has to be drilled to install each fastener. Then (a) the hole has to be filled with glue or mortar (adhesive and grouted fasteners), (b) the lateral surface of the fastener (“expansion sleeve”) is forced to expand against the sides of the drilled hole, by applying a controlled torque (expansion fasteners), and (c) the head of the fastener is forced to create an undercut in the hole sides or to expand into a predrilled undercut, by applying a controlled displacement to the head cone of the fastener (undercut fasteners, Cook et al., 1992, [4], Fig. 1). While the mechanical response at room temperature of post-installed fasteners has been studied for a long time (see also Eligehausen and Ozbolt, 1998 [5]), very limited attention has been devoted so far to high temperature and fire (Reick, 2001; Eligehausen et al., 2002 [6-7]), probably on the assumption that concrete itself has good insulating properties. This is true on the whole, but a prolonged fire may induce a sizable in-depth damage in the concrete, and fastener capacity may be substantially reduced in either of the two following cases: the fastener has been fixed (a) before the fire, when the concrete was undamaged, or (b) after the fire, when the concrete had undergone some damage.
199
(a)
(b)
(c)
(d)
(e)
predrilled undercut
non-predrilled undercut
adhesive
grouted
expansion
Fig. 1 - Various types of post-installed fasteners or anchors: (a, b) undercut, with/without predrilled undercut; (c) adhesive; (d) grouted; and (e) expansion; (a, b, e) mechanical fasteners. Within this context, the objective of this research project is to investigate to what extent thermallydamaged concrete affects the mechanical response of post-installed fasteners after a fire, the attention being limited to undercut devices, whose failure generally ensues from concrete fracture (“breakout failure”, with the formation of a typical “concrete cone”). Even if expansion fasteners are more extensively used, undercut fasteners have a better performance under and after a fire, since for the same nominal depth of the drilled hole undercut fasteners have a larger effective depth (Figs. 1a,b); as a result, the point where the load is transferred is farther from the heated surface, with less concrete damage. Other types of fasteners are not considered for a variety of reasons. Expansion fastenings generally fail in a more complex and unpredictable mode, because of the slip of the fastening (“pull-through failure”), often accompanied by a partial concrete fracture (“pullout failure”, CEB, 1994 [1]; Cattaneo and Guerrini, 2004 [8]). Adhesive and grouted fastenings are characterized by the key role of the glue and of the mortar, whose failure may be followed by concrete fracture. In all cases, the yielding of the shank, the lateral bursting of the concrete and the splitting of the cover cannot be ruled out, since these failure modes are likely to occur, the first when concrete is lightly damaged (e.g. the fire has a limited duration), the second and the third when the fastener is close to a free surface, and the third also when fasteners are too close. In all three cases, the full concrete capacity is not developed. Finally, limiting the attention to the residual capacity of a fastener greatly simplifies the tests (that are carried out at room temperature), without altering the nature of concrete damage, that mostly depends on the maximum temperature reached during the heating process (RILEM, 1985; Felicetti and Gambarova, 1998; Phan and Carino, 2001; Cheng et al., 2004 [9-12]). As a consequence, the residual capacity of a fastener is a good indication of its high-temperature capacity.
2.
Experimental program
As already mentioned, this project refers to non-predrilled, undercut medium fasteners, that are an interesting case in terms of fire-sensitivity and pull-out capacity, since large fasteners exhibit less damage in the concrete for any reasonable fire duration (due to their larger depth), and small fasteners are of less importance, because of their limited capacity. A single diameter was considered (nominal diameter of the shank N = 10 mm; net diameter = 8.6 mm; outside diameter of the embedded body do = 18 mm; suggested nominal depth of the drilled hole hN = 10N = 100 mm, Fig. 2). The residual capacity was investigated, after heating a number of concrete blocks (Figs. 3 and 4) in order to simulate different values of the fire duration. The holes were drilled after cooling the concrete blocks to room temperature, and then the fasteners were fixed to the damaged concrete. As a rule, the effective depth of the fasteners was limited to 80% of the suggested nominal depth, in order to increase the thermal effects and to simulate the actual situation ensuing from concrete spalling at high temperature (see the last paragraph of Test Results). In each test, reference was made to the temperature reached at the effective depth (depth of fastener head): 200, 250, 300, 350 200
and 400°C at 80 mm from the heated surface (Fig. 5). The thermal analyses were carried out by means of the ABAQUS code, taking advantage of the diffusivity measured in the early phase of this project (Fig. 6).
hN ∅N Fig. 2 - Typical post-installed mechanical fastener, with non-predrilled undercut. 200 400 15
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Fig. 3 - Side view and back view of a concrete block fixed to the furnace mouth and provided with 3 thermocouples (block No. 10), to monitor the temperature build-up during the heating process. Concrete: fc = 52 MPa, c = 383 kg/m3, w/c = 0.50, siliceous aggregates. 800
temperature [°C]
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time [h] Fig. 4 - Temperature build-up, as measured by the 3 thermocouples inserted in the concrete block and by the thermocouple of the furnace.
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400°C dT/dt = 1°C/min (T ≤ 750°C) ISO 834
70
y [mm]
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T [°C] 200 250 300 350 400
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ISO834 85' 110' 135' 165' 200'
this study 585' 665' 845' 1090' 1330'
y
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temperature [°C]
Fig. 5 - Temperature profiles evaluated with ABAQUS, in accordance with the thermal ramp adopted in this project and with the standard fire ISO 834. Note that for the same final temperatures at the effective depth h = 80 mm, the duration of the heating process is very different (see Table). 1.2 this study EC2 upper bound EC2 lower bound
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6
D x 10 [m /s]
1
0.6 0.4 0.2 0 0
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400
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temperature [°C] Fig. 6 - Plot of the thermal diffusivity of the concrete adopted in this project (fc = 52 MPa). The maximum temperature reached during the tests was limited to 750°C, in order to avoid concrete calcination after the cooling process. A preliminary test, with the front surface of the concrete block heated at the maximum heating rate allowed by the furnace, came to an end because of the explosive spalling of most of the front surface (vh = 10°C/min’ for T = 20-300°C, and down to 3°C/min’ for T = 300-750°C, one order of magnitude less than in standard fire). As a consequence, in the routine tests a much lower heating rate was adopted (vh = 1°C/min’, Fig. 4). On the whole, twenty pull-out tests were performed on as many concrete blocks: x
5 preliminary tests at 20°C (virgin material, fc = 40 MPa): 2 unsuccessful tests for lack of grip in the concrete – mixed failure (fastener slip and concrete fracture); 2 tests with h = 0.70 hN = 70 mm - conical fracture in the concrete (for the calibration of the C-C Method); 1 test with h = hN = 100 mm - yielding of the shank.
x
1test at high heating rate (fc = 52 MPa in the virgin material): gone awry because of concrete spalling.
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x
2 tests at 20°C (virgin material, fc = 52 MPa): h = 0.70 hN = 70 mm - conical fracture in the first test and shank yielding in the second test (very close pullout loads).
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10 tests after heating the blocks to 200, 250, 300, 350 and 400°C at 80 mm from the heated surface: h = 0.80 hN = 80 mm – conical fracture in the concrete; each pullout test was repeated twice and the repeatability was remarkable indeed (fc = 52 MPa at 20°C, virgin material).
x
2 tests after heating the blocks to 300 and 400°C at 80 mm from the heated surface: h = hN = 100 mm – conical fracture in the concrete (fc = 52 MPa at 20°C, virgin material).
(b)
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temperature [°C]
loading ring
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Fig. 7 - (a) Loading set-up; (b) tduced concrete damage; and (c) specimen geometry.. The pull-out tests were performed by means of a simple steel rig (Fig. 7), consisting of a loading ring , three inclined legs, a reaction plate and a hydraulic actuator. One LVDT was used to measure the displacement of the fastener, and to control the test (all tests were displacement - controlled, with 'G/'t = 0.5 mm/min’).
1.
Test results
The core of the tests results is represented by the 10 tests carried out after heating the concrete blocks to 200, 250, 300, 350 and 400°C at 80 mm from the heated surface. As already mentioned, the 2 tests performed in each case gave very similar results, in terms of fastener capacity and loaddisplacement curve, as shown in Fig. 8a in the case T = 250°C. In general, a clear-cut conical fracture occurred (Fig. 8b), with/without thin radial cracks along the loaded block extremity. Five typical load-displacement curves are shown in Fig. 9. Both the peak load (= ultimate capacity) and the shape of the curve are markedly affected by the temperature field represented by the temperature reached at the effective depth. The peak load substantially decreases with the temperature and the softening branch becomes more regular and less steep.
203
Fig. 8 - Load-displacement curves – T = 250°C at h = 80 mm, fc = 52 MPa : Tests BI-4-250A and BI-7-250A. Views of the conical fracture of specimen BI-7-250A in the insert. 50
load [kN]
40
BI-4-200B BI-4-250A
30
BI-5-300A 20
BI-6-350A
10 BI-10-400A 0 0
5
10
15
displacement [mm] Fig. 9 - Typical load-displacement curves, for 5 different values of the temperature reached at the effective depth h = 80 mm. In Fig. 10, the peak loads measured in the 15 successful tests exhibiting a conical fracture, and in the 2 tests characterized by the yielding of the shank are indicated (x, ' and + for fc = 52 MPa). The 3 tests with reduced effective depth (h = 0.70 hN = 70 mm, fc = 40 and 52 MPa, symbols R and ') were instrumental in evaluating the “virtual” peak load at 20°C (virgin materials) associated with concrete fracture, since in this situation shank yielding always controls fastener failure. In the so-called Concrete-Cone Method (C-C Method, CEB, 1994 [1]) the peak load - or ultimate capacity - has the following, well-known formulation: Pu = k fc 0.5 h1.5 20
(1)
where fc = fc and k is a parameter whose value depends on fastener type (k = 10.9 in authors’ tests with h = 70 mm and N = 10 mm). Because of its reliability, the C-C Method was used to evaluate the peak loads for h = 80 and 100 mm (symbols and u in Fig. 10). What appears very clearly is that (a) the peak load tends to be a linearly-decreasing function of the temperature reached at the effective depth (be it 80% or 100% of the depth suggested by the producer), and (b) the failure mode is markedly affected by the temperature, since at low-medium temperatures the limiting factor is shank yielding (below 100°C and 300°C for h = 0.80 hN and 1.00 hN respectively), while at medium-high temperatures fastener failure is controlled by concrete fracture.
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peak load Pu [kN]
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+
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60
*
45
shank yielding
30
+
15 0 0
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T [°C] at the effective depth h = 80 mm Fig. 10 - Peak loads of the fastening tested in this project - Concrete failure fc = 52 MPa : (x, +) h = 80 mm, () h = 100 mm, () h = 70 mm; fc = 40 MPa : (R) h = 70 mm; steel failure : ( ) fc = 52 MPa, h = 70 mm; (¡) fc = 40 MPa, h = 100 mm; C-C Method: ( ) h = 80 mm, (u) h = 100 mm. In Fig. 11 the values of the peak load are put in a dimensionless form (PuT/Pu20). It appears that the capacity can be represented by means of straight lines radiating from the capacity at 20°C. In Fig. 12, for h = 80 mm, the test results are compared with those predicted by the C-C Method. The thick and dashed curves are based on the compressive strengths corresponding to the temperature at the effective depth in the former case, and to the mean temperature along the fracture surface in the latter case (the fracture surface is here described by means of a 2nd-order parabola). In both cases, the C-C Method is unable to describe the mechanical decay of the fasteners, which has to do more with concrete decay in tension than in compression. (It is well known that concrete tensile strength is more affected by high temperatures, than the compressive strength).
1.4 h/hN = 0.8 h/hN = 1.0
1.2
test results C-C method
1
PuT/Pu 20 , Puy /Pu
20
shank yielding
0.8 shank yielding
0.6 0.4
hN = 10∅N = 100 mm
0.2 0 0
50
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250
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350
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450
T [°C] at the effective depth h = 80 mm Fig. 11 - Test results put in a dimensionless form : PuT/Pu20 and Puy20/Pu20.
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peak load Pu [kN]
90
test results C-C method C-C method (T at h = 80 mm) C-C method (mean value for T)
75 60 45
shank yielding
30 15 0 0
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250
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350
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450
T [°C] at the effective depth h = 80 mm Fig. 12 - Test results versus C-C Method (thick and dashed curves, h = 80 mm): thick curve concrete strength at the temperature at the effective depth; and dashed curve concrete strength at the mean temperature along the fracture surface. Finally, a preliminary answer to the question to what extent the capacity measured under low heating rates (as in the tests performed in this project) is overestimated compared to that under high heating rates (as in a standard fire) comes from a limit-analysis model, whose development is still in progress (D’Agostino and Genoni, 2004 [13]). In the range T = 200-400°C (at the effective depth of 80 mm) the capacity under the standard fire ISO 834 is 25-30% less than in the tests performed so far, as shown in Fig. 13. Once the model is fully checked against the test results and becomes operational, it will be possible to evaluate fastener capacity and to plot it as a function of fire duration, for any type of fire and concrete thermal properties.
peak load Pu [kN]
90
heating
spalling
refurbishing
75
h hN
60
concrete layer shank yielding
45
dT/dt = 1°C/min (T ≤ 750°C)
30
ISO 834
15 0 0
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T [°C] at the effective depth h = 80 mm Fig. 13 - Plots of the ultimate capacity for two different heating processes: thin curve slow heating ('T/'t = 1°C/min’, T d 750°C, this project); and thick curve ISO 834. Going back to Fig. 13, the insert gives an explanation why considering a reduced effective depth (as in this project, 80% of the nominal depth suggested by the producer) is reasonable for a fastener after a fire. Because of the high thermal gradients during the fire, concrete spalling is a likely occurrence, and after the fire the original geometry has to be reestablished, by casting a new layer of concrete. Since the newly-cast concrete cannot be fully relied on, it is like having a reduced-
206
depth fastener, even if the hole of the fastener has been drilled in accordance with the nominal depth. Note that the two curves shown in Fig. 13 were obtained by means of the limit-analysis model developed by D’Agostino and Genoni (2004) [13].
4. x x
x
Concluding remarks Post-installed mechanical undercut fastener exhibit a strong temperature sensitivity, since their residual ultimate capacity appears to be a linearly-descending function of the temperature reached at the effective depth during the heating process. The residual ultimate capacity markedly depends on the effective depth, since the deeper the drilled hole, the less damaged the concrete and the more efficient the fastener, whose capacity is limited by the yielding of the shank at low-medium values of the fire duration: for example, in a medium-capacity anchor (N = 10 mm) 100°C at the effective depth of 8N turns the failure mode from shank yielding to concrete fracture, while the same occurs at 300°C at the effective depth of 10N. The C-C Method - extensively used and very reliable when fasteners are installed in virgin concrete – tends to grossly overevaluate fastener residual capacity, if concrete compressive strength is given the value corresponding to the temperature reached at the effective depth or to the mean thermal field between the head of the fastener and the heated surface.
x
There is a strong correlation between the residual capacity after a relatively slow heating process (typical of the electric furnaces used in a laboratory) and the fast heating process of the standard fire. However, slow heating processes are instrumental in avoiding concrete spalling.
x
In a lab, the thermal process should always be monitored, in order to check the “reference” parameter (the temperature at the effective depth in this study), and the thermal properties should always be evaluated, to improve the numerical analysis of the thermal field (concrete diffusivity was evaluated in this study, on the basis of the local values of the temperature).
Acknowledgements The financial support by Italcementi Group – C.T.G. (Bergamo, Italy) is gratefully acknowledged, under the supervision of CIS-E (Constructions and Structural Engineering in Europe – Milan, Italy). Special thanks should be conveyed to MS Eng. Gian Luca Guerrini of Italcementi - C.T.G. for his valuable suggestions on the organization of the experimental activity.
References [1] [2] [3] [4]
[5]
[6]
CEB, “Fastenings to Concrete and Masonry Structures”, State-of-the-Art Report, Bulletin d’Information No. 216, Thomas Telford Ed., London, 1994, 249 pp. CEB, “Design of Fastenings in Concrete”, Design Guide – Parts 1,2,3, Bulletin d’Information No. 233, Thomas Telford Ed., London, 1997, 83 pp. ACI, “Evaluating the Performance of Post-Installed Mechanical Fasteners in Concrete and Commentary”, ACI 355.2/ACI 355.2R, Concrete International, February 2001, pp. 106-136. COOK R.A., COLLINS D.M., KLINGNER R.E. and POLYZOIS D., “Load-Deflection Behavior of Cast-in-Place and Retrofit Concrete Anchors”, ACI Structural Journal, Technical Paper Vol. 89, No. 6, 1992, pp. 639-649. ELIGEHAUSEN R., and OZBOLT J., “Size Effect in Design of Fastenings”, Special Volume on “Mechanics of Quasi-Brittle Materials and Structures”, HERMES (Paris, France), 1998, pp. 95-118. REICK M., “Brandverhalten von Befestigungen mit grossen Randabstand in Beton bei zentrischer Zugbeanspruchung” (Fire Behavior of Fasteners Embedded in a Concrete Mass
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and Subjected to a Pull-out Force), PhD Dissertation, News of the Dept. of Building Materials - IWB, V.2001/4, University of Stuttgart, 2001, 166 pp. [7] ELIGEHAUSEN R., KOZAR J., OZBOLT J. and PERIKSIC G., “Transient Thermal 3-D FE Analysis of Headed Stud Anchors Exposed to Fire”, private communication, 2002. [8] CATTANEO S. and GUERRINI G., “Mechanical Fasteners Installed in High-Performance, Fiber-Reinforced Concrete” (in Italian), Nat. Conf. of the Italian Society for R/C and P/C Structures – AICAP, Verona (Italy), May 26-29, 2004, pp. 101-112. [9] RILEM-Commitee 44-PHT, “Behavior of Concrete at High Temperatures”, Ed. by U. Schneider, Department of Civil Engineering, Gesamthochschule Kassel, Kassel (Germany), 1985, 122 pp. [10] FELICETTI R., and GAMBAROVA P.G., “Effects of High Temperature on the Residual Compressive Strength of High-Strength Siliceous Concretes”, ACI Materials Journal, Technical Paper Vol. 95, No. 4, 1998, pp. 395-406. [11] PHAN L.T., and CARINO N.J., “Effects of Test Conditions and Mixture proportions on Behavior of High-Strength Concrete Exposed to High Temperatures”, ACI Materials Journal, Vol. 99, No. 1, 2002, pp. 54-66. [12] CHENG F.P., KODUR V.K.R. and WANG T.C., “Stress-Strain Curves for High Strength Concrete at Elevated Temperatures”, ASCE Journal of Materials in Civil Engineering, Vol. 16, No. 1, 2004, pp. 84-90. [13] D’AGOSTINO L., and GENONI A., “On the behavior of mechanical fasteners installed in fire-damaged concrete members” (in Italian), MS Dissertation, Milan University of Technology, October 2004, 345 pp.
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Session 5 Assessment after Fire and Structural Repair
Digital Camera Colorimetry for the Assessment of Fire-Damaged Concrete Roberto Felicetti*
Page 211
Petrografic Analysis of Fire-Damaged Concrete Neil Short and John Purkiss* Damage Assessment in Actual Fire Situations by Means of Non-Destructive Techniques and Concrete Tests Andrea Benedetti and Enrico Mangoni The Drilling-Resistance Test for the Assessment of the Thermal Damage in Concrete Roberto Felicetti
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Digital Camera Colorimetry for the Assessment of Fire-Damaged Concrete
Roberto FELICETTI Associate Professor DIS - Politecnico di Milano Milan, ITALY
Summary In this paper a new colour measurement technique is presented, aimed at objectively detecting the slight colour change that usually takes place in concrete heated above 400°C. Contrary to some recent proposals available in the literature, this method is based on a common low-cost digital camera and no demanding sample preparation nor expensive laboratory equipment are needed. An appropriate procedure for the digital image processing has been defined in order to better control the effect of the inherent material heterogeneity. Finally, the tests on a couple of concrete panels subjected to strong thermal gradients allowed to ascertain the benefits of this approach in the assessment of damage within structural members exposed to fire. Keywords: colorimetry; concrete damage; material assessment; Non-Destructive Testing (NDT); residual properties.
1. Introduction Concrete is known to undergo several chemo-physical transformations at increasing temperature: the physically combined water is released above 100°C; the silicate hydrates decompose above 300°C and the portlandite dehydrates above 500°C; some aggregates begin to convert or to decompose at temperatures above 600 °C (D-E SiO2-conversion, decomposition of limestone). The mechanical response of the material is weakened concurrently and the compressive strength is usually expected to be reduced slowly below 450-500°C and rapidly above 500°C [1]. Assessing this more or less pronounced material weakening is quite a difficult task, because very strong thermal gradients are experienced by the structural members during a fire and the thermal damage is likely to decrease from a maximum to nil within a few centimetres depth. The problem is further emphasized by the wide range of possible fire scenarios and material thermal and mechanical properties at issue [2]. Besides the strength decay, several noticeable effects can be ascertained with direct visual observation of the structural member surface: cracking, spalling, vitrification and colour change. Concerning this latter property, the colour of concrete generally changes at increasing temperature from normal to pink or red (300-600°C), whitish grey (600-900°C) and buff (900-1000°C). The pink-red discolouration ensues from the presence of iron compounds in the fine or coarse aggregate, which dehydrate or oxidise in this temperature range. The strength of this colour change depends on the aggregate type and it is more pronounced for siliceous aggregates and less so for calcareous and igneous aggregates [3]. Detecting this first colour alteration is of great interest because its appearance usually coincides with the onset of a significant loss of concrete strength as a result of heating. Recently, some authors showed that a closer and more objective inspection of the colour changes in heated concrete can be viably achieved by means of the modern colour measurement systems. In a study on the effects of fire in the Mont Blanc Tunnel [4] a colorimeter has been directly applied onto the surface of the concrete samples, showing a good correlation between the colour measure and the maximum experienced temperature (Fig. 1). This type of instrument usually 211
performs an average measurement on a small spot (about 10 mm diameter). Hence some attention is necessary to control the possible influence of the coarse aggregate. In this example, the chromatic alteration of concrete has been expressed in the CIE Lab 1976 colour system, involving three simultaneously varying parameters (L, a, b) in the analysis of the results. By repeating the measurements on the thin slices cut from a concrete core (Fig. 2) the thermal damage profile within a structural member can finally be detected. Another interesting application of colorimetry to heated concrete is based on a optical microscope combined with a digital image analysis workstation [3]. Thanks to optical magnification and image resolution, a point by point examination of the material constituents and the outline of the colour profiles are possible. This advantage comes at the price of an accurate preparation of the samples, which are preliminarily impregnated with a colourless resin and then cut, ground and polished for the examination in reflected light. The most interesting outcome of the cited work is that expressing the colour measure in terms of hue, saturation and intensity (HSI colour space) allows to recognize that only the first parameter seems to be sizeably affected by high temperature and therefore is worth of being considered in the material investigation (Fig. 3). Following the above encouraging results, the aim of the present work is to ascertaining whether a similar analysis can be performed by simply taking a picture of the concrete samples via a common low-cost digital camera and by properly processing the resulting image file. In principle, the following advantages are to be expected from this method:
Fig. 1 - Concrete colour change after heating (Mont Blanc tunnel lining [4] - CIE Lab 1976 system - initial colour L0, a0, b0 not indicated).
Fig. 2 - Sliced concrete core to outline the colour profile in a fire damaged structure [4].
Fig. 3 - Hue alteration for different concrete mixes after heating (hue level = 0÷255) [3].
x x
no special preparation of the concrete sample is needed and a fast in-situ analysis is feasible; the whole colour profile can be reconstructed from one side picture of a concrete core;
x x
the cement mortar and the aggregate can be recognized on the picture and analyzed separately; the method is based on a commonly available low-cost device.
Even if only a fair accuracy of the colour measure is likely to be obtained, the basic idea supporting this approach is that just the colour change from virgin to heated concrete is of prime interest for this application, rather than an absolute and accurate evaluation of the colorimetric parameters.
2. A brief introduction to colorimetry The concepts involved in understanding colour and its measurement are complex [5, 6] and only the basic notions will be recalled, which are functional to the scopes of this work. The colour radiating from the opaque surface of a body is the combined effect of the spectral power distribution of the light striking the surface (the radiation power at each wavelength O) and of
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spectral power distribution S(O) (% relative to O = 560 nm)
illuminant
human eye's colour receptors
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spectral radiance of the sample
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Fig. 4 - Colour formation as a result of the spectral power distribution of the illuminant and the reflectance of the colour sample and definition of a colour space through a set of three colour matching functions [5, 6]. the reflectance factor of the body (the amount of light that is reflected at each wavelength - Fig. 4). The product of these two functions yields the power of the light reflected by the opaque surface (the spectral radiance), which can be measured in the whole spectrum by means of a spectrophotometer. In effect, the colour sensitive receptors in the human-eye retina (long, medium and short cones) are not able to precisely perceive the amount of reflected light at each point in the visible spectrum. They actually perform a weighed average of the power of light striking them, through their respective sensitivity curves (colour-matching functions). Hence, the colour perceived by the brain is the sum of the three different stimuli ensuing from as many different types of receptors, each of them being more or less sensitive to the different parts of the visible spectrum. For this reason, a set of three independent numbers is sufficient to completely describe a colour as it is perceived by the human brain, which is the actual scope of colorimetry. For practical reasons, different sets of three colour-matching functions are adopted for colour measurement, each one defining a 3D colour space. Among the available standard systems are the CIE 1931 RGB system (Red, Green and Blue) and the CIE 1931 XYZ system ( x (O ), y (O) and z (O) colour-matching functions - Fig. 4), established by the Commission Internationale de l'Éclairage. A common feature of these colour systems is that changing the light intensity (colour brilliance) in principle affects all the three coordinates in fixed proportions but not the quality of the colour. Then, only two independent coordinates are actually needed to fully describe the kind of colour and a more concise description can be attained by intersecting the generic 3D vector C with a plane (e.g. X + Y + Z = 1 - normalized coordinates x = X / [X + Y + Z] ) and projecting the corresponding point C' on one reference plane (e.g. C'' on the X-Y plane, xy chromaticity diagram, Fig. 5 and 6). Other colour descriptions are also possible, which account for the non-linear perceptual response of the human-eye receptors (CIE Lab, CIE Luv) or which are better suited to specific applications (television and computer graphics - YIQ, HSI, etc). An effective way to depict the range of the visible colours on the xy chromaticity diagram is to plot the curve associated to the spectral colours, each of them corresponding to a monochromatic radiation of a definite wavelength O (spectrum locus - the curved boundary of Fig. 6). Any other visible colour can then be created by mixing spectral radiations of different intensity and the corresponding point inside the spectrum locus can be worked out by means of the centroid rule. Two special cases are the purple line (all the possible mixes of red and blue which define the lower boundary of the visible domain) and the white point in the middle of the diagram, which
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1.0
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y 0.8
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yellow 58 0
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spectrum locus ( O = 380 ÷780nm)
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D65 C
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X+Y+Z = 1
blue
0.0 0.0
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Fig. 5 - CIE 1931 XYZ colour space with the normalization plane X + Y + Z = 1, the spectrum locus of the visible monochromatic radiation and its projection on the Z=0 plane.
6 20
sR red
0.2
380
6 00
A
B
sB
0.2
line pl e pur
0.4
0.6
x 0.8
Fig. 6 - CIE 1931 xy chromaticity diagram with the Standard RGB reference for digital image encoding (dashed triangle) and the standard illuminants (central symbols).
represents the stimulus ensuing from a light of constant spectral power distribution. It is worth to note that the achromatic body (having the same reflectance to all the visible radiations) will actually take the colour of the illuminating source under which the observation is performed. This evidence makes clear that any description of colour with the aid of numbers should come with the specification of the light source adopted during the measurement. Several standard illuminants have been defined by the CIE: the D illuminants (DT(K)/100 related to specific colour temperatures T rather than real light sources), the A illuminant (representing a tungsten filament bulb lamp), the B illuminant (similar to D50 and representing the daylight at noon), the C illuminant (similar to D65 and representing the daylight under a cloudy sky) and the F illuminants (related to a series of fluorescent lamps). Keeping as a reference the achromatic point under a definite standard light (the D65 as a rule), it is possible to describe a colour measure on the chromaticity diagram in more meaningful terms by defining the hue (kind of colour, dominant wavelength) as the angular coordinate relative to the red spectral bound (O = 780 nm) and the saturation (purity) as the relative radial distance from the achromatic point (0 at the achromatic point - 100% on the spectrum locus - [6, 7] see Fig. 8).
3. Colorimetry based on the digital camera The image formation in commonly available digital cameras is based on a sensor placed on the focal plane of the lens, in the shape of a fine array of light-sensitive elements (Photodiodes, Metal Oxide Semiconductors, etc. [7]), each one representing a pixel of the final digital image. By means of selective optical filtering, these elements are made sensitive only to a specific part of the visible spectrum (namely Red, Green or Blue) and then arranged in a mosaic pattern in order to monitor the three light components in any part of the image. Unfortunately, the spectral sensitivity of the each group of sensors is generally different from the corresponding colour-matching function standardized by the CIE, yielding unavoidable distortions in the resulting colour measurement. Moreover, the capability of computer monitors and printers to reproduce a wide range of colours is limited compared to the gamut of visible colours. Therefore, a dedicated standard RGB system has been established (sRGB - triangle in Fig. 6), which tightly encompass the capacity of digital image devices and prevents any inapplicable information to be stored in the computer memory. The definition of this standard includes also a power transformation (J correction) from the 0-255 range of the 8 bit binary data to the 0-100% range of each colour channel, which anticipately accounts for the non-linear response of the computer monitor and allows to display the digital image as it is with adequate results [8].
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In order to ascertain the effects of these limitations on the colour measurement of opaque materials, a broad series of physical colour samples has been examined using both a portable colorimeter (Minolta Chroma meter cr-100 D65) and a low cost digital camera (Nikon Coolpix 4300). In this latter case, the pictures have been taken in a laboratory light-box under 5 different illuminants (CIE-standard A, F2, D50 and D65 and the built-in flash). For each illuminant, two methods have been adopted to compensate the effect of the light source on the measurement of the achromatic samples (white balance): the automatic mode of the digital camera and the manual adjustment by shooting a reference white plate under the related illuminant. In the case of the flash illuminant, the manual white balance actually corresponds to the adoption of a dedicated factory-set correction. The colour samples were available in the form of a colour atlas (Natural Colour System Fig. 7 - Example of a page of the NCS Fig. 7), whose 40 pages are the groups of samples colour atlas: on the right corner is the most originating from the blend of a definite hue (c = saturated physical sample available for a chromaticness) and different amounts of black (s given hue, on the top corner are the lightest = blackness) and white (w = whiteness, c + s + w and least saturated samples for the same = 100). Beyond the four cardinal hues (Red, hue (which is the case of concrete). Yellow, Green and Blue) and their intermediate tones (Y50R, G50Y, B50G and R50B), all the pages in the red-yellow range have been considered, with the aim of focusing the attention on the red shift of concrete colour after the exposure to fire (16 pages in total # 700 samples). A first check has been carried out by measuring the hue value of the most saturated colour sample of each page (c = 60÷90), which can be assumed to go with the rotation angle around the D65 point on the chromaticity diagram (x = 0.3127, y = 0.3290 - Fig. 8). The results show a fairly good accuracy in the red-green range (hue = 0÷140 grad, O = 780÷520 nm), even if a strong dependence on the light source can be recognized approaching the cyan colour (hue # 200 grad, O # 495 nm). The manual adjustment of the camera white balance provided only minor improvements for the strongly saturated samples. It has to be noted that a three-steps transformation was needed to plot these curves: a) a non-linear transformation from the 8 bit RGB digital image to the 0-100% sRGB system (J correction - equivalent to a power function with exponent J = 2.2): sRGB = [(RGB8bit / 255 + 0.055) / 1.055] 2.4 (for RGB8bit 10, linear otherwise) b) a linear transformation from the sRGB to the CIE 1931 XYZ coordinate systems: X Y Z
=
0.41245 0.35758 0.18042
0.21267 0.71516 0.07217
0.01933 0.11919 0.95023
x
sR sG sB
c) a normalization to the x-y chromaticity coordinates, which reduces the effects of light intensity, material reflectance and exposure time during shooting: x = X / (X + Y + Z) and y = Y / (X + Y + Z) . Even if sizably better results might have been obtained via a proper optimization of this procedure, it has been preferred to release the implementation of this colour measurement technique from a specific preliminary calibration of the digital camera, and a fully standard transformation has been adopted [8].
215
Concerning the application to the colorimetry of concrete, this material is known on the whole to exhibit a light grey colour, which actually means that its reflectance is almost constant at any wavelength (achromatic body) and to some extent lower than a white surface. For this reason, a second check has been performed on the lightest and least saturated (nearly achromatic) colour samples of the NCS atlas, under the aforementioned five standard illuminants and two white balance methods (Fig. 9). 1.0
0.8
spectrum locus
sG
0.6
10%
40
c olorimeter c amera
y
hue error (grad)
D65
F2 (fluorescent)
20
illuminant
5%
A
saturation
(tungsten filament)
100%
0%
0 50%
0.4
(~ daylight at noon)
sR
hue
D 50
D65
O = 780 nm
0.2
0.2
0.4
0.6
D 65
-5%
(~ cloudy sky)
flash
auto white balance
x
sB
0.0 0.0
-20
hue (grad)
-40 0
0.8
100
200
300
-10%
400
Fig. 8 - Chromaticity diagram of the most saturated physical colour samples in the NCS colour atlas and hue error of the digital camera under different standard illuminants. 1.0
0.36
blacknes s
y
s = 5-10
spectrum locus
0.8
y
0.35
D 65 (~ cloudy sky)
c =90 0.4
5 D65
0.34
0.34
50 30
sR
D65
0.33
0.2
s =5 c =5
s= 5 c= 5
0.33 D65
x
sB
0.0 0.0
0.2
0.4
0.6
0.8
0.32 0.30
x 0.31
0.32
0.33
0.34
0.36
0.40
y
D 50 (~ daylight at noon)
0.35
c = 5 - 90
sG
y
manual wb
chromaticness
0.6
0.36
colorimeter (D65) camera auto wb
F2
x 0.31
0.32
0.33
0.34
0.36
y
(fluoresc ent)
0.32 0.30
y
A (tungsten filament)
Flash
0.38 0.34
0.34
0.36
D65 D65
0.34 D65
0.32
0.32
s= 5 c= 5
x
0.30 0.30
0.34
0.38
0.30 0.28
0.32
s =5 c =5
x 0.30
0.32
0.34
0.36
0.30 0.30
s =5 c =5
x 0.31
0.32
0.33
0.34
Fig. 9 - Chromaticity diagrams of the least saturated physical colour samples in the NCS colour atlas: general view of the contour size at decreasing chromaticness c and enlarged plots at chromaticness c = 5 and blackness s = 5 under different standard illuminants.
216
It can be observed that the shape and extension of the resulting colorimetric contours is not much affected by the illuminant-white balance combination, whose effect can be summarized in a simple shift of the diagram. It means that the digital camera is not always accurate in absolute terms, but it keeps its sensitivity to colour variations in any observation condition, casting the basis for the viability of this fire damage assessment method. Nonetheless, the hue angle based on a standard reference pole (e.g. the D65 illuminant) would lead to inconsistent conclusions in most cases, given the short distance from the pole of the points pertaining to the not-saturated samples. In order to release the in-situ material damage assessment from the environmental lighting conditions, the built-in flash of the digital camera with automatic white balance will be kept as a reference hereafter.
4. Digital camera colorimetry of fire damaged concrete The first difficulty that needs to be faced in the case of concrete colour measurement is due to the inherent heterogeneity of the material, which is well recognizable at the pixel colour level. It can be observed that the dispersion of the results in the 3D XYZ colour space is mostly due to local intensity variations (dark vs. light particles), whereas the x-y chromaticity coordinates are less sensitive to this effect, thanks to the normalization on the X + Y + Z = 1 plane. Beyond this, the uncertainty of the colour measure on the chromaticity plane is more pronounced along the x = y direction (i.e. towards the yellow spectral radiation), even if a marked reduction (-15÷80%) can be achieved by simply masking the coarse aggregate before analysing the image. These aspects are illustrated by the chromaticity diagram of a pristine ordinary concrete core (siliceous aggregate) repeatedly measured on a digital image over a running 10x10 pixel averaging window (Fig. 10 max aggregate size # 200 pixel). In order to ascertain the effect of thermal exposure on the material chromaticity, two good quality concretes have been considered in this study: an ordinary concrete (siliceous aggregate - da = 16 mm - cubic strength Rc = 50.4 N/mm2) and a lightweight concrete (expanded clay aggregate da = 16 mm - cubic strength Rc = 51.1 N/mm2). Their strength decay curves were determined on 150 mm cubes tested at room temperature after uniform heating (residual condition, Tmax = 200, 400, 600 and 800°C), and they proved to be very close to the Eurocode 2 standard curve (Fig. 11). The material colour at each temperature has been measured via the digital camera by taking pictures of the cores cut from the uniformly heated cubes (Ø = 43 mm - 3 cores for each materialtemperature combination). As observed in the concrete lining of the Mont Blanc tunnel [4], a variation toward both the yellow and red directions can be recognized at increasing temperature (Fig. 12). The former effect is more pronounced, but it is influenced by a growing dispersion of the results (lengthened standard deviation ellipses). On the contrary, the red shift is not as marked but it should be more easily detected, being less affected by the material heterogeneity. 0.35
NCS atlas (c = 5 - w = 5) colorimeter camera
y
(flash - auto wb)
ordinary concrete
0.34
masked aggre gate 10 x10 pi xe l / p oint
flash - auto wb
0.33
D65
masked
full 0.32 0.30
0.31
standard deviation ellipses
0.32
x 0.33
Fig. 10 - Point by point chromaticity diagram of an ordinary concrete core compared to the least saturated colour samples of the NCS atlas; pictures of a pristine concrete sample (full image and after masking the coarse aggregate) and of a heated concrete sample.
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For this reason, the chromaticity variation along the R T R 20 (1,-1) direction is likely to be a good scalar index for the c / c (%) assessment of the maximum temperature experienced 100 within a concrete structural member. As suggested by Short et al. [3], the hue angle referred to the D65 point is 80 also a good option, because it inherently filters the radial scattering in the yellow direction and accounts for the red shift in the form of a clockwise rotation around the 60 reference pole. However, given the strong influence of any ordinary 20 bias error due to the illuminant-white balance 40 (R C =50.4 N/mm 2) combination, this parameter is not recommended in the lightweight 20 case of colour measurement based on a digital camera. 20 (R C =51.1 N/mm 2) The reliability of the proposed test method in the Eurocode 2 T (°C) assessment of the residual damage profile within concrete 0 members exposed to fire has been finally checked on a 0 200 400 600 800 couple of 80 mm thick concrete panels made of the two cited concretes. These specimens have been exposed to a Fig. 11 - Residual cubic strength of marked thermal gradient (> 5°C/mm) by arranging them in the concretes herein considered. place of the furnace door, while keeping cold the opposite face with a fan (Fig. 13). The maximum temperature profile within each panel has been determined by means of 3 embedded thermocouples and the associated residual 0.35 strength contour has been worked out through the full image y masked aggregate pertinent strength decay curve (Fig. 15). std dev ellipse (masked aggr.) After cooling, 4 + 4 through cores have been cut from Mont Blanc tunnel [4] the panels and their colour profiles have been determined via the digital image analysis. Even adopting a relatively 800°C narrow averaging window (21 pixels # 1.7 mm along the 0.34 1 600 longitudinal axis, the whole core diameter in the 1 transversal direction), the thermally damaged concrete 400 D 65 layer is clearly revealed by the '(x - y) plot (Fig. 14). ordinary Moreover, the profiles pertaining to the 4 nominally concrete 20 identical cores showed a good repeatability of the results 0.33 flash illuminant auto white balance (Fig. 16). The same cannot be stated concerning the 200 orthogonal '(x + y) scalar parameter, which proved to be x too sensitive to the local chromatic variations. By carrying the breakpoints of the colour variation 0.31 0.32 0.33 profiles over the maximum temperature and residual strength profiles, it can be concluded that the onset of 0.35 ordinary concrete mortar chromatic alteration corresponds to a 470°C maximum y LW C mortar temperature and a 65% residual strength for both the LW C full image concretes herein investigated. These temperature and damage thresholds are slightly higher compared to like yellow results available in the literature ([3] - see Fig. 3), but they 0.34 (O =575 nm) 20°C seem still adequate to the purpose of the structural 200 assessment after a fire. 400 600 800
5. Conclusions
flash illuminant auto white balance
0.33
In this study, a simplified approach to colorimetry has been proposed as a method for the assessment of the damage profile within concrete members after a fire. The method is based on the analysis of the side picture of a concrete core, taken via a low-cost digital camera. The preliminary comparison with a portable colorimeter over a broad range of colour samples and the succeeding experimental program on two concrete mixes at increasing
218
D 65
red
x
(O = 780nm)
0.31
0.32
0.33
0.34
0.35
Fig. 12 - Effect of high temperature on the chromaticity of the ordinary and the lightweight concretes.
ce a t fa d f ho col
0.008
ce
color variation averaging window (21 pix els # 1.7mm)
' x - y)
0.004
depth 0.000
' x + y)
-0.004
ordinary concrete - core # 3 0
Fig. 13 - Furnace setup for imposing a thermal gradient to the concrete panels. levels of thermal damage allowed to formulate the following set of conclusions: x The digital camera proved to be quite a sensitive device for the assessment of the chromatic change of opaque materials, despite of the sizable effect of the illuminant, white balance and hue combination on the colour measure accuracy. This evidence should be carefully considered when a colour variation index related to a fixed reference point is selected for the inspection of greyish materials like concrete (nearly achromatic). x The considerable amount of data available in a single digital image (many thousands of pixels) allows to separately analyse the cement mortar and the aggregate and to outline some statistical trends ascribable to the inherent heterogeneity of the material. Both the concrete mixes herein considered exhibited a more pronounced colour scattering in the direction of the yellow radiation, even if a 15÷80% reduction can be achieved by simply masking the coarse aggregate before analysing the image. x Unfortunately, the most evident average colour shift of heated concrete is not always easy to be detected, being aligned with the direction of maximum uncertainty in the colour measurement. However, the '(x - y) scalar index of colour change defined on the CIE 1931 xy chromaticity diagram seems to be a good compromise between the conflicting requirements of preserving the sensitivity of the method while limiting the dispersion of the results. x A final check on two concrete panels exposed to marked thermal gradients allowed to ascertain the ability of this method to reveal how deep the material has been significantly impaired in a structural member exposed to fire. 219
depth (mm)
(masked aggregate)
-0.008
20
40
60
80
Fig. 14 - Scalar parameters for outlining the colour variation in a heated concrete member. 100%
1000
T 20 R c /R c
°C 800
T
LWC 80%
65%
ordinary concrete
600
60%
470°C
400
40%
LWC
200
20%
depth (mm)
0 0
20
40
0% 80
60
Fig. 15 - Maximum temperature and residual strength profiles within the heated panels. 0.008
color variation '(x - y) ordinary concrete (masked aggregate)
0.006
average 0.004
breakpoint 0.002 0.000
depth (mm)
-0.002 0
0.006
20
40
60
80
color variation '(x - y) lightweight concrete (masked aggregate)
0.004
0.002
0.000
depth (mm)
-0.002 0
20
40
60
80
Fig. 16 - Colour variation profiles in the heated panels measured on 4 cores via the digital image analysis.
Summing up, the digital camera is a commonly available device which proved to be a fast and objective tool for detecting the well known irreversible colour change undergone by concrete exposed to high temperature. Even if no direct relationship exists between this colour alteration and the decay of the material mechanical properties, the onsets of both phenomena usually lie in the same temperature range. Hence this Non-Destructive Testing technique should be of valuable help in the assessment of the residual capacity of R/C structures after a fire.
Acknowledgements A grateful acknowledgement goes to Gian Andrea Basilico and Davide Cabrini for their enthusiastic cooperation in carrying out the tests in partial fulfilment of their MS degree requirements. Special thanks also to Dr. Cristina Boeri of the Colour Lab - Politecnico di Milano for making available the colorimetric devices and the colour samples that have been used in this work.
References [1]
CIB W14 Report, "Repairability of Fire Damaged Structures", DRYSDALE D.D. and U. SCHNEIDER U. (Editors), Fire Safety Journal, V.16, 1990, pp. 251-336.
[2]
FELICETTI R., GAMBAROVA P.G., SILVA M. and VIMERCATI M., "Thermal Diffusivity and Residual Strength of HPLWC Exposed to High Temperature", Proc. of the 6th Int. Symp. on Utilization of HSC/HPC, Leipzig (Germany), V. 2, 2002, pp. 935-948.
[3]
SHORT N.R., PURKISS J.A. and GUISE S.E., "Assessment of Fire Damaged Concrete Using Colour Image Analysis", Construction and Building Materials, n. 15, 2001, p. 9-15.
[4]
FAURE R.-M. and HEMOND G., "Application de Méthodes pour l'Analyse d'un Béton après un Incendie" - web publication on www.equipement.gouv.fr/cetu/Securite/ , 2004 (in French).
[5]
BERGER-SCHUNN A., Practical Color Measurement, John Wiley, New York, 1994, 179 p.
[6]
SIOF - The Italian Society of Optics and Photonics, Misurare il Colore, OLEARI C. (Editor), Hoepli, Milano, 1998, 378 p. (in Italian).
[7]
JÄHNE B. and HAUßECKER H. (Editors), Computer Vision and Applications, Academic Press, S.Diego, 2000, 679 p.
[8]
STOKES M., ANDERSON M., CHANDRASEKAR S. and R. MOTTA, "A Standard Default Color Space for the Internet - sRGB", web publication on www.w3.org/Graphics/Color/sRGB, 1996.
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Petrographic Analysis of Fire-Damaged Concrete Neil SHORT Senior Lecturer Aston University Birmingham, UK
John PURKISS Lecturer Aston University Birmingham, UK
Summary This paper considers the potential of petrography and image analysis for use in assessment of firedamaged concrete. Investigations involved the analysis and quantification of changes in colour and the nature and intensity of cracking, found after subjecting concrete to both steady-state and transient heating regimes. The steady-state investigations showed that after heating to a range of temperatures there was a good correlation between measurements of colour change / crack density and the residual compressive strength of the concrete. Colour / crack density measurements taken on samples after transient heating have shown that the depth to which the compressive strength of concrete is likely to have been significantly affected, can be determined. The use of these techniques to provide useful information on the temperature gradients established, damage incurred in concrete elements after a fire, and their relation to other tests, are discussed. Keywords:
1.
concrete, fire, damage assessment, petrography, colour, crack density.
Introduction
In order to assess the integrity of concrete after a fire it is important to ascertain (i) the thermal gradients that were established in various structural elements at the height of the fire and (ii) quantification of any consequential damage. Assessment usually starts with visual observation of colour change, crazing, cracking, and spalling. On heating above 300°C, the colour of siliceous aggregate concrete is said to change from normal to: pink or red (300-600°C), whitish grey (600900°C), and buff (900-1000°C) [1]. The pink / red discolouration results from the presence of iron compounds, in the fine or coarse aggregate, which dehydrate or oxidise in this temperature range. This colour change is useful since its appearance coincides with the onset of a significant loss of concrete strength as a result of heating. Thus in practice any concrete which has turned pink / red after a fire is regarded as being suspect of deterioration. Cutting back the concrete should give a good idea as to the depth to which temperatures greater than 300°C have occurred. However, the method is subjective and the colour change to pink / red is less prominent (and thus more difficult to judge by eye) with calcareous or igneous aggregates and may not occur at all with some siliceous aggregate concretes. Visual observations may then be supported by various tests that give an indirect indication of the condition of the concrete. These include: core tests, rebound hammer test, ultrasonic pulse velocity test (UPV), Windsor probe and the BRE internal fracture test, their advantages and disadvantages being described in detail elsewhere [2,3]. Additionally, techniques developed and still at the research stage include: thermoluminescence [4], a stiffness damage test [5], a fire behaviour test [6], and a thermo-mechanical model [7]. Microscopy and image analysis applied to polished or petrographic thin sections, has been used extensively in investigations of concrete microstructure. Much of this includes phenomena related to mechanisms of concrete deterioration in general, with only a small amount of work related to fire-damaged concrete [8,9]. Attempts have been made at the assessment of cracking using petrographic thin sections [10] and scanning electron microscopy [11,12], though these were of a very qualitative nature. Whilst all these tests are valuable aids in assessment, they do not give a complete picture of the extent of deterioration. For further understanding we initiated a fundamental study to assess the
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potential of petrography and image analysis for use in investigations of fire-damaged concrete. This involved the analysis and quantification of changes in its colour and the nature and intensity of cracking found, after subjecting concrete to both steady-state and transient heating regimes. This paper gives an overview of the results we have obtained, the potential for further work and practical application. More detail may be found elsewhere [13-15].
2.
Experimental
2.1
Materials and sample fabrication
An ordinary Portland cement (OPC) and blended cements prepared from OPC and 30% pulverisedfuel ash (PFA) or 50% ground granulated blast furnace slag (BFS) were used with a medium zone quartz sand and 5-20 mm siliceous gravel. In addition, the influence of other aggregates was investigated using OPC concretes made with, crushed limestone, granite or Lytag. The mixes were 1 : 2.1 : 4.2 cement / sand / coarse aggregate, designed to give equivalent workability and 60-day cube strengths typical of good quality structural concrete. A relatively high water/cement ratio, of between 0.62 - 0.66, was used to avoid the use of plasticizers. Quality control was maintained by measuring slump, fresh wet density and 28-day cube strengths. Mixes were cast into standard cubes (100 mm), beams (500 x 100 x 100 mm) or cylinders (300 mm length x 150 mm diameter). Thermocouples were embedded at various distances from the surface to measure sample temperatures. Specimens were de-moulded after 24 hours, cured under water for 28 days and then stored in air with a controlled RH and temperature. When samples were 60 days old they were dried in an oven at 105°C for 48 hours in order to prevent explosive spalling on firing. This regime provided well-cured samples and minimised any effect of accelerated hydration when heated. 2.2
Steady-state heating regime
Cube and beam samples were heated to equilibrium temperatures of 175, 250, 300, 350, 400, 450, 500 and 700°C in a proprietary kiln type furnace. The rate of heating was approximately 6°C / minute. The specimens were heated to the test temperature, soaked at that temperature for 1 hour, then allowed to cool in the furnace with the door open. A range of tests was carried out on unheated samples (control) and specimens that had been allowed to cool to room temperature after the heating cycle (residual). These tests included colour / crack density measurements, residual compressive and flexural strength, dynamic modulus, ultrasonic pulse velocity, surface hardness, mercury intrusion porosimetry and differential thermal / thermogravimetric analysis. Mechanical tests were carried out in accordance with the relevant sections of BS1881 [16]. In this paper only residual compressive strengths are reported and compared with the changes in colour / crack density. Other test results are reported elsewhere [14,15] although their implications are discussed. 2.3
Transient heating regime
During an actual fire, temperatures within a concrete section do not generally reach equilibrium values. A thermal gradient is established with the temperature of the outside layers being drastically increased, whilst the temperatures of the inner concrete may be comparatively low. As a result of this, development of the pink/red colour and cracking are restricted to a surface section. A simple electric furnace was constructed with a heating element at one end, allowing the establishment of a temperature gradient along the axis of a concrete cylinder specimen. The furnace was calibrated using a heat flux meter to give rates of heating at the concrete surface equivalent to heat fluxes of 80, 110 and 140 kW/m2 which are typical of low, medium and high intensity fires. 2.4
Colour measurement
The concepts involved in understanding colour and its measurement are complex and are considered briefly in an earlier paper [13]. In practice it was found that the colour changes after firing could be described simply in terms of changes in hue. Hue is the attribute by which the eye distinguishes different parts of the spectrum e.g. red, yellow, green etc., and is measured in terms of wavelength. The hue of a specific colour may then be represented by its position on a horizontal circle. The zero on this circle depends on the measuring system used. In the present work, the instrument analyser defined pure red as zero and 360q and any other hue may then be quantified as
222
an angle. For computer purposes the 0-360q range is re-scaled to fit a 0-255 instrument display, so that pure red is actually 0 and 255 with the other colours in between. Samples were impregnated with a colourless resin, cut, ground and polished for examination in reflected light. Using an Olympus polarising microscope combined with a Sight Systems Ltd., Colour Manager, Image Analysis Workstation and associate software, it was possible to determine changes in values of hue. 2.5
Crack density measurement
A 10 mm thick slice (of 100 x 100 mm cross-sectional area) was cut from the centre of a cube. The edges of this slice were then trimmed off to leave a section 50 x 80 mm in area which was vacuum impregnated with a low viscosity resin, glued to a glass slide and polished to give a petrographic thin-section. The thin-sections were examined in filtered transmitted light at a magnification of 40 so that the cracks present in an area of approximately 10 x 10 mm could be observed. Photographs were taken of each of these 10 x 10 mm areas and the total length of the cracks measured. A photograph of a calibrated graticule was taken at the same magnification and used to calculate the exact area over which the crack lengths were measured. Crack density is expressed in terms of mm of crack length per cm2 of concrete. For each 80 x 50 mm cross-section examined, the crack value quoted is the mean of the crack measurements taken from the forty different 10 x 10 mm areas photographed. Similar procedures were employed to obtain thin-sections and crack density measurements from the concrete cylinders. More detailed information covering the various steps in thin-section preparation and crack measurement is reported elsewhere [14].
3.
Results and discussion
3.1
Colour changes
3.1.1 Visual observations Visual observations of polished cross-sections of unheated (control) and fired samples were made and are presented elsewhere [13]. The visual perception was that samples which had been subjected to a steady-state heating regime at 350°C and above had turned red or become a deeper red colour. The surface section of cylinders heated from one end face had undergone a colour change near the surface compared with the interior, although the interface between them was rather indistinct. 3.1.2 Steady-state heating regime Initially measurements of colour were made for a sample area, 50 mm x 80 mm, showing a range of visual colours. Essentially the analyser records an image of this area, divides it into 512 x 512 pixels (i.e. a total of 262,144) and determines the hue for each pixel. The results presented in Fig. 1, show the frequency of occurrence for the hue levels from 0 to 89, where the different levels represent the red to green part of the visible region of the electromagnetic spectrum. In order to preserve the clarity of the information the results are plotted as histograms in bandwidths of 10 i.e. 0-9, 10-19 etc. It is evident that for both control and fired samples, the frequency of response is concentrated in the 0-39 levels, representative of colour in the red-yellow region. Values in levels 40-255 were virtually zero. Heating to equilibrium temperatures of 350°C caused a shift in the frequency so that for levels 20-29 there is drop in frequency of occurrence from 178,000 to 56,000; whilst in the 10-19 levels there is an increase from 76,000 to 203,000. Such a shift indicates a change in colour to a larger red component. Colour changes occurring on heating were then expressed as frequency of occurrence in the 019 levels as a percentage of the total frequency in all levels. Fig. 2 shows the % hue in the 0-19 levels for samples heated to different temperatures. It is evident that the red colour started to develop significantly for samples soaked in the temperature range 250-350°C. This colour change developed quickly at 350°C whilst only very slowly at 250°C (bearing in mind the soaking time of one hour at the equilibrium temperature). Soaking at temperatures in the range 350-500°C then showed a small decrease in red colour. It should be noted that the values plotted in Fig. 2 represent a mean red colour for the sample cross-sectional area and that within this area there are differences in colour between the mortar matrix and the various components of, in this case, the siliceous gravel aggregate [13].
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250000 Control
Frequency
200000
Heated to 350°C 150000 100000 50000
. Yellow
Red
0
0-9
Green
10 19 20-29 30-39 40-49 50-59 60-69 70-79 80-89
Hue Level Fig. 1 - Frequency of occurrence for the levels of hue from 0-89. The colour changes observed with samples made with blended cements were very similar to those shown in Figs. 1 and 2. This demonstrated that development of red colour was not greatly influenced by the iron oxide content of the cement since these varied widely [13]. In the case of concretes made with different aggregates the colour changes were not as distinct, but differences between fired and control specimens were still measurable. 80
60 50
60 40
50 40
30
30
20
20
Hue Strength
10
10
0 0
100
200 300 400 Temperature (ºC)
Strength (MPa)
% Hue in 0-19 Levels
70
500
0 600
Fig. 2 - Hue and residual compressive strength vs temperature. The results clearly demonstrate that this technique can be used to quantify colour changes in concrete as a result of heating and is a considerable improvement on using subjective visual assessment. Average cube strengths at 60 days for the OPC siliceous aggregate concretes were 56.0 MPa. Figure 2 shows that there is a slight reduction in the residual compressive strength of samples soaked at temperatures up to 350°C. Soaking at temperatures greater than 350°C led to a substantial reduction in residual compressive strength. Comparing the colour changes with residual compressive strength it is evident that the substantial change in strength loss, coincides with the full development of red colour. Thus, the full development of a red colour in concrete subjected to high temperatures may be used as an indication of significant loss in compressive strength.
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3.1.3 Transient heating regime Figure 3 shows the temperature distribution, immediately prior to cooling, found for a concrete cylinder heated from one end face. The temperature at the surface reached approximately 680°C and the 300°C isotherm was about 30 mm from the exposed surface. Fig. 3 also shows the corresponding colour change with distance from the exposed surface. Values represent the colour found in consecutive, overlapping, parallel sections, 7.5 mm depth. The maximum development of red colour occurred from the surface to depths of about 30 mm. At depths of greater than 30 mm, the red colour diminishes rapidly and has essentially disappeared at depths in excess of 45 mm. The transition may be estimated at about 35 mm from the surface i.e. equivalent to temperatures just below 300qC. Although not applied in the present work the transition depth may be determined by complex statistical analysis as derived by Kriging and discussed in Isaaks et al. [17]. 700
Temperature (ºC)
600
Temperature
40
Hue
35
500
30
400
25
300
20 15
200
10
100
% Hue in 0-19 Level
45
5
0
0 0
15
30
45
60
75
90
105 120 135 150
Distance (mm)
Fig. 3 - Temperature and colour distribution in concrete heated from one end face. Thus even if the temperature distribution was not known, then from a knowledge of colour change and an understanding of the relationship between these parameters and compressive strength (as shown Fig. 2), it is possible to define the maximum distance from the surface (in this case around 35 mm) where significant reductions in residual compressive strength are likely to be found. 3.2
Crack density
3.2.1 Steady-state heating regime The effect of temperature on crack density (expressed in mm of crack length/cm2 of concrete) for specimens made with siliceous aggregate and OPC, is shown in Fig. 4. Each of the points on this graph are the mean values of the crack lengths measured from forty 10 mm squares covering a 50 mm x 80 mm section. Some minor cracking, from e.g. shrinkage and defects in the aggregate, was evident in control specimens and values of this initial (unfired) crack density C0 , for the various concrete mixes are given in Table 1. The temperature at which thermally induced cracking starts, Tcd , may be estimated from the plots of crack density vs. temperature and these values are also given in Table 1. Once cracking starts the crack density then increased linearly with increase in temperature. For samples made with OPC and limestone or granite aggregates similar trends were observed and values of Tcd are given in Table 1. For comparison, the temperatures at which substantial reductions in residual compressive strength start, Tcs were estimated and are also given in Table 1. Agreement between transition temperatures determined from the crack density measurements (Tcd) and the strength measurements (Tcs) are good, except for the OPC/PFA – siliceous aggregate concrete. The reason for the discrepancy in the latter case is not clear, although it is also the concrete with the largest initial crack density, C0. Another possibility is that a finer network of cracks is produced [18]. Crack length distributions were not measured in the present
225
60
3
50
2.5
Strength Crack density
40 30
2 1.5
20
1
10
0.5
0 0
100
200
300
400
500
Crack density (mm/cm²)
Compressive Strength (MPa)
work. Comparison of crack density with residual compressive strength at equivalent temperatures, plotted in Fig. 5, gave a good correlation with R2 = - 0.93. Overall these results show that measurements of crack density give a good indication of residual compressive strength after firing.
0 600
Temperature (ºC)
Fig. 4 - Crack density and residual compressive strength vs temperature. Table 1 - Values of initial crack density (C0) and the temperatures (T) at which substantial loss in compressive strength is initiated. Concrete Type
C0 (mm/cm2)
Tcd (qC)
Tcs (qC)
OPC – Siliceous Gravel
0.29
350
325
OPC / PFA - Siliceous Gravel
0.36
250
325
OPC / BFS - Siliceous Gravel
0.26
350
350
OPC - Limestone
0.31
300
325
OPC - Granite
0.24
400
400
3.2.2 Transient heating regime Figure 6 shows the temperature distribution, immediately prior to cooling, found in a siliceous aggregate concrete cylinder made with OPC and heated from one end face. The temperature at the surface reached approximately 680°C and the 325°C isotherm (cf. Table 1) was about 35 mm from the exposed surface. The corresponding measurements of crack density are also shown in Fig. 6. It is evident that the greatest crack density of around 3 mm/cm2, was at the exposed face of the concrete and this gradually decreased as measurements were taken further away from the surface. Between 30-35 mm from the heated face the values reached a minimum of about 0.3 mm/cm2, consistent with those normally occurring in unfired concrete. Similar sets of results were found for samples made with concretes of other compositions. Thus even if the temperature distribution was not known, then from a knowledge of the crack density, and an understanding of the relationship between this parameter and compressive strength, it is possible to define the maximum distance from the surface (in this case up to about 30 mm) where significant reductions in residual compressive strength are likely to be found.
226
2
Crack Density (mm/cm )
7 OPC 6
OPC/PFA OPC/BFS
5
Limestone
4
Granite
3 2 1 0 0
0.2
0.4
0.6
0.8
1
1.2
Normalised Residual Compressive Strength (MPa) Fig. 5 - Correlation between crack density and normalised residual compressive strength.
Temperature Crack Density
Temperature (ºC)
600
4
500 400
3
300
2
200 1
100 0
Crack Density (mm/cm²)
5
700
0 0
15
30
45
60
75
90
105 120 135 150
Distance from heated surface (mm) Fig. 6 - Temperature and crack desnsity distribution in concrete heated from one end face. 3.3 Other measurements 3.3.1 Mechanical properties The reduction in residual surface hardness showed similar trends for each of the different concrete mixes. To a certain extent the results mirrored those of the residual compressive strength although the temperature induced effects start at lower temperatures. This observation may be associated with the fact that this test only detects surface changes and may therefore emphasise crack formation and resultant breakdown at the surface due to differential thermal expansion. Significant drops in residual flexural strength occurred at temperatures up to 300°C for all concretes studied. As this is before the onset of macro cracking the two parameters cannot be correlated. This loss can be taken as indicative of any reduction in bond between aggregate and matrix. All the concretes showed a reduction in residual dynamic modulus with increase in temperature, so that by heating at 300qC the residual values were only approximately 20% of unfired samples. These results indicate significant change in microstructure (e.g. porosity, micro227
cracking) of samples although these do not lead to significant loss of strength. It is therefore only a useful technique in terms of quality control and indication of changes occurring at lower temperatures. Residual ultrasonic pulse velocity showed an almost linear reduction with increasing temperature, so that by heating at 300qC the values were only approximately 50% of unfired samples. 3.3.2 Changes in mineralogy A combined differential thermal and thermo-gravimetric analysis of the mortar matrix showed [15] that a series of endothermic reactions occurred including: dehydration of CSH gel (100-120°C), dehydration of calcium hydroxide (450-550°C) and decomposition of calcium carbonate (750850°C). Whilst useful information regarding mineralogical changes was obtained neither technique detected anything that might be specifically associated with the compressive strength deterioration at temperatures of around 300-350°C. This suggests that loss in compressive strength may arise from changes in both micro- and macro-structure due to loss of interlayer water; loss of bond between aggregate and the matrix or cracking in the matrix due to incompatibility of thermal strains and temperature weakened tensile strengths. Results from mercury intrusion porosimetry studies [15] suggested that between 300 and 400qC there was first a coarsening of the pore structure followed by an increase in total porosity. Scanning electron microscopy studies [11] have indicated that micro-cracking occurs; first in the vicinity of Ca(OH)2 (at ~ 300qC) and then around unhydrated cement grains (at ~ 400qC). However, with both these techniques the evidence for a link between structural changes and degradation in mechanical properties is limited and further work is required.
4.
General discussion
Both pulse velocity (the effect of time to transmit a waveform through a material) and dynamic modulus (the enforced elastic vibration of a material) will be affected by any material degradation including micro- and macro- cracks due to loss of bond and thermal incompatibility. Thus both these measurements will show immediate decrease on heating. Compressive strength measures the mechanical response of a (cracked) matrix. Figs. 2 and 4, show that the cracking is negligible at temperatures below about 300°C. In pure compression the application of load closes any microcracks with little extra damage to the specimen and thus measured strengths (and resultant stressstrain behaviour) [19] will be little affected. With the onset of macro-cracking, above 350°C, the initial portion of loading causes extra damage by trying to overcome the effect of the cracks, before the reduced strength core starts taking load and gives much reduced strengths. For elements in flexure there are two cases; (i) where the concrete compression zone is remote from the fire (sagging moments) and (ii) where the concrete compression zone is not (hogging moments). In the former case the concrete temperatures will be relatively low and the temperature in the reinforcement will govern the extent of cracking due to greatly reduced Young’s Modulus of steel. In the latter case a similar effect to pure compression will occur.
5.
Potential for image analysis
Petrographic techniques are now being used much more widely for the investigation of cementitious materials [8,9] to yield information on e.g. the quality of concrete such as cement content, water / cement ratio and quantifying the mechanisms and damage that may result from a wide range of degradation processes. A wide range of microscopes and specimen preparation equipment is available. Digital cameras are now the norm and associated software make handling images much easier. Whilst at the start of our investigations there were good reasons for analysing images using hue, saturation and intensity colour space, this may not now be the best option. We are currently looking at using software using red, green, blue colour space that is downloadable from the web. Similarly in our work, measuring the cracks was a tedious operation but methods are currently under investigation whereby this process may be automated [20,21]. Using such techniques would allow much more information to be obtained e.g. crack size distributions. Compared to other techniques only small diameter cores would be required from a damaged structure and specimen
228
preparation is relatively easy. Compressive and other tests on cores gives average values along the centre line whereas the petrographic techniques discussed here are capable of giving an exact distribution of temperature or cracking etc. In the light of these observations and our results, we feel that petrographic techniques offer considerable potential for this type of investigation.
6.
Conclusions
(a) Colour image analysis has been used to quantify colour changes that occurred during the heating of good quality structural concrete. It was shown that full development of red colour coincided with a significant reduction in residual compressive strength. For fire damaged concrete, colour measurements may be used to determine the thermal history by providing information regarding the temperature distribution, particularly the 300qC isotherm that existed at the height of a fire and thus it is possible to estimate the depth of the heat affected zone. Actual colours observed depend on the types of aggregate used to make the concrete. They are most pronounced for siliceous aggregates used in this investigation and less so for limestone, granite and Lytag although even in these cases it is still possible to measure differences on heating. (b) It has also been demonstrated that petrographic techniques may be used to determine the nature and density of cracking which has developed at elevated temperatures. There was a good correlation between measurements of crack density and measurements of residual compressive strength and this applies to concretes made with different cements and aggregates. Measurements of crack density taken on samples after transient heating can be used to identify the depth to which the compressive strength of the concrete is likely to have been significantly affected. (c) Thus petrographic analysis measuring either colour or crack density changes can provide very useful information for the evaluation of fire-damaged concrete. This is especially so since further analyses can also provide information on the quality of the original concrete such as cement content and water/cement ratio.
Acknowledgements The authors gratefully acknowledge the financial support of the EPSRC, grant reference number GR/J11546, which enabled this work to be carried out. We also wish to thank Sarah Guise who carried out the practical work for her doctoral thesis and Tony Morris and Raymond Connolly for very helpful discussions.
References [1]
BESSEY G.E., “The Visible Changes in Concrete or Mortar Exposed to High Temperatures”, Investigations on Building Fires, Part 2, National Building Studies Technical Paper No. 4, HMSO London, 1950, pp. 6-18.
[2]
THE CONCRETE SOCIETY, Assessment and Repair of Fire-Damaged Concrete Structures, Technical Report No. 33, London, 1990, pp. 26-30. BUNGEY J.H., Testing of Concrete in Structures, 1989, Surrey University Press.
[3] [4]
CHEW M.Y.L., “Effect of Heat Exposure Duration on the Thermoluminescence of Concrete”, ACI Materials Journal, Vol. 90, 1993, pp. 319-322.
[5]
NASSIF A.Y., “A New Classification System for Fire-Damaged Concrete Based on the Strain Energy Dissipated in a Hysteresis Loop”, Magazine of Concrete Research, Vol. 52, 2000, pp. 287-295.
[6]
DOS SANTOS J.R., BRANCO F.A., and DE BRITO J., “Assessment of Concrete Structures Subjected to Fire-the FBTest”, Magazine of Concrete Research, Vol. 54, 2002, pp. 203-208.
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[7]
LUCCIONI B.M., FIGUEROA M.I., and DANESI R.F., “Thermo-Mechanic Model for Concrete Exposed to Elevated Temperatures”, Engineering Structures, Vol. 25, 2003, pp. 729742.
ST JOHN D.A., POOLE A.W., and SIMS I., Concrete Petrography, Arnold, 1998, pp. 308316. [9] GRATTAN-BELLEW P.E., “Microstructural Investigation of Deteriorated Portland Cement Concretes”, Construction and Building Materials, Vol. 10, 1996, pp. 3-16. [10] RILEY M.A., “Possible New Method for the Assessment of Fire-Damaged Concrete”, Magazine of Concrete Research, Vol. 43, 1991, pp. 87-92. [11] PIASTA J., “Heat Deformations of Cement Phases and Microstructure of Cement Paste”, Materials and Structures, Vol. 17, 1984, pp. 415-420. [8]
[12] CIONI P., CROCE P., and SALVATORE W., “Assessing Fire Damage to R/C Elements”, Fire Safety Journal, Vol. 36, 2001, pp. 181-199. [13] SHORT N.R., PURKISS J.A., and GUISE S.E., “Assessment of Fire Damaged Concrete using Colour Image Analysis”, Construction and Building Materials, Vol. 15, 2001, pp. 9-15. [14] SHORT N.R., PURKISS J.A., and GUISE S.E., “Assessment of Fire-Damaged Concrete using Crack Density Measurements”, Structural Concrete, Vol. 3, 2002, pp.137-143. [15] SHORT N.R., PURKISS J.A., and GUISE S.E., “Assessment of Fire Damaged Concrete”, Concrete Communication Conference 2000, BCA, Crowthorne, 2000, pp. 245-254. [16] BRITISH STANDARDS INSTITUTION, Methods of Testing Concrete, BS1881, BSI, London, 1983. [17] ISAAKS H., and MOHAN SRIVASTAVA R., An Introduction to Applied Geostatics, Oxford University Press, 1989. [18] XU Y., WONG Y.L., POON C.S., and ANSON M., “Influence of PFA on Cracking of Concrete and Cement Paste after Exposure to High Temperatures”, Cement and Concrete Research, Vol. 33, 2003, pp.2009-2016. [19] SCHNEIDER U., “Behaviour of Concrete under Thermal Steady State and non-Steady State Conditions”, Fire and Materials, Vol. 1, 1976, pp.103-115. [20] AMMOUCHE A., RISS J., BREYSSE D., and MARCHAND J., “Image Analysis for the Automated Study of Microcracks in Concrete”, Cement and Concrete Composites, Vol.23, 2001, pp. 267-278. [21] SOROUSHIAN P., ELZAFRANEY M., and NOSSONI A., “Specimen Preparation and Image Processing and Analysis Techniques for Automated Quantification of Concrete Microcracks and Voids”, Cement and Concrete Research, Vol. 33, 2003, pp.1949-1962.
230
Damage Assessment in Actual Fire Situations by Means of Non-Destructive Techniques and Concrete Tests Andrea BENEDETTI Professor DISTART Department University of Bologna Bologna, Italy
Enrico MANGONI Associate Professor Civil Engineering Dept. University of Florence Florence, Italy
Summary Damage assessment in post-fire situations is discussed with reference to integrated non-destructive test procedures, that are presented within the context of a real fire accident, where extensive laboratory and site analyses were carried out. The investigation on the fire compartment and the tests on concrete make it possible to define the damage field in the structural elements, and to identify the optimal repair and strengthening technique, in order to achieve a safety margin comparable to the original one. Keywords: precast concrete, P/C members, real fires, concrete damage, ultrasonic investigation, drilled concrete cores, disk test (on concrete).
1.
Introduction
The assessment of the damage suffered by a R/C structure in case of fire requires the coupling of a great experimental skill and of a sound theoretical understanding of the physical phenomena that lead to such a damage. Furthermore, the damage levels are not uniformly distributed and are timedependent after the event, as a consequence of quenching, wetting, pollution, stress-induced corrosion and chemical reactions. Modern fire investigation is a constantly-evolving discipline due to the impact of the firesimulation capabilities allowed by computational fluid dynamics (CFD); moreover, starting from the pioneeristic work at Lund University [1], concrete nonlinear thermo-mechanical softening has been thoroughly investigated, and a family of constitutive laws of increasing complexity and efficacy have been formulated [2]. However, the experimental evaluation of the damage level presents some critical aspects and though many nondestructive techniques are found in the literature [3] - the comparison of the experimental results with the prediction of the theoretical models has been so far successful only with reference to the laboratory tests carried out in a furnace. Due to its practical relevance, site investigation of fire accidents is well documented in the literature, but the assessment of the damage field is hardly feasible [4]. Consequently, it is important to define standardized investigation procedures, in order to make it possible to compare different field measurements.
2.
The fire in the Ferrari’s Test Center
The Ferrari’s Test Center is a typical industrial compartment, placed inside a larger building and limited by internal partitions; the windows and doors of the compartment comply with strict functionality (access from other compartments, need of natural lighting and car access, Figs. 1,2 and 3). The office zone is divided by a mezzanine. The roof of the building consists of precast shed elements supported by a series of large-span, P/C beams; the roof windows are equipped with polycarbonate alveolar glazing sheets. The fire load present in the building falls in three main categories: (a) office and laboratory furniture; (b) cars and car components; and (c) flammable materials for installations and finishing. The causes of the accident are not known, but after the flash-over, people working in the night shift in nearby buildings launched the alarm because flames were visible from the windows and the gases were given off the roof. The damage pattern inside the building suggests a strong temperature anisotropy in the transversal section; in particular, the geometry of the openings and the presence of the mezzanine 231
activated a hot-gas circulation which concentrated heat fluxes close to the external wall containing the openings. On the other hand, the melting of the polycarbonate roof sheets allowed the gas to freely move in the vertical direction. As a result, the average temperature in the compartment was not as high as should have been expected (see Figs. 3 and 4).
Fig. 1 - Plan of the Ferrari’s Test Center Compartment.
Fig. 2 - Lateral prospect and section of Ferrari’s Test Center.
Fig. 3 - Internal view of the test center after the fire. 232
The temperature distribution can be worked out once the heat-release rate (HRR) has been defined on the basis of the fire load. With reference to [5], the HRR of closely-spaced cars can be assessed taking advantage of the calorimeter data measured in the tests on burning cars. In particular, the main characteristic of car fires is a total energy release close to 4 GJ per car (burning time from 30 to 40 minutes). In the present analysis, the HRR of four Ferrari cars has been added to the HRR of office furniture and flammable car components. These assumptions led to the temperature-time curve shown in Fig. 6.
Fig. 4 - Views of the roof and of the external wall after the fire.
400,0 350,0 300,0 250,0 200,0 150,0 100,0 50,0 0,0
0
20
40
60 Time [min]
80
100
120
Fig. 5 - HRR curve of the fire compartment.
It should be mentioned that the burning of cars and car components was only partial, so that an efficiency factor ( 1) was applied to their fire load. The temperature analysis required the definition of the compartment characteristics; looking for a simple two-zone transient solution [6], the geometry of the perimeter walls had to be defined for each side. In the present case different opening factors for each wall were introduced, but the temperature time-evolution did not include the spatial distribution of the temperature (Fig. 6). One of the most critical issue is the time evolution of the opening areas; in particular, it was decided to adopt an initial value for the opening area corresponding to the compartment leakage, and to consider the subsequent glass breaking due to the flash-over. The melting of the polycarbonate was supposed to occur at a gas temperature of 150°C. 233
Concrete and steel damage can be ascertained once the temperature distribution inside any R/C element is known. To this end, the thermal analysis was carried out by using the code STRAND 7, which solves nonlinear thermal problems in accordance with any given temperature-time curve (Fig. 6). All the thermal properties of the materials were introduced in agreement with [6] and [7]. Gas Temperature 800 700 600 500 400
Hot Zone
300
Cold Zone
200 100 0 0
20
40
60 Time [min]
80
100
120
Analysis Name:
Fig. 6 - Computed time-temperature curve of the compartment fire.
Fig. 7 - Temperature distribution across the beam main section. Fig. 7 illustrates the thermal map of the main beam section at the peak of the fire. In order to perform a damage analysis, it is necessary to introduce appropriate stress-strain laws for both the concrete and the reinforcement, taking into account the temperature-induced strength and stiffness decay. According to the full-damage hypothesis, no strength recovery was assumed after concrete quenching. In so doing, the damage level is directly related to the peak temperature reached in each concrete fibre. In the following the attention is focused on the comparison between the computed damage level and the damage level obtained by means of non-destructive site and laboratory tests on concrete structures and drilled cores.
234
3.
Analytical fire-damage evaluation
The fire damage can be expressed in terms of reduction of concrete compressive strength and elastic modulus. The exact evaluation of the damage should take into account microcrack formation due to the thermal, load-induced and transient-creep strains, but also steam pressure and chemical deterioration due to dehydration should be considered. However the strength-reduction curves incorporate all relevant factors in an heuristic way, so that - as a first approximation – these curves can be directly used to quantify the scalar damage in terms of properties decrease. Concerning the elastic modulus, attention has to be paid to the correct evaluation of its temperature-dependent evolution; more precisely, the initial modulus can be defined as the tangent to the concrete mono-axial compressive stress-strain curve; thus the temperature influence can be introduced in the following way: Ec, fi
3 f ck , fi 2 H c1, fi
Ec0 k E (T c )
E c0
kc (T ) kH (T )
(1)
1
kc/kH kc2
A direct definition of the elastic-modulus reduction curve is given in [6], as the 0.6 square of the compressive-strength reduction factor. The diagrams 0.4 corresponding to the two formulations are plotted in Fig. 8. 0.2 By using the temperature distribution 0 given by the section maps, it is possible to 0 200 400 600 800 compute the local cumulative damage T [°C] level, by using the temperature-dependent Fig. 8 - Elastic-modulus reduction curves used in the damage relationships. analysis. 0.8
In order to compare the analytical results with those coming from the nondestructive investigations, the three main paths shown in Fig. 9 were taken into account. The ultrasonic pulsevelocity was monitored in 10 contiguous beams, in different sections: a preliminary investigation was carried out in 3 sections of 2 side beams; afterwards, all beams were monitored in 5 sections 5.0 m apart. Finally, a number of closely-spaced sections were monitored in a reference beam (sections 0.8 m apart). The travelling time of an ultrasonic pulse passing through one of the reference sections can be readily computed once the local elastic modulus distribution is known. Using the ratio of the actual velocity to the initial one as a damage indicator, the theoretical damage due to flaws and micro cracks can be obtained as follows:
D us
Vus (T ) Vus 0
x2 x1 x2
³
x1
ds k E (T (s ))
(2)
In Fig. 10 the distribution of the damage index Dws is plotted along the path B for the two expressions of the elastic-modulus degradation. Due to the asymmetry of the ambient temperature field, the computed values are reliable only close to the external wall. Furthermore, the comparison with the experimental values of the ultrasonic pulse-velocity requires a suitable across-compartment shape-function; the experimental evidence seems to suggest a logarithmic data-distribution. In Table 1, the mean deviation of the experimental points is reported with reference to three distribution functions.
235
Interpolation Stepwise Linear Logarithmic
Data Set A 755.51 696.36 643.03 [m/s]
Data Set B 575.78 689.37 715.23 [m/s]
Data Set C 469.82 479.73 472.05 [m/s]
Table 1 - Interpolation error of the transversal distribution function. However, by assuming a very simple linear interpolation of the values, with no damage in correspondence of the inner partition wall, it is possible to check the validity of the abovementioned hypotheses on the evaluation of the damage field along the concrete beams. Figs. 11, 12 and 13 show the results concerning the three paths introduced in Fig. 9. The existence of a continuous damage distribution along any line at right angles to the external surfaces of the concrete elements exposed to the fire has been pointed out by many researchers; Benedetti [8] introduced an optimization procedure to describe the residual-modulus distribution in a concrete section, by using indirect or side ultrasonic-pulse measurements. Other techniques can be used for the damage assessment, like drilling concrete cores in the damaged elements. These cores should be drilled only in “regularly-damaged zones”, i.e. far from spalling-prone zones and localized cracks. 0.8
kc2
kc2
0.7 0.6 0.5
kc/kH
Dus
0.4 0.3
kc/kH
0.2 0.1 0
100
200
300
400
X [cm]
Fig. 9 - NDT measurement paths in the beams.
Fig. 10 - Damage index Dus = Vus(T)/Vus0 along the path B, as a function of the distance from the vertical left face of the lower flange.
The cores can be scanned on paths orthogonal to the axis, but a correlation between the pulse velocity and the local strength is mandatory if the damage has to be reliably assessed. By cutting the cores in standard cylinders (height equal to the diameter), the resolution is too low since the damaged external layer is typically 40 to 80 mm thick. However, it is possible to obtain an indication of the strength decay by using the so-called “flatdisk punching test”. This test is carried out by pressing a disk (thickness tD = 1/4 - 1/5 of the diameter dD) between two small cylinders (diameter close to tD, Fig. 14), that are in turn pressed between the platens of a press. Further details of the testing procedure can be found in [9, 10]. Cutting drilled cores into thin disks allows for many types of investigation, since each disk is almost uniformly damaged by the heating. Among the several parameters that may be investigated in this way, pulse velocity, microcrack density, porosity, color hues and calcium-oxide content can be cited. Last but not least, the compressive strength obtained by punching the disks makes it possible to establish a relationship between various NDT techniques and the damage expressed as a function of the strength reduction. The correlation curve can be used to grade the measurements obtained on site and to build up the spatial distribution of the damage in the compartment.
236
In Fig. 15 the optimal correlation curve between the ultrasonic pulsevelocity and the residual strength is plotted. The scatter is in general less than that of the pulse velocity. The residual-strength profiles in the beam webs were determined by using the above-mentioned procedure (three contiguous 20 mm-thick disks and a 60 mm-long control cylinder of 60 mm). In Fig. 16 the theoretical profile is compared with the mean values obtained by averaging the results obtained in 10 drilled cores. As shown in Fig. 16, the mean values very well confirm the hypothesis of no recovery from the deterioration induced by the peak temperature. However it should be observed that the scattering of the experimental values is as large as +/- 25%, which is very common in the site investigations of real fire accidents.
4000
Vus [m/s]
3500 3000 2500 2000 1500 1000
x [m]
500 2.5
5
7.5
10
12.5
15
17.5
20
17.5
20
4000 3500
Vus [m/s]
3000 2500 2000 1500 1000
x [m]
500 2.5
5
7.5
10
12.5
15
4000
Vus [m/s]
3500 3000 2500 2000
Experimental Exp. interpolated
1500 1000
x [m]
500 2.5
5
7.5
10
12.5
15
Analytical kc/kH 17.5
Analytical kc2
20
Figs. 11, 12 and 13 - Comparison of the experimental and analytical pulse-velocities along the paths A, B and C (see Fig. 9).
80 70
31.4+0.146·(Vus /1000)4
fck [MPa]
60 50 40 30 1500
2000
2500
3000
3500
4000
Vus [m/s]
Fig. 14 - Disk punching-test for the evaluation of the compressive strength.
Fig. 15 - Correlation between the disk strength and the pulse velocity.
237
fck,fi/fck
1.2 1 0.8
Mean Experim.
0.6
Data range
0.4
x [mm]
0.2 0
20
40
60
80
Analytical kc/kH
100
120
Fig. 16 - Beam-web damage measured from drilled cores and computed from temperature.
4.
Strengthening procedure
The damaged layer of the concrete is approximately 20 mm thick. As a consequence, the reduction of beam capacity is very limited, as far as concrete is concerned. However, once the validity of the data interpretation is confirmed and the yield-stress reduction of the prestressing wires is evaluated (on the basis of the thermal maps), the safety check at the ultimate limit state in post-fire conditions can be easily performed.
Bending Moment [MNm]
3,5 3,0 2,5 2,0 1,5
Design Load Moment Undamaged Resstance
1,0
Fire Damaged Resistance 0,5
FRP Strenghtened Moment
0,0 0
4
8
12
16
20
24
Beam Abscissa [m]
Fig. 18 - Repaired beam strengthFig. 17 - Bending-moment diagrams in the ened with four C-FRP laminas thermally-damaged and repaired beams. glued to the extrados.
Each beam is prestressed by means of 26 ½ “ strands, placed in such a way that the computed temperature peaks ranged from 150°C to 380°C. According to the thermal analysis, the strengthreduction factors had values comprised between 0.08 to 0.42 (mean value 0.22; needless to say, the residual strength was the unity minus the reduction factor, times the initial strength). Since the residual resistant moment appeared to be slightly insufficient to cover the bendingmoment diagram of the design live loads (Fig. 17), the beams were strengthened by applying a set of 4 carbon-fibre (FRP) laminas to the extrados of the lower flange, for a total external reinforcement area of 500 mm2. The FRP anchorages were dimensioned by adopting a recentlypublished design procedure [11]. In the end, the safety factor turned out to be larger than the initial one, which means that the original capacity of the beams was fully recovered.
238
5.
Conclusions
In this paper a few experimental and analytical procedures are examined with reference to a real fire. The proposed techniques can predict the damage distribution in any R/C and P/C member subjected to a fire-induced thermal shock, by assuming that (a) the strength and stiffness reductions after the fire are related only to the maximum temperature reached during the fire in any point of the structure, and (b) these reductions are not affected by the water poured on the structure to extinguish the fire. These hypotheses are instrumental in identifying the damage profiles, starting from the calculated thermal maps; at the same time, the damage levels are directly evaluated by testing a number of specimens extracted from the structural members. With regard to this point, the combination of a recently-introduced technique (involving the testing of thin disks cut from drilled concrete cores) with the analytical results seems to be very promising. The experimental investigation presented and discussed in this paper makes it possible to verify the potential of combining various techniques to assess the distributed deterioration of concrete. More specifically, the disk-cutting technique applied to drilled cores appears to be a valuable tool for studying the possible correlation among several parameters related to concrete deterioration. With reference to this issue, the theoretical and experimental damage distributions turned out to be in very good agreement. Last but not least, this paper is focused on how to repair and strengthen a series of fire-damaged beams, in order to restore their original load-bearing capacity. Contrary to the limited reduction of concrete mechanical properties, the yielding strength of the strands exhibits a sizeable fire-induced reduction, and the ensuing capacity loss is close to 25 % of the original capacity of the beams. Consequently, high-strength carbon laminas were adopted as the best means to increase the safety margin to a sufficient level.
References [1]
[2] [3]
ANDERBERG, Y., THELANDERSSSON J., “Stress and deformation characteristics of concrete at high temperatures” Technical report 54, Lund Institute of Technology, Lund, Sweden, 1976. LUCCICONI B.M, FIGUEROA M.I., DANESI R.F., “Thermo-mechanic model for concrete exposed to elevated temperatures”, Engineering Structures, 25, 2003, pages 729–742 TAY D. C. K., TAM C. T., “In situ investigation of the strength of deteriorated concrete”, Construction and Building Materials, 10, n. 1, February 1996, Pages 17-26.
[4]
BENEDETTI A., “Damage evolution and strengthening of industrial buildings acted on by large fires”, IABSE Symposium, S. Francisco, 1995.
[5]
JOYEUX D., “Natural Fires in Closed Car Parks – Car Fire Tests”, CTICM Report INC – 96/294d – DJ/NB, august 1997, pages 1-32.
[6]
ENV 1991-1-2: 2002, “Eurocode 1: Actions on Structures – Part 1-2: General Actions – Actions on Structures Exposed to Fire”, CEN, Brussels ENV 1992-1-2: 2002, “Eurocode 2: Actions on Structures – Part 1-2: General Actions – Actions on Structures Exposed to Fire”, CEN, Brussels BENEDETTI A., "On the Ultrasonic Pulse Propagation into Fire Damaged Concrete", ACI Structural Journal, 95, n. 3, May 1998. CHEN W. F., Limit Analysis and Soil Plasticity, Elsevier, 1975.
[7] [8] [9]
[10] HENZEL J., SIEGHART K., “Determination of the strength of mortar by compression tests on small specimens ”, Darmstadt Concrete, 2, 1987. [11] APRILE A., BENEDETTI A., “Coupled flexural-shear design of R/C beams strengthened with FRP”, Composites Part B: Engineering, 35, Issue 1, January 2004, Pages 1-25.
239
The Drilling - Resistance Test for the Assessment of the Thermal Damage in Concrete Roberto FELICETTI Associate Professor DIS - Politecnico di Milano Milan, ITALY
Summary In this paper, the measure of the drilling resistance is regarded as a method to ascertain the thermal damage undergone by concrete members after fire. Some preliminary tests on a good quality concrete were functional in defining the optimal bit diameter and drilling thrust. A further study on uniformly damaged ordinary and lightweight concrete cubes (Rcm = 50 N/mm2) allowed to ascertain the sensitivity of the method. Finally, some tests on concrete panels exposed to a marked temperature gradient confirmed the reliability of this technique for the assessment of the damage depth within structural members exposed to fire. Keywords: concrete damage; concrete fracture, material assessment; Non-Destructive Testing (NDT); residual properties.
1. Introduction Concrete is known to exhibit a good behaviour at high temperature, thanks to its incombustible nature and low thermal diffusivity [1], which guarantee a slow propagation of thermal transients within the structural members. As a consequence, very strong temperature gradients are experienced by the reinforcement cover during a fire and the material thermal damage rapidly decreases from a maximum to nil within a few centimetres depth [2]. For this reason, assessing the residual capacity of concrete structures exposed to fire is quite a difficult task, because the traditional destructive or non-destructive testing techniques are generally not suitable for the inspection of such a highly heterogeneous material. The possible approaches to this problem generally involve the inspection of the average response of the concrete cover, a point by point analysis of small samples taken at different depths or some special techniques aimed to interpret the overall response of the concrete member after fire (Table 1). In this context, the measurement of the drilling resistance appears to be a promising and fast technique, which allows to continuously “scan” the material response at increasing depth. Several examples of this kind of approach to the assessment of construction materials are available in the literature. A first application [3] was based on the measurement of the thrust to be exerted on the drill to drive the bit at a constant rate in the tested material (bit Ø = 4-8 mm, max hole depth = 15÷20 mm for concrete and mortar). Recently, this method has been proposed also as a means to validate the performance of the surface treatments on stone materials [4] and it is in the process of being standardized by CEN TC 246 - Natural Stones. An alternative indicator of the material response is provided by the resistant torque at constant turning and feed rates, which is currently adopted for ascertaining the preservation of wooden structures [5]. It is worth to note that the resistant torque actually corresponds to the power spent to drive the bit, being the drill turning rate almost constant. In principle, the nice advantage of focusing on the drilling work is that a change on the exerted thrust concurrently affects the power consumption (J/s) and the advancing rate (mm/s). Then, their ratio, namely the specific work that has to be spent to drill a unit deep hole (J/mm), is expected to be marginally affected by the thrust. This assumption was confirmed in a broad series of tests on the mortar layers of different brick masonry walls (bit Ø = 4÷6 mm, max hole depth = 5÷10 mm [6]). A relationship between the drilling work and the material fracture properties was also proposed in the 241
Table 1 - Possible approaches to Non-Destructive assessment of fire damaged concrete structures. Average response of the concrete cover
Point by point response of small samples
Special interpretation techniques
Schmidt rebound hammer Windsor probe Capo test BRE internal fracture Ultrasonic Pulse Velocity
Small scale mechanical tests Differential Thermal Analysis (DTA) ThermoGravimetric Analysis (TGA) Dilatometry (TMA) Thermoluminescence Porosimetry Colorimetry Micro-crack density analysis Chemical analysis
UPV indirect method Impact echo Sonic tomography Modal Analysis of Surface Waves (MASW) Electric Resistivity
cited study. As a matter of fact, releasing the test method from an accurate control of either the thrust or the bit feed rate allows to considerably simplify the experimental apparatus. Concerning the application to fire damaged concrete structures, the thickness to be inspected usually extends to several centimetres and a hammer drill is generally recommended to prevent an excessive bit wearing and overheating. In this case, the sensitivity to the exerted force is partly masked by the hammering action [3] and the dissipated work further appears to be the most promising indicator of the material soundness. Once a constant drill bit performance is guaranteed via the hammering action, the most interesting feature of the drilling technique is that the deep virgin material is inspected in the final stage of the drilling process. Hence, a reference drilling resistance is available for each test and no special calibration curves should be needed for the evaluation of the thickness of damaged concrete.
2. Experimental setup The drilling resistance has been measured by modifying a Hilti TE 6-A battery hammer drill in order to monitor the electrical power consumption, the bit rotation and the hole depth (Fig. 1). Thanks to the significant motor power (350W) and the effective electro-pneumatic hammering action (impact energy = 1.5 J) this tool allows to drill small diameter holes in good quality concrete at quite a fast rate (about 5-10 mm/s for Ø = 6-10 mm). After proper transformation and analog filtering, the electrical signals are acquired by a PCMCIA A/D card (National Instruments - DAQ Card 6036E) and processed by a dedicated software, in order to work out different test parameters such as the motor rate and acceleration, the instantaneous total power consumption and the net drilling work per unit depth (J/mm - regarded as the “drilling resistance” hereafter - Fig. 2). measured parameters chuck rotation T (rad) - photodiode current I (A) - Hall effect transd. DC tension V (V) - Hall effect transd. hole depth d (mm) - potentiometer worked out parameters chuck rotation rate Z = dT / dt total electric power Ptot = V · I idle resistant torque Ti = A + B Z + C dZ/dt idle power Pi = Ti · Z net drilling work Wnet = ³ (Ptot - Pi) dt drilling resistance DR = 'Wnet / 'd Fig. 1 - The battery hammer drill fitted with the electronic circuits and the displacement transducer; list of the parameters directly measured and worked out during the test. 242
Po wer (W)
20
R cm # 60 N/mm2 Ø bit = 10 mm
total
400
400 W J/mm 300
pristine concrete
drill start-up (# 2 mm)
cutting edge sinking (# 3 mm)
net drilling power (W)
# 30% Ø
net
200
Thrust = 170 N
100
idle
100
Depth (mm)
0 0
20
40
0.6
drilling time (s/mm)
200
300
0.8 s/mm
Ø
0.2 drilling resistance (J/mm)
0 0
60
0.4
20
Depth (mm) 40
0
60
Fig. 2 - Total and net drilling power and definition of the drilling resistance (J/mm) as the product of the net drilling power (W = J/s) and the drilling time (s/mm).
3. Test procedure Several preliminary tests on both a virgin and a thermally-damaged good quality concrete (Rcm # 60 N/mm2 - max aggregate size = 16 mm - T = 20°C and 600°C) have been performed, aimed to define a simple test procedure able to guarantee repeatable results. In the final arrangement, the bit is firstly pointed against the sample to be tested and the drill is pushed to preload the hammering mechanism. Then the drill is activated at the maximum power, in order to ensure a constant performance during the whole process. In this way, only the first 2-3 mm are expected to be somehow influenced by the drill start-up and by the initial sinking of the bit cutting edge. Concerning the thrust to exert on the drill, all the tests have been performed downwards in the vertical direction, putting different weights on top of the drill. It has been found that the maximum total thrust should not exceed the value of 200 N, so as to limit the bit wearing and overheating. On the opposite side, a thrust of at least 50 N is needed to guarantee the effectiveness of the electropneumatic hammering action. Within this range, the thrust doesn’t significantly affect the drilling resistance of pristine concrete, whereas the sensitivity to thermal damage improves approaching the upper limit (Fig. 3). The same conclusion is valid for the drilling time (i.e. the inverse of the feed rate), confirming the regularizing effect of the hammering action. Then, all the succeeding laboratory tests have been performed by adding a dead weight of 100 N to the self weight of the drill (about 70 N). In any case, the recommendation of keeping the thrust nearly constant during the test should guarantee consistent results for in-situ applications. As for the bit diameter (Hilti TE-CX - Ø = 6÷14 mm), it has been found that a small bit (6 mm) exhibits a higher sensitivity to the material inherent heterogeneity (Fig. 4), whereas a large bit (14 mm) is prone to overheating problems and is too demanding for the drill motor. Moreover, looking at the torque at the chuck, it has been observed that the most regular response at increasing hole depth is obtained in the case of a 10 mm bit, which has been adopted for all the succeeding tests. 6.0
20
R cm # 60 N/mm 2
4.0
Øbit = 10 mm
pristine concrete
1 mm DR (J/mm)
2.0
heated up to T= 600°C
Depth (mm)
0.0 0
20
40
60
80
pristine concrete 60
heated up to T= 600°C
40
20
20
R cm # 60 N/mm 2 Øbit =10 mm
pristine concrete
0.3
Drilling Time (s/mm)
Net drilling work (kJ)
70 N 170 N
D rilling Resistance (J/mm)
80
Thrust
0.2
heated up to T= 600°C
0.1 20
R cm # 60 N/mm 2 Øbit = 10 mm
Thrust (N)
Thrust (N)
0
0 50
100
150
200
50
100
150
200
Fig. 3 - Effect of the exerted thrust on the drilling resistance (J/mm) and time (s/mm) of both a pristine and a thermally damaged concrete. 243
pristine concrete 20 R cm # 60 N/mm 2
4.0
Torque deviation - RMS (Nm)
Torque (Nm)
6.0
Øbit = 6 mm
Thrust = 170 N
2.0
Øbit = 10 mm linear fit
Depth (mm)
0.0 0
20
40
60
1.0 pristine concrete 20
R cm # 60 N/mm 2
0.8
thrust=170 N
0.6 max
0.4 0.2
min Bit diameter (mm)
0.0
80
6
8
10
12
14
Fig. 4 - Variation of the net torque at the chuck due to the inherent material heterogeneity and torque deviation from linearity with different drill bit diameters.
DR (J/mm)
DT (s/mm)
thrust= 170 N Ø bit = 10mm
40 30
0.15
20
0.10 0.05
ordinary
10
lightweight
200
400
600
ordinary lightweight
T(°C)
0 0
thrust =170N Øbit =10mm
0.20
T(°C)
0.00
800
0
200
400
600
800
Fig. 5 - Effect of the thermal damage on the drilling resistance DR and drilling time DT.
R Tc / R 20 c (%)
DRT / DR20
100
550°C 100%
80
400°C
60
ordinary
ordinary 2 (R 20 C =50.4 N/mm ) lightweight 2 (R 20 C =51.1 N/mm )
40 20
0
200
400
600
lightweight
50%
Drilling Resistance Drilling Time
T (°C)
Eurocode 2 0
decay onset
T(°C)
0% 0
800
Fig. 6 - Residual cubic strength of the thermally damaged concretes herein investigated.
244
200
400
600
800
Fig. 7 - Relative decay of the drilling parameters.
4. Sensitivity to thermal damage Once the optimum bit diameter and drilling thrust have been defined, a series of tests on concrete cubes (150 mm) has been performed in order to ascertain the sensitivity of this method to different levels of thermal damage. An ordinary concrete and a structural lightweight concrete (average cubic strength Rcm = 50 N/mm2 - max aggregate size = 16 mm) have been tested as they were or after a slow thermal cycle up to 200, 400, 600 and 800°C (heating rate = 0.5°C/min, cooling rate 0.2°C/min). These concretes exhibited very similar compressive strength decays (Fig. 6), with a significant loss at temperatures higher than 400°C, in accordance with Eurocode 2 (Part 1.2: General rules – Structural fire design, draft October 2002). On the contrary, the drilling resistance is an almost constant or even increasing function of temperature up to about 400°C (Fig. 5), possibly because of the increased material deformability and nearly constant fracture energy, which are generally associated to the material thermal damage [7]. Nevertheless, a marked drilling resistance decrease takes place at higher temperatures, as soon as the severe strength decay offsets the improved material ductility (RcT < 0.5 ÷ 0.7 Rc20°C). Due to the softer aggregate, the lightweight concrete is definitely easier to be drilled, but the temperature effect is still recognizable in relative terms (Fig. 7). The same trends can be observed for the drilling time, although this parameter proved to be less sensitive to the thermal damage, especially in the case of lightweight concrete. For this reason, only the drilling resistance will be considered in the following sections. Other tests, not reported in this paper, proved the viability of this technique also in detecting voids, defects and layers of distinct materials (plaster, insulation, etc).
5. Tests on concrete panels In order to ascertain the reliability of the proposed test method in assessing the damage gradient within a concrete member exposed to fire, a couple of concrete panels has been exposed to a marked thermal gradient (> 5°C/mm) by heating them on the one side while keeping cold the opposite side with a fan (Fig. 8 - thickness = 80 mm). The maximum temperature profile has been determined by means of three embedded
Fig. 8 - Concrete panel fitted with thermocouples and exposed to a thermal gradient.
DR 120 (J/mm)
ordinary concrete
80
40 average depth (mm)
0 0
20
40
60
lightweight concrete
DR 40 (J/mm) 30 20 10
depth (mm)
0 0
20
40
60
Fig. 9 - Drilling resistance profiles through the ordinary and lightweight concrete panels after heating the left side.
245
thermocouples, allowing to recognize the isotherms corresponding to the onset of the drilling resistance decay (about 550 °C and 400°C for ordinary and lightweight concrete respectively). The drilling tests conducted on the same panels clearly reveal the effect of the thermal gradient (Fig. 9), albeit the result is partially masked by the inherent material heterogeneity ascribable to the aggregate. However, this disturbance can be easily cleaned out by averaging the results of a few repeated tests. Moreover, the plots of the relative drilling resistance (i.e. referred to the innermost material response) further help in recognizing the external damaged layer, regardless of the initial value of the drilling parameters at room temperature (Fig. 10). The depth of the isotherm corresponding to the onset of the drilling resistance decay can be easily detected from these latter diagrams.
6. In-situ application The opportunity for a further check on this damage assessment technique was provided by a standard fire test on a concrete duct for electric cabling protection in railway tunnels (ISO 834 fire curve, 90 min duration - Fig. 11). The test was run in a vertical furnace, after closing the specimen in a low-grade reinforced-concrete box. As a consequence, the 0.2 m thick concrete wall on the back of the duct was partly exposed to the burners and partly protected by the tested specimen itself. Even not being the object of the fire test, this panel is an interesting example of the possible not uniform damage pattern resulting from a severe fire. Hence, the temperature of the exposed portion has been monitored on both faces and at half thickness, allowing to plot the maximum temperature profile experienced by this concrete member (Fig. 12). After cooling, the wall has been examined by drilling a series of holes along 5 rows (from A to E - 3 holes for each row). The average diagrams pertaining to each row clearly reveal which part of the structure went through a severe thermal exposure (rows from A to C) and which one was only marginally
DRT /DR 20
ordinary concrete
100% 80% 60% LWC 40% 20% depth (mm)
0% 0
20
40
60
800
T (°C) 600
550°C
ordinary concrete 400
400°C
LWC 200 depth (mm)
0 0
20
40
60
100% LWC 80%
74%
ordinary concrete
60% 53%
40% 20% depth (mm)
0% 0
20
40
60
Fig. 10 - Relative drilling resistance average profiles and connections to the temperature and residual strength profiles.
246
impaired during the fire test. It is worth to note that only about 5 minutes were needed to perform the whole series of tests and the results were immediately available for the interpretation thereafter. This is definitely the main benefit of this kind of NDT technique.
7. Conclusions In its different forms, the drilling resistance test is an accepted Non-Destructive Testing technique for the assessment of some building materials such as wood and stone. The viability of the method in the case of reinforced concrete structures and its potential for the assessment of the thermal damage undergone during a fire have been checked in this paper, allowing to formulate the following set of conclusions:
Fig. 11 - Fire test setup including the concrete duct to be tested and the back wall which was subsequently examined via the drilling resistance technique.
DR
x A hammer drill is recommended in order to quickly inspect the concrete cover preventing an excessive bit wearing and overheating. In this case, the sensitivity to the exerted thrust is markedly reduced and no special control of either the drilling force or the feed rate is needed. A medium size drill bit (Ø # 10mm) exhibits a regular response despite of the inherent material heterogeneity (max aggr. size # 16 mm).
30
x The dissipated work per unit drilling depth (J/mm) appears to be the most sensitive indicator of the material soundness. A correlation between this parameter and the material compressive strength cannot be easily worked out, given the strong influence of other properties like the fracture energy and the aggregate hardness. However, the drilling resistance keeps its significance in relative terms and the comparison with the inner virgin material provides meaningful information on the thickness of the outer fire damaged concrete.
0
(J/mm)
20 A B C D E
10
depth (mm) 0
1000
20
40
60
T (°C)
800 maximum temperature envelope
600 400
at the burners turning off
200
x Even if only a sizeable thermal damage can be detected via the drilling resistance method (RcT < 0.5 ÷ 0.7 Rc20°C), it should be noted that similar damage levels are considered in the popular “Reduced crosssection method” for the design of concrete structures under thermal loads and for the evaluation of the residual capacity after a fire (critical temperature = 500°C).
depth (mm)
0 0
20
40
60
Fig. 11 - Average drilling resistance profiles along five equally spaced lines and maximum temperature envelope in the exposed part of the back wall.
247
x The drilling resistance test proved to be a fast and reliable method also in the case of in-situ application and realistic fire conditions. The immediate availability of the results is expected to be of valuable help in the assessment of concrete structures surviving complicated fire scenarios.
Acknowledgements A grateful acknowledgement goes to Massimiliano Bondesan and Gianluca Pizzigoni for their lively cooperation in carrying out the tests in partial fulfilment of their MS degree requirements. Special thanks also to Daniele Bonetti (D. Bonetti & Co. - Dalmine - Italy) for the valuable suggestions concerning the signal conditioning and data acquisition of the modified drill. The author is also indebted to MS Engr. Paolo Mele and Giuseppe Grella of CSI (Italian Experimental Center - Bollate, Italy) for their support to the experiments following the fire test. Last but not least, the author wishes to acknowledge Hilti Corp. (Schaan - Principality of Liechtenstein) for making available the drill and its accessories.
References [1]
FELICETTI R. and GAMBAROVA P.G., "High-Performance Light-Weight Concrete: Material and Sectional Properties during and after a Fire", Proc. Int. Conf. on Advances in Concrete Structures, Xuzhou (China), V.1, 2003, pp. 89-99.
[2]
CIB W14 Report, "Repairability of Fire Damaged Structures", DRYSDALE D.D. and U. SCHNEIDER U. (Editors), Fire Safety Journal, V.16, 1990, pp. 251-336.
[3]
CHAGNEAU F. and LEVASSEUR M., "Contrôle des matériaux de construction par dynamostratigraphie", Materials and Structures, V.22, 1989, pp. 231-236.
[4]
TIANO P. and VIGGIANO A., "A new diagnostic tool for the evaluation of the hardness of natural and artificial stones", Int. Journal for Restoration of Buildings and Monuments, V.6, n.5, pp. 555-566.
[5]
RINN F., "Eine neue Bohrmethode zur Holzuntersuchung", Holz-Zentralblatt, V. 34, n.115, 1989, pp. 529-530.
[6]
GUCCI N. and BARSOTTI R., "A non-destructive technique for the determination of mortar load capacity in situ", Materials and Structures, V.28, 1995, pp. 276-283. FELICETTI R. and GAMBAROVA P.G,. "On the Residual Properties of High Performance Siliceous Concrete Exposed to High-Temperature", A Volume in Honour of Prof. Z.P. Bazant’s 60th Birthday, G. Pijaudier-Cabot, Z. Bittnar and Bruno Gerard, Hermes Science Publ., Paris,1999, pp.167-186.
[7]
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Session 6
Real Fires, Large-Scale Tests and Model Validation
Fire Engineering Design of Concrete Structures Tom Lennon*
Page 251
Fire Tests on Single-Shell Tunnel Segments Made of a New High-Performance Fireproof Concrete Ekkehard Richter*
261
On the Role of Concrete Slabs in Composite Steel-Concrete Structures Subjected to Fire Ahmed Allam, Richard Witasse and Giovanna Lilliu
269
The Effects of the Restraint Conditions on the Fire Resistance of Tunnel Structures Céline Féron
271
Test Results on the Fire Resistance of Precast Plates and Panels Provided with Polystyrene Void Formers Andrea Franchi
281
Spalling of Self-Compacting Calcareous High-Strength Concrete after a Firei Karl Kordina
285
Fire Behaviour of HPLWC Hollow-Core Slabs: Full-Scale Furnace Tests and Numerical Modelling Annibale L. Materazzi and Marco Breccolotti
289
Slender Steel-Concrete Columns in Fire: Testing and Modelling by Means of Simplified Approaches Annibale L. Materazzi, Emidio Nigro and Marco Breccolotti
295
Fire-Resistance of Precast Elements: Research Activity within the Italian National Project “Ulisse”i Sergio Tattoni
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Fire Engineering Design of Concrete Structures Tom LENNON Principal Consultant FRS, The Fire Division of BRE Garston, Watford, UK
Summary This paper discusses issues relating to the structural fire engineering design of concrete structures. The philosophy of large scale fire testing and performance based design is discussed in the context of a full-scale fire test carried out on a seven storey concrete framed structure at BRE’s large scale test facility at Cardington. The results and observations from the test are discussed and recommendations made for future work in this area. Keywords: fire engineering, concrete structures, large scale testing, demonstration.
1.
Introduction
Fire resistance requirements for buildings are specified in the National Building Regulations for individual countries. All buildings must meet certain functional requirements covering means of escape, internal fire spread, external fire spread and access and facilities for the fire service as laid down in the regulations. In the UK, the Building Regulations are only intended to ensure reasonable standards of health and safety for persons in or about the building. They are not designed to limit structural damage other than to achieve this aim and they are not designed to minimise financial losses arising from a fire. This has important implications for the fire engineering design of buildings where the requirements of the regulations may be insufficient to meet the needs of the client. For present purposes the most important requirement in the UK regulations is that dealing with internal fire spread as related to structural elements which states: “The building shall be designed and constructed so that, in the event of a fire, its stability will be maintained for a reasonable period”. In the UK Approved Document B [1] provides detailed guidance on ways to demonstrate compliance with the functional requirements. However, it is important to emphasise that it is the requirement which is mandatory NOT the guidance. This allows for alternative approaches to meeting the requirements which can be developed in collaboration with Building Control Officers. In general the most common route to demonstrating compliance has been to follow the guidance in the document. The requirement for the building to maintain stability for a reasonable period has traditionally been related to a required time for survival in a standard fire test. The detailed drawbacks and advantages of the standard test are discussed elsewhere in this document. The fire resistance requirements contained in the guidance to the approved document relate directly to fire resistance time and it is often incorrectly assumed that there is a one to one relationship between survival in a fire resistance test and survival in a fire. This is clearly not the case. The design criterion is that the fire resistance is greater than the time required by the regulations based on the assessment of the building as belonging to a particular purpose group. This is the method by which the vast majority of buildings are designed. The prescriptive nature of the regulations has hindered the development of a more rational approach to the design of buildings for fire. For concrete structures traditional fire “design” consists of choosing minimum dimensions in terms of section size and cover to the reinforcement based on results from fire tests carried out on representative samples of typical forms of construction. However, much of this information is very old and is not necessarily directly applicable to modern forms of construction. A recent study [2] has investigated the background to the code provisions for the UK.
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2.
Justification for full-scale fire tests
Full-scale fire tests are complex and expensive to undertake. This section provides a justification for investing the time, trouble and money required. Design methods for concrete structural elements are based on the strength (or resistance) of the structural element at elevated temperature such that: Ed,fi Rd,t,fi(1) Where:
(1)
Ed,fi is the design effect of actions for the fire situation Rd,t,fi is the corresponding design resistance in the fire situation
There are two problems associated with the traditional approach: 1. The temperature regime used to assess structural behaviour often bears little relationship to the thermal environment in real fire compartments. 2. The resistance is that of an individual element rather than a complete structure. It is clear from past experience that traditional methods of assessing the structural performance of concrete in fire do, in most cases, work. However, what is equally clear is that current methods are generally overly conservative and do not provide a rational basis for assessment. One of the objectives of the Cardington fire test was to attempt to quantify the safety margins currently adopted in an attempt to optimise the use of resources to provide a safe and efficient design solution. There is a growing opinion that the structural contribution of complete buildings is underutilised in current design procedures particularly for the fire limit state. This, together with evidence from three dimensional numerical models and investigations from real fires [3], suggest that the fire resistance of complete structures is significantly better than that of the single elements from which fire resistance is universally assessed. Computer programs for predicting structural behaviour at elevated temperatures have developed beyond the available experimental data required for validation. Before such analytical techniques can be used with any confidence it is necessary to verify them against test results from real buildings subject to real fires. Whilst it is possible to study structural behaviour by examining fire damaged buildings, interpretation of the findings is complicated by the lack of information on heating rates, temperatures and the stresses imposed on the members at the time of the fire. It has long been recognised that global frame behaviour differs from an assessment based upon the performance of the individual elements which go to make up the frame. The experience gained from investigations following the catastrophic gas explosion at Ronan Point which led to a progressive structural collapse highlighted the need for the engineer to consider global behaviour which, in this instance, led to a failure mechanism not considered at the design stage. Subsequent robustness requirements have led to improvements in the design and construction of framed structures. Just as a consideration of overall building behaviour can lead to previously unconsidered modes of collapse so such a design philosophy may reveal beneficial aspects of frame behaviour. As well as potential disasters to be avoided there may be potential advantages to be utilised. Alternative methods of sustaining the applied loading may be available. The principles of assessing the structural performance of individual members when subject to realistic loading regimes and realistic boundary conditions are particularly relevant when considering the fire resistance of a framed structure. The simplifying assumptions of idealised loading and boundary conditions alluded to above are present in traditional fire tests carried out in standard furnaces. There are however additional complications with furnace testing which further limit the applicability of the results. The failure criteria for such tests are based on arbitrary values often chosen to prevent damage to the furnace. The standard time/temperature response bears little relation to real fires and does not include the effects of differing ventilation conditions or the influence of the thermal properties of compartment linings. The degree to which temperature uniformity is present in real compartments is not addressed and direct flame impingement may also have an influence which is not considered. It is clear that complicated three dimensional behaviour in a complex thermal environment can only be addressed using realistic full scale tests.
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3.
Fire engineering design, thermal exposure, time equivalence and risk based approaches
In the UK new fire engineering design standards [4] are being developed based on a risk based approach to define appropriate periods of fire resistance for elements of structure. The new method like the European Natural Fire Safety Concept set out in Annex E of the fire part of the Eurocode for Actions [5] is material independent and considers the influence of fire load density, compartment geometry, thermal properties of compartment lining materials, amount of ventilation available for the combustion process, active suppression measures and the height and nature of the occupancy on the performance of the structure. As in Europe much of this work has been instigated and supported by the steel industry. There is an urgent requirement for the European concrete industry to understand the implications of these parameters on the performance of concrete structures and to undertake the fundamental research needed to enable such methods to be validated for concrete structures. The European fire engineering methods are based on varying the design fire load density to take into account all relevant factors while the UK method is based on the concepts of parametric fires and equivalent time of fire exposure. 3.1
Parametric approach
The parametric approach set out in Annex A of EN 1991-1-2 provides a simple method for estimating compartment time-temperature response based on a consideration of the ventilation conditions, the fire load and the thermal properties of the compartment lining. The parametric approach provides a quick and easy approximation of compartment gas temperatures ideally suited for use on modern spreadsheets. The approach has been extensively validated over a number of years. It applies only to the post-flashover phase which is of primary concern when considering structural issues and assumes a uniform temperature within the compartment. The basic formulation in Annex A of EN 1991-1-2 is as follows: 4g = 20 + 1325(1-0.324e-0.2t* - 0.204e-1.7t* - 0.472e-19t*)
(2)
where: 4g = temperature in the fire compartment t* = t.* t = time(h) * = [O/b]²/(0.04/1160)² b = (UcO) O = opening factor (Avh/At) Av = area of vertical openings h = height of vertical openings At = total area of enclosure U = density of boundary enclosure c = specific heat of boundary of enclosure O = thermal conductivity of boundary
(°C) (h) (-) (J/m²s½K) (m½) (m²) (m) (m²) (kg/m³) (J/kgK) (W/mK)
The temperature within any given compartment is assumed to vary as a simple exponential function of modified (or parametric) time depending on the variation in the ventilation area and the properties of the compartment linings. The values 0.04 and 1160 refer to the opening factor and thermal properties of the compartment used in the development of the approach. A parametric calculation with the same values corresponds to a time-temperature response very similar to the standard fire curve. In the original draft for development of the Eurocode released for use in the UK with the UK National Application Document [6] there were a number of restrictions on the use of this formula which greatly limited the scope of application. Most of these have now been removed as validation for the approach has been developed and the method may now be used for most common building types. The calculation procedure provides the engineer with a rate of temperature rise varying with time. In order to estimate the duration of the fire, the relationship between the fire load and the
253
opening must be considered. The maximum temperature in the heating phase occurs at a time tmax given by: tmax = maximum of 0.2 x 10-3 x qt,d/O or tlim
(3)
Where: qt,d is the design value of the fire load density related to the total surface area of the enclosure. Values of qt,d should be in the range from 50 to 1000MJ/m². and tlim is a minimum value for the duration of the fire based on slow, medium or fast fire growth rates. For office accommodation a medium fire growth rate should be assumed corresponding to a value of tlim equal to 20 minutes. For most practical combinations of fire load, compartment geometry and opening factor tmax will be in excess of the 20 minute limit The temperature-time curves for the cooling phase are then given by: Ĭg = Ĭmax – 625(t*-t*max) for t*max 0.5 Ĭg = Ĭmax –250(3-t*max)(t*-t*max) for t*max < 2 Ĭg = Ĭmax –250(t*-t*max) for t*max 2
(4) (5) (6)
Figure 1 shows an example of a parametric calculation together with test results indicating the accuracy of the approach. comparison between EC1 parametric calculation and measured values 1200
1000
temperature (deg C)
800
600
400
200
0 0
10
20
30
40
50
60
70
time (mins) test 1
prediction
test 2
Fig. 1 - Comparison between parametric prediction and measured values. 3.2
Equivalent time of fire exposure
EN1991-1-2 includes a method for determining the appropriate fire resistance period for design based on a consideration of the physical characteristics of the fire compartment. This is effectively a “halfway house” between the nominal curves so familiar to many and the behaviour of a realistic fire compartment. The method relates the severity of a real fire in a real compartment to an equivalent period of exposure in a standard test furnace. The relevant input parameters are the amount of fire load, the compartment size (floor area and height), the thermal properties of the compartment linings and the ventilation conditions. The formulation in the Eurocode (based on fire load density related to floor area) is: te,d = (qf,d . kb . wt) kc
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(6)
where: te,d is the equivalent time of fire exposure for design (min) qf,d is the design fire load density (MJ/m²) kb is a conversion factor dependent on thermal properties of linings wt is the ventilation factor kc is correction factor dependent on material Note: for protected steel and reinforced concrete kc = 1.0, where no detailed assessment of the thermal properties is made the factor kb = 0.09 (National annex value). The ventilation factor wf = (6/H)0.3 [0.62+90(0.4 – Įv)4] in the absence of horizontal openings in the compartment Where:
H is the height of the fire compartment (m) Įv = Av/Af where Av and Af are the ventilation and floor area respectively (m²)
The verification is then that the fire resistance of the member is greater than the time equivalent value. The concept of time equivalence is illustrated in figure 2 with respect to the maximum temperature of a structural member and the time taken for that member to achieve an identical temperature in a standard furnace test.
Fig. 2 - Graphical illustration of time equivalence.
4.
Full-scale fire test
A large fire test has been undertaken as part of the performance based research programme for the European Concrete Building Project [7]. The main aim of the test was to investigate the behaviour of a full-scale concrete framed building subject to a realistic fire scenario and realistic levels of imposed load. The test building is a seven storey in situ flat slab structure comprising three bays by four bays, each 7.5m wide, with two core area containing steel cross bracing to resist lateral forces. A fire compartment with a floor area of 225m² was constructed between the ground and first floors using concrete blocks lined with a single layer of fire resisting plasterboard. The location of the fire compartment is shown in plan and elevation in figures 3 and 4. the purpose of this paper is to highlight some of the issues raised through full-scale testing not to provide a detailed analysis of the results and observations from the test. More detailed information on the performance of the structure is available[8,9]. 4.1 Structural performance The structure showed no signs of collapse during or after the fire. Three particular issue have been highlighted from the observed and measured behaviour of the building during and after the fire test.
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A
C
B
D
7500
7500
7500
7500
1
2
2 No. openings 3.2m by 4.25m (Total area = 27.2m2)
External column 400x250mm Internal column 400mm2
Vertical steel cross bracing
Fire compartment area
3750
7500
V4
3750
V12
7500
V11
140 thk blockwork wall with one skin of plasterboard 7500
V9
V8
3
4
V6
V5
3750
V13
3750
Denotes location of vertical displacement measurement (refer Fig.11)
Vertical steel cross bracing
5
Fig. 3 - Plan of building showing location of fire compartment. 5
4
3
2
1
2nd
500
3750 3750 3750 3750
3rd
250
4th
3750
5th
3750
Fire compartment
6th
3750
7th
1st
Fig. 4 - Cross-section through the building showing the location of the fire compartment.
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4.1.1 Performance of High Grade/High Strength concrete columns One internal column (C3) was fully exposed to the fire and eight columns (internal and external) were partially exposed. All the ground floor columns were C85 high-strength concrete with limestone aggregate and micro silica. To reduce the effects of spalling 2.7kg/m³ of polypropylene fibres were added. At 28 days the measured cube strength was 103N/mm² and the moisture content just prior to the test was 4.2% by weight. All columns performed well in the fire with no sign of surface spalling. Inspection of the central column following the test showed longitudinal cracking around the edge of the column but no signs of explosive spalling. The performance of the fully exposed internal column is illustrated in figures 5 and 6.
Fig. 5 - Longitudinal cracks in column C3.
Fig. 6- Removal of concrete from corner of column C3.
4.1.2 Spalling to the underside of the first floor During the fire test extensive spalling occurred to the underside of the first floor slab. The extent of the spalling which completely exposed the bottom reinforcement is shown in figure 7. Examination of the area of spalling and the observations recorded during the test suggests that high compressive stresses were induced in the slab due to restraint to thermal expansion provided by the surrounding cold structure. Other contributory factors include: x use of gravel aggregate x higher than anticipated concrete strength x high moisture content It is likely that the high in plane stresses were beneficial in supporting the applied load through the mobilisation of compressive membrane action. This mode of behaviour is different to the flexural mode assumed in design based on the results from fire tests on isolated members. 4.1.3 Lateral movement of external columns Expansion of the heated slab led to significant lateral displacement of the edge columns along gridline D. The residual lateral displacements away from the fire compartment are illustrated in figure 8. These horizontal movements will lead to additional moments in the column due to the eccentricity of loading (P-į effect) which need to be taken account of in design.
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Fig. 7 -Spalling of underside of floor slab. Residual horizontal column movement - Cardington fire test
D5
column location
D4
D3
D2
D1
0
10
20
30
40
50
60
70
80
displacement (mm)
Fig. 8 - Residual horizontal deflection of columns.
5.
Discussion
This paper has attempted to identify a number of issues related to the performance of concrete structures in fire. Developments in fire engineering design are described in relation to the regulatory framework for fire resistance. Aspects of structural behaviour related to observations from a fullscale fire test are discussed. There remains a need to develop knowledge in this area to allow designers to make optimum use of a material with a history of good performance in fire. The intention is to promote collaboration and co-ordination of research in this area to enable design rules to be developed that take into account a realistic assessment of the actions on the building during a fire and identify realistic modes of failure and load-carrying mechanisms.
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6.
Conclusions
The paper has highlighted a number of issues related to the performance of concrete buildings in fire. There is a need to initiate a co-ordinated programme of research in order to understand the complexities of the behaviour of realistic structures subject to realistic fires in order to fully realise the potential of a construction material with inherent fire resistance. The Cardington fire test has identified a number of issues such as the mobilisation of compressive membrane action in flat slabs, the lateral stability of edge columns and mechanisms of spalling related to normal and high strength concrete. Such issues can only be addressed through large scale testing. The European concrete industry requires a strategy for research related to the performance of concrete structures in fire that takes into account developments in fire engineering design and relates structural performance to a realistic assessment of the actions in place during a fire.
Acknowledgements The support of the Concrete Centre and the British Cement Association is gratefully acknowledged. The work of Professor Colin Bailey of UMIST (formerly of BRE) is acknowledged in relation to the Cardington fire test.
References [1]
OFFICE OF THE DEPUTY PRIME MINISTER, The Building Regulations 2000, Approved Document B, Fire Safety, 2000 edition consolidated with 2000 and 2002 amendments, HMSO, 2004.
[2]
LENNON T, “Fire Safety of Concrete Structures: Background to BS8110 Fire Design”, BRE Bookshop, Watford, UK, 2004, 44 pp.
[3]
TOVEY A K and CROOK R N, “Experience of Fires in Concrete Structures”, ACI Symposium on evaluation and repair of fire damage to concrete, San Francisco, 16-21 March, 1986, American Concrete Institute, Detroit, Ref. SP-92.
[4]
BRITISH STANDARDS INSTITUTION, DD9999, “Code of Practice for Fire Safety in the Design, construction and use of Buildings, Expected publication date 2005.
[5]
BRITISH STANDARDS INSTITUTION, BS EN1991-1-2, Eurocode 1: Basis of design and actions on structures Part 1.2: Actions on structures exposed to fire, London, 2002. BRITISH STANDARDS INSTITUTION, DD ENV1991-2-2, Eurocode 1: Basis of design and actions on structures Part 2.2: Actions on structures exposed to fire (together with United Kingdom National Application Document), London, 1996.
[6]
[7] [8]
[9]
CHANA P, “The European Concrete Building Project”, The Structural Engineer, Jan 2000, 78, No. 2, 12-13. LENNON T, BAILEY C, CLAYTON N, “The Performance of High Grade Concrete Columns in Fire”, Proceedings of the 6th International Symposium on High Strength/High Performance Concrete, Leipzig, June 2002. BAILEY C, “Holistic Behaviour of Concrete Buildings in Fire”, Proceedings of the Institution of Civil Engineers, Structures & Buildings, 149, Issue 4.
259
Fire Tests on Single-Shell Tunnel Segments Made of a New High-Performance Fireproof Concrete Ekkehard RICHTER Senior Engineer Institute for Building Materials, Concrete Construction and Fire Protection (IBMB), Braunschweig University of Technology Braunschweig, Germany
Summary A series of fire tests carried out on loaded single-shell tunnel segments have shown the advantages of a newly-developed special fireproof concrete. Concrete spalling during the fire exposure was minimal and the material turned out to be able to meet the increased requirements concerning the safety and durability of the tunnels throughout the entire operating period. Keywords:
large-scale fire test, tunnel, high temperature, single-shell tunnel segments, concrete with plastic fibres, explosive spalling.
1. Introduction Preventive structural fire protection in tunnels is becoming more and more important on account of several recent serious fire disasters. Preventive structural fire protection should thus exclude - to the greatest possible degree - any substantial negative effects on the bearing capacity, with specific reference to tunnel roof vault and tunnel ceiling during and after a fire. There are various technical possibilities. In new structures, the ideal solution is certainly offered by specially-conceived cementitious composite, that do not require any kind of fire protection. In a far-reaching research project, Hochtief AG in collaboration with the Institute for Building Materials, Concrete Construction and Fire Protection (iBMB) developed such a special, high-performance fireproof concrete called “System Hochtief”. In the last phase of the research project, large-scale fire tests were carried out with loaded tunnel segments made of concrete “System Hochtief”. The aim of the fire tests was to demonstrate that these tunnel segments fulfil all requirements of structural fire protection in railway and road tunnels without special fire protection measures. Tunnels have to be conceived in such a way that a fire cannot produce damages that jeopardize the load-bearing capacity or the structural integrity of the tunnel as a whole or of any of its major elements. Fires must not impair the serviceability of a tunnel (e.g. tightness of underwater tunnels), and the structure must not suffer from inadmissible permanent deformations. Rehabilitation measures must ensure the lowest possible input in terms of time, equipments and cost [1].
2.
Fire tests
2.1
Test specimen
Fire tests were carried out with two tunnel segments, which were cast in realistic steel formwork. The tunnel segments were approximately 5 m long, 1.5 m wide and 0.5 m thick (Fig. 1). Both tunnel segments were made of concrete C 55/67 with aggregates of siliceous sand and gravel and basalt. The plastic fibre content was 4 kg per cubic meter of concrete. Just before starting the fire test the compressive strength of the concrete was in average 90 N/mm2 and the moisture content was approx. 3 % by weight. The fire test was carried out with a simply supported unrestrained tunnel segment. The specimens were tested using one set of support conditions. At both supports the specimens were free to rotate. At one support they were free to expand axially, at the other support the axial deformation was resisted. The tunnel segment was installed in a way to form a vault above the furnace, providing a rising height of 0.55 m. The internal dimensions of the furnace chamber were
261
width | 2.6 m, length | 3.9 m and height | 1.3 m. (Fig. 2).
Fig. 1 - Test specimen.
Fig. 2 - Test set-up (Drawing by Hochtief AG): Pressen { hydraulic jack; Brandraum { furnace;
Prüfkörper (Tübbing) { tunnel segment (tubbing); Widerlager { horizontal support; Brandkammerwand { wall of the furnace; Ölbrenner { oil burner; Stahlaussteifung { steel stiffening; Schamotte-Aufmauerung { firebrick.
The interior faces of the chamber were lined with fire resistant bricks. Additional bricks were place on the bottom of the furnace to reduce the volume of the chamber. Inside seven oil burners were arranged. Two oil burners on each wall except for one longitudinal wall where only one burner was placed. In the first test the tunnel segment was loaded with 50 % and in the second test with 100 % of the actual service load. The load condition “100 %” caused compressive stress of approx. 24 N/mm2 on the bottom of the fire exposed surface of the tunnel segment. The thermal restraint forces after 60 minutes fire exposure were determined by calculation and added to the service load. In this way the tunnel segments were already high loaded at the beginning of the fire test although it is known that this may cause an enhanced risk of spalling. Loading was applied by six vertical (PV) and two horizontal hydraulic jacks (PH) located outside the furnace. The load of the tunnel segment was increased by five load increments until full load. During the tests the vertical and horizontal loads were kept constant. 2.2 Measurements During the fire tests the furnace gas temperatures were measured 100 mm from the fire-exposed surface at three measuring-points. The temperatures measured by furnace thermocouples were averaged, and the average was used for controlling the furnace temperature. The temperatures of each tunnel segment were measured at three cross-sections using so-called “temperature measuring ladders” with 8 thermocouples (Fig. 3). The distances of the thermocouples to the fire-exposed surface were 2, 4, 6, 8, 10, 15, 20 and 30 cm. The temperature measuring ladders
262
were located at the longitudinal axis of the tunnel segments approx. at every quarter of the length (1/4L, 1/2L and 3/4L).
Fig. 3 - Temperature measuring ladder. In addition the vertical deflections of the crown of the tunnel segment and the horizontal displacement at the support with free axial expansion were recorded continuously. The spalling and cracking behaviour as well as the emergence of moisture on the unexposed surface of the tunnel segment was checked visually, and the observations made were logged. Fire tests were undertaken with the EBA temperature-time-curve [2], i.e. a fire was simulated along the line of what can be anticipated during fires in railway tunnels. The furnace temperature was controlled to rise from 20 °C to 1200 °C in 5 minutes, remaining at this level for 55 minutes and decreases to 20 °C in 110 minutes. 2.3
Test results
Fig. 4 - Comparison of given furnace temperatures and those measured during the fire test.
263
In Fig. 4 the given furnace temperatures are compared with those measured during the test. Fig. 4 shows good agreement between given and measured temperatures. Especially the increase of temperatures of about 200 K/min in the first stage of the test was nearly exact reproduced. In this stage of the fire spalling will mostly occur.
Fig. 5 - Temperature distribution in the concrete (measuring cross-section 1, 2 and 3). The measured temperatures inside the concrete cross-section are shown in Fig. 5. The temperatures of measuring points with the same distance to the fire-exposed surface are very close together, i.e. the entire cross-section of the tunnel segment showed a nearly uniform temperature distribution. The evaluation of the temperature distribution in Fig. 5 revealed that temperatures in the concrete at 6 cm cross-sectional depth generally remain at approx. 365 °C. In other words, a reinforcement layer placed at a cross-sectional depth of 6 cm nearly fulfils the requirement contained in the German Standard for road tunnels (ZTV-ING, Part 5, chapter 1 [4]). In [4] the maximum temperature in the bearing reinforcement is limited to 300 °C in the event of fire. In both tests no explosive spalling occurred. This observation was confirmed by the results of examinations of the fire-exposed surface of the tunnel segments. In the area of the cement-matrix the surface was tough and without cracks (Figs. 6a and 6b). The colour was something between bright yellow and bright brown. The aggregate grains near the surface were also tough and without cracks, their colour was dark brown until black. Single aggregate grains jutted out of the surface like „pockmarked“. The aggregate grains looked something like cold lava.
Fig. 6a - Fire-exposed surface after test.
264
Fig. 6b - Detail of Fig. 6a.
3.
Numerical modelling
3.1
Introduction
This chapter starts with the comparison of calculated and measured deformation during the loading procedure at ambient temperature. Hereafter the fire tests are simulated with FEM analysis. Both material and geometrical non-linearity’s are included. The temperatures inside the cross-section obtained from tests and calculations are compared. The thermo-mechanical models of concrete with basalt aggregates are described and are used for the calculation of deformation behaviour during fire test. 3.2
Loading at ambient conditions
As pointed out in chapter 2.1 the loading of the tunnel segments were increased by five load increments until full load. During the tests the vertical and horizontal loads were kept constant. In Fig. 7 the measured vertical and horizontal deformations are compared with those calculated. The calculated values correspond reasonably well with the measured values.
Fig. 7 - Comparison of measured and calculated deformations during loading.
3.3
Fire conditions
3.3.1 Member temperatures In Fig. 8 calculated temperatures are compared with those measured at various depths for the three measuring cross-sections of one tunnel segment. It can be seen that there is good agreement between calculated (red lines) and measured (blue lines) temperatures, especially in the early stage of the test. At later stages the member temperatures decrease due to the decreasing furnace temperature (see Fig. 4), which might account for the deviation between calculated and measured temperatures at this stage of fire exposure. The numerical model for calculation of the temperatures in the cross-section does not take into account the cooling phase. Furthermore no adequate thermal material properties are available for decreasing temperatures. Due to lack of data of these properties, the program uses the thermal properties for increasing temperatures even in the cooling phase.
265
Fig. 8 - Comparison of measured and calculated temperatures.
3.3.2 Material properties Concrete strength and the type of aggregate present in the concrete influence the structural- and deformation-behaviour of a tunnel segment. Relevant formulas for the thermal and mechanical properties of concrete as a function of temperature in the range of 20-1200°C are given in Eurocode 2 Part 1-2 [5] for normal concrete made of siliceous and carbonate aggregate. The stress-strain curves and the thermal strains for the concrete given in Eurocode 2 Part 1-2, have to be modified taking into account the fibres and the basalt aggregate used in the concrete mix. While the presence of fibres has little influence on the thermal and mechanical properties of concrete [6] the influence of the basalt aggregate has to be taken into consideration. Data about the thermal and mechanical behaviour of concrete with basalt aggregate is available in [7, 8 and 9]. These data was used to modify the material models given in Eurocode 2 Part 1-2. In Fig. 9 the thermal strains and in Fig. 10 stress-strain relationships for concrete with basalt aggregate were compared with those given in Eurocode 2 Part 12.
Fig. 9 - Comparison of thermal strain for concrete with basalt aggregates with those given in Eurocode 2 Part 12.
266
Fig. 10 - Comparison of stress-strain curves for concrete with basalt aggregates with those given in Eurocode 2 Part 1-2.
3.3.3 Horizontal and vertical deformations The thermal strains (Fig. 9) and the stress-strain curves (Fig. 10) for concrete with basalt aggregate, both expressed as function of temperature are built into the computer program TUSSI [10]. In Fig. 11 the calculated and measured horizontal and vertical deformations are shown for the tunnel segment with 50 % loading.
Fig. 11 - Comparison of measured and calculated horizontal (hv) and vertical (wv) deformations for tunnel segment with 50 % loading.
It can be seen that the computer model predicts reasonably well, the trend in progression of deformations with time. However, the agreement between calculated and measured deformations depends to a high degree on the thermal and mechanical properties of concrete, which are used in the calculations. To illustrate the sensitivity on the deformations due to the type of aggregate, the analysis was carried out with thermal strain and stress-strain curves for siliceous aggregate (Eurocode 2 Part 12) and those for basalt aggregate. It can be seen that the difference between calculated and measured deformation reduces considerably when basalt aggregate is assumed. Due to lack of experimental data the numerical models for thermal strains and stress-strain relationships do not take into account the cooling phase. Both thermal and thermal-mechanical numerical models without consideration of cooling effects might cause slightly higher differences between measured and calculated deformations at later stages of the fire exposure.
4.
Discussion and conclusions
This paper reports on fire tests with high loaded reinforced concrete block segments, which are used for single-shell tunnel linings. The segments were manufactured of a special, high-bearing capacity fireproof concrete. The mechanical load consisted of the full service load and the thermal restraining forces, which appear after approximately 60 minutes fire duration. The thermal load was represented by the so-called “EBA”-temperature-time-curve. Mechanical and thermal loads result in a high stress level on the fire-exposed surface, which increases the risk of explosive spalling. In both tests the tunnel segments showed no explosive spalling during the fire exposure. After the tests the fire exposed surface was tight and without cracks. The second part of the report deals with modelling of temperature and deformation behaviour of fire exposed tunnel segments. Both temperatures and deformations can satisfactorily be predicted with the numerical models, differences appear for decreasing temperatures due to lack of adequate material data input.
267
Acknowledgements The test results presented in this paper were part of a far-reaching research project, which was supported by Hochtief AG. The author would like to express his appreciation for the financial support.
References [1]
[2]
KORDINA K., “Brandentwicklung in Unterirdischen Verkehrsanlagen und Beanspruchung der Umschließungsbauteile”. Contribution in: Research colloquium at the University of Karlsruhe, Sep. 1982. Special research department 148 “Behaviour of structural elements exposed to fire”, Braunschweig University of Technology, 9/1982. HOSSER D., RICHTER E., and PALIGA K., “Final Report: Fire Protection of Tunnel Shells – Fire Tests, Stage A”. Report of the Institute for Building Materials, Concrete Construction and Fire Protection, Braunschweig University of Technology in order of Hochtief AG, Essen, June 1998.
[3]
Guideline “Anforderungen des Brand- und Katastrophenschutzes an den Bau und Betrieb von Eisenbahntunneln”, Bonn, Eisenbahnbundesamt, 1997.
[4]
ZTV-ING. Teil 5 Tunnelbau. Zusätzliche Technische Vertragsbedingungen und Richtlinien für den Bau von Straßentunneln. Abschnitt 1 Geschlossene Bauweise. Verkehrsblatt-Sammlung Nr. S 1056, Stand 01/03
[5]
Eurocode 2 – Design of Concrete Structures – Part 1-2: General Rules, Structural Fire Design. 1995.
[6]
HOSSER D., RICHTER E., and PALIGA K., “Final Report: Grundsatzuntersuchungen zur Optimierung des Baulichen Brandschutzes in Tunneln”, Report of the Institute for Building Materials, Concrete Construction and Fire Protection, Braunschweig University of Technology in order of Kombinatie Middelplaat, Westerschelde v.o.f. KMW, 12/1997. SCHNEIDER U., DIEDERICHS U., ROSENBERGER W., and WEIß R., “Hochtemperaturverhalten von Festbeton”, Special Research Department 148 “Behaviour of Structural Elements Exposed to Fire”, Braunschweig University of Technology, Report 19781980, Part II, 06/1980.
[7]
[8] [9]
SCHNEIDER U., DIEDERICHS U., and ROSENBERGER W., “Basalt-Beton: Eigenschaften und Verwendung”, Bonn, Basalt-Union GmbH, 1981. NAUSE P., “Berechnungsgrundlagen für das Brandverhalten von Druckgliedern aus Hochfestem Beton”, Report No. 176. Institute for Building Materials, Concrete Construction and Fire Protection, Braunschweig University of Technology, (publication in preparation).
[10] KIEL M., “Analyse Brandbeanspruchter, ebener Rahmentragwerke mit dem ComputerProgramm TUSSI (Tunnel Structural Fire Safety Investigation) – Ein Beitrag zum Definierten Objektschutz”, Special Research Department 148 “Behaviour of Structural Elements Exposed to Fire”, Braunschweig University of Technology, Report 1978-1980, Part II, 06/1980.
268
On the Role of Concrete Slabs in Composite Steel-Concrete Structures Subjected to Fire Ahmed ALLAM Senior Fire Safety Consultant Halcrow Group Ltd London, UK
Richard WITASSE TNO DIANA BV Delft, The Netherlands
Giovanna LILLIU TNO DIANA BV Delft, The Netherlands
Summary In this paper some preliminary results concerning the finite-element simulation of the Cardington fire test are presented. A simplified 3D model of the test set-up is considered, where geometrical non-linearity is taken into account, as well as temperature dependant non-linear material behaviour. Keywords:
1.
full-scale fire tests, composite structures, non-linear geometrical and material behaviour.
Introduction
In order to assess the capability of the commercial Finite Element software DIANA to analyze composite structures under fire load, and to extend in the future this capability, Halcrow Fire and TNO DIANA are currently collaborating in simulating the Cardington full-scale test by means of the finite element method. The Cardington test, conducted in the mid 90s, confirmed the opinion of many engineers that assessment of fire resistance of isolated steel members, as prescribed by the standards, was far underestimating the resistance of the whole steel frame. Furthermore, the Cardington test showed the necessity to model correctly the action of concrete floors, as they appeared to play a significant role in preventing structural collapse. In this paper the preliminary study of a simplified model of the Cardington test is considered to evaluate the influence of thermal load and tensile membrane action in the concrete slab.
2.
Numerical simulation of the Cardington Fire Test
2.1
Test set-up
The Cardington full-scale frame was a eight-storey building with a footprint of 45 m by 90 m, and 35 m total height. Two 4 m by 4.5 m stairwells, and a 9 m by 2.5 m lift core were placed at the ends and centrally within the building, respectively (see Fig. 2.1). The test frame was subjected to a series of fire tests to investigate the overall behaviour of the structure under various types of compartment fires, as depicted in Fig. 1. 2.2
Finite Element Model
The three-dimensional Finite Element model used in the present study only considers one storey of the complete building and, because of symmetry, half of the plan (see Fig. 2). The columns and the beams are modelled with fully integrated beam elements, both along the longitudinal axis and over the I-shaped cross section. The concrete floors are modelled with 8-noded quadrilateral isoparametric curved shell elements. The reinforcement has been modelled by means of grid-shaped embedded steel layers, with no slip between steel and surrounding concrete. A smeared crack model is adopted for modelling concrete in tension. Non-linear behaviour of concrete under compression is modelled by combining the smeared crack model with a plasticity model. Steel is modelled as elasto-plastic material with Von Mises yield surface. Mechanical concrete and steel properties are considered temperature dependent, as prescribed by the EC 4. The fire load is simulated by applying temperature gradients throughout the beams and the floor slabs, while the columns are considered not to be heated up.
269
9.00 m
9.00 m
9.00 m
9.00 m
205
6.00 m
9.00 m
6.00 m
9.00 m
215
Fig. 1 - Cardington fire-test lay-out. 2.3
Fig. 2 - Finite Element model.
Results
The numerical results show that in the first stage, as a consequence of the restrained extension exerted by the column, the heated beam experiences large run-away deflections and pull-in the cool column. In the second phase, especially when the temperature is higher than 500 °C, the high restraint imposed by the columns and the large deformations in the heated beams bring to second order forces in the doubly-curved shells, that may become very significant and, eventually, cause failure of the fire compartment when fracture of the reinforcing steel would occur [1].
Fig. 3a - Horizontal displacement for column (node 205).
Fig. 3b - Mid-span deflection for beam (node 215).
Fig. 3c - Deflection profile at temperature 420 °C (time 0.36).
Fig. 3d - Deflection profile at temperature 732 °C (time 0.64).
References [1]
ALLAM A., “The Large-Deflection Behaviour of Structural Frames in Fire”, PhD thesis, Department of Civil and Structural Engineering, University of Sheffield, UK, February 2003.
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The Effects of the Restraint Conditions on the Fire Resistance of Tunnel Structures Céline FERON Civil Engineer CETU Bron, France
Summary Fire resistance of tunnel structures has to be checked whenever users’ and rescue-teams’ safety is at stake. With reference to an example concerning a critical structural element in a tunnel (a R/C road slab dividing the upper traffic passageway from the underlying safety ducts), different design methods are presented and compared, and a simple model representing a beam is used to evaluate the influence of the restraint conditions. Keywords:
1.
tunnel, temperature, stresses, beam element model, finite element analysis.
Introduction
This paper aims at presenting the different methods that can be used in the design of tunnel structures in fire conditions. According to the French regulation [1], tunnel structures have to resist different types of fires, depending on their functionality. For example, the lining of a tunnel built in a stable ground has no specific fire resistance requirement, provided that a local failure does not result in a progressive longitudinal collapse; a cut and cover section supporting a roadway has to resist the standard ISO time-temperature curve for 2 hours, if the traffic can be stopped rapidly; a wall between a shelter and the tunnel has to resist the increased hydrocarbon fire (HCM) for two hours. Hence, the time temperature curve on the heated side can either be the ISO-curve or the HCMcurve, but fire engineering is not permitted. The time-temperature curve is ruled, and can not be the result of a fire scenario including parameters such as the air speed, the ventilation and the cross section. From this time-temperature curve, the thermal field in the structural element can be computed, and then used as an input data for a mechanical verification. This paper will not deal with the way of working out the thermal field, but will start with the temperature values on the structural element resulting from the two types of fires described below.
2.
Chosen example
2.1
Cross section
The example considered in the following is a road slab placed inside a tunnel and separating the traffic passageway (above the slab, where the fire is assumed to occur) from the underlying safety ducts. This kind of multiple-cell cross section is a convenient solution for transversal ventilation, and has been chosen in the Mont Blanc tunnel (Fig. 1). In case of fire, the smoke is extracted into a polluted-air duct, and fresh air is input from the fresh air-ducts. One of the fresh air ducts can be used to evacuate the shelters. In that specific case, the French regulation specifies that the road slab separating the evacuation tunnel from the fire has to resist an extremly violent fire. To this purpouse, the slab has to be designed to resist temperatures resulting from the hypothesis of an increased hydrocarbon fire in the tunnel, defined by the following time-temperature curve: T(t) = 20 + 1280 (1 – 0.325e-0.167t – 0.675e-2.5t)
(1)
Depending on the distance from the extraction point, the temperature inside the polluted-air duct can be the same as in the tunnel (very close to the extraction point) or about 20°C (far away from the extraction point). These two extreme configurations lead to very different efforts in the structure. Both of them have to be checked. 271
Fig. 1 - Chosen cross-section. 2.2
Thermal analysis
2.2.1 Evaluation of the temperatures The temperature fields are obtained by solving the heat equation:
UC wT div(k(T) wT )
(2)
k(T) wT HV(T 4 Text4 )D c (T 20) wt k(T) wT D c (T 20) wt
(3)
wt
wt
The bondary conditions are: x
On the heated side:
x
On the fresh air side:
(4)
With: x x x x x x
Density U =2400 kg/m3 taken from XP ENV 1992-1-2 [2] k(T) thermal conductivity (W/m/K) C(T) heat capacity (J/K/kg) V Stefan-Boltzmann constant (5.67 10-8 W/m2/K4) taken from XP ENV 1991-2-2 [3] H (-) emissivity 2 Įc (W/m /K) convection coefficient
2.2.2 Temperature fields The temperature fields are computed with the above hypotheses, in the two following configurations (Fig. 2). The wall and the slab both have a thickness of 20 cm.
272
0,2
0,2
0,18
0,18
0,16
0,16 0,14
0,06
10 min 0,12 30 min 60 0,1 min 90 min 0,08 120 min 0,06
0,04
0,04
0,02
0,02
0,12
10 min 30 min 60 min 90 min 120 min
depth (m)
depth (m)
0,14
0,1 0,08
0
0 0
200
400
600
800
1000
1200
0
200
T(°C)
400
600
800
1000
1200
T(°C)
Fig. 2 - Heating configurations: Left: fire above the slab and hot smoke in the vicious air duct (slab heated both sides); Right: fire above the slab and cooled smoke in the vicious air duct (slab heated one side).
3.
Beam element versus finite element analysis
3.1
Use of beam elements models
In order to design that kind of structural element, the most commonly used tool is a beam element model. With this kind of tool, the cross section is represented this way:
y h z B
Fig. 3 - Beam element model and cross section. Each beam is defined by its cross section and Young’s Modulus. Concentrated or linearly-distributed loads can be input. Imposed strains can also be input, defined by a a medium value and a gradient. The problem is to input: x a non linear temperature field (Fig. 2); x a temperature-dependent Young’s modulus E. Assuming that plane sections remain plane, an equivalent linear strain is introduced. This linear strain is evaluated assuming a constant Young’s modulus, in order to lead to the same values of internal forces N and M as those induced by the thermal strain with a temperature-dependent Young’s modulus. The strain diagram we are looking for can be expressed in the following way:
H eq ay b
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With a constant Young’s modulus E, the resulting internal forces are:
³
N eq
³
M eq
h/2
h / 2
h/2
h / 2
EH eq dy
EH eq ydy
³
³
h/2
E (ay b)dy
h / 2
h/2
h / 2
Ebh
E (ay b)( y h / 2)dy
(5)
Ea
h3 12
(6)
These internal forces must have the same value as those induced by the thermal strain Hth in the heated section. Considering that Hth=Į'T we have:
M th
³
h/ 2
h/ 2
a
h/2
h / 2
h/ 2
³
E(T)H th(y h / 2)dy
³
h / 2
The two equations Neq Nth and M eq
³
h/ 2
E(T)H thdy
³
Nth
h / 2
E(T)D'Tdy
(7)
E(T)D'T(y h / 2)dy
(8)
h/ 2
h/ 2
M th alllow to evaluate the two unknown variables a and b:
E(T)D'T(y h / 2)dy h E 12 3
and b
³
h/2
h/ 2
E(T)D'Tdy Eh
(9)
In our example, h=20 cm, the temperature fields T(y) are represented in Fig. 2, and E(T) is taken from XP ENV 1992-1-2 [2]. In the beam element model, the cross section is represented by beam elements with a rectangular cross section b × h = 1 m × 20cm of concrete with a Young’s modulus of 35 GPa. This leads to the following imposed strain, which can be converted in a thermal input dividing by Į = 1E-5m/m/°C. Table 1 - Input parameters. Time 10 30 60 90 120
Heated on one side b/Į (°C) a/Į (°C/m) 19.4 -400.5 34.0 -438.3 48.6 -273.1 58.9 -49.3 65.7 147.6
Heated on both sides b/Į (°C) a/Į (°C/m) 38.2 0 65.7 0 73.9 0 63.6 0 47.4 0
In the following chapter, these values will be used to check the influence of the restraint conditions on the fire resistance of the slab. 3.2
Finite element analysis
The beam element model is a very convenient tool, and, provided that the input thermal strains are correctly chosen, gives a good approximation in terms of structural safety. Yet, the design can be improved, and the use of finite element tools gives a more precise description of the stress distribution. Indeed, if we can meet the same internal forces M and N with beam element models and finite element analysis, the second one is necessary to check the internal stresses due to the non-linearity of the temperature distrbution. These stresses are a major factor in the study of spalling, which is
274
partly due to the restrained dilation of the heated face [4] (the other part being vapour pressure). Moreover, finite element analysis allows to take into account the constitutive laws of the materials and phenomena such as dehydration and its influence on elasto-plastic parameters more precisely [5]. Based on the previous example (a 20 cm thick section), the mechanical results of both analyses were compared. The thermal input is the same in the two cases. For the sake of simplicity of the finite element analysis, the comparison was limited to the results of a beam, which can be either clamped or simply supported at both edges. First, the elastic modulus E was assumed to be constant (35 000 MPa), in order to evaluate the effect of the temperature. Even in the case of simply supported beam, high internal stresses arise in the cross section (Fig. 4). Yet, the decrease of the elastic modulus E with the temperature T was not taken into account at that stage and the actual stresses are lower.
Fig. 4 - Finite element analysis of the simply supported beam: internal strsses. If the beam is clamped at both edges, we can compare the efforts obtained in both models. They are very close, and from this starting step, the finite element analysis allows to perform a more detailed design, including chemical effects and plasticity. At present time, this kind of analysis is only used for research purposes [6]. Table 2 - Comparaison of models for the anchored beam. Beam element model 1.24 25.95
M (MNm) N (MN)
3.3
Finite element analysis 1.23 25.91
Sectional analysis
After the stresses have been evaluated by means of the beam element model, the internal forces M and N in each section are compared to the bearing capacity of the section, placing the point P (M,N) in the M/N diagram of the heated section. To take into account the reduction of the resistance of the concrete and of the steel with temperature, sections are reduced in the same proportion as resistance: heq
h
³ ) (T(y))dy c
0
Aseq ) s As
Another method consists in neglicting all the concrete above 500°C [7], which leads to similar heq. 275
eh
eh
Asheq
Asheq heq
B
heq
Asb
Asbeq
eb
eb
Fig. 5 - Heated cross section:B Left: heated on one side (above); Right: heated on both sides.
Initially, h = 20cm, eh = eb = 3 cm, Ash = Asb = 24.54 cm2 (5)25). Concrete compressive strength is assumed to be 25 MPa and steel yield strength 500 MPa. The reduction coefficients )c and )s are taken from XP ENV 1992:1-2 [2]. Table 3 - Heated cross section Time heq 10 30 60 90 120
18.7 17.4 16.2 15.3 14.6
Heated on one side Asheq eh 24.54 1.7 17.39 0.4 3.64 -0.8 2.77 -1.7 2.47 -2.4
heq 17.5 14.8 12.4 10.1 7.7
4.
Influence of the restraint conditions
4.1
Presentation
Heated on both sides Asheq=Asbeq eh=eb 24.54 1.7 17.36 0.4 3.19 -0.8 2.67 -2 2.03 -3.2
Parameters of various nature, such as restraint conditions, load distribution and type of aggregates [8], can influence the fire resistance of a structure. One of the restraint conditions that can be chosen during the design phase is the kind of restraint at the edges. Typical configurations can be simply supported, clamped or hinged edges. The fire resistance of those two configurations will be compared in the following, with the polluted-air duct heated or not.
1
2
3
4
5
1
2
3
4
5
Fig. 6 - Modelised structures
We assume that during the fire there are no other loads than the self weight and the temperature.
276
4.2
Simply-supported edges
4.2.1 Hot smoke in the polluted-air duct During the fire, the deformed shape of the structure is the following: 1
2
3
4
5
Fig. 7 - Deformed shape of the heated structure. x x x
At t = 10 min and t = 30 min, the critical section is located just left of node 2. There is tension on the cold side, and the section resists; at t = 60 min, the critical section is located at the right of node 3. There is tension on the cold side, and the section resists; at t = 90 min, the critical sections are located at the right and left of node 4. The side in tension is the hot side. On the right, the section is heated on both sides, and thus is less resistant. The internal forces are above the resistant forces, and a plastic hinge will form just right of node 4. The structure may resist longer, but the analysis was stopped.
4.2.2 Cooled smoke in the polluted-air duct The main difference is that the curvature between nodes 4 and 5 is much more important, because the heating of that part is not symmetric anymore. During the fire, the deformed shape of the structure is the following: 1
2
3
4
5
Fig. 8 – Deformed shape of the heated structure. x x x x
4.3
At t = 10 min and t = 30 min, the critical section is located just right of node 4. There is tension on the cold side, and the section resists; at t = 60 min, the critical section is located at the left of node 4. There is tension on the cold side, and the section resists; at t = 90 min, the critical section is located at the left of node 2. There is tension on the cold side, and the section resists; at t = 120 min, the critical section is located at the left of node 3. There is tension on the hot side and the section does not resist. The stresses are above the bearing capacity of the section, and a plastic hinge will form just left of node 3. The structure may resist longer, but the analysis was stopped at that level. Hinged edges
4.3.1 Hot smoke in the polluted-air duct During the fire, the deformed shape of the structure is as shown in Fig. 9.
277
1
2
3
4
5
Fig. 9 - Deformed shape of the heated structure. x x
At t = 10 min, the critical section is located just under node 4. There is tension on the cold side, and the section resists; at t = 60 min, the whole slab is very strongly compressed. The weakest part of the slab, which is heated on both sides between nodes 4 and 5, can not resist this level of stress. The slab crushes between 10 and 30 min.
4.3.2 Cooled smoke in the polluted-air duct During the fire, the deformed shape of the structure is as follows: 1
2
3
4
5
Fig. 10 - Deformed shape of the heated structure. x At t = 10 min, the critical section is located just right of node 4. Very high compression combined with a flexural moment due to the asymmetric temperature field leads to the failure of the section.
4.4
Comparative study
From this analysis, we can see that the different restraint conditions have a significant influence on the resistance of the structure. Table 4 - Fire resistance for the different restraint conditions. Time Simple supports Hinges
Heated one side 90 min< t
