Simplified seismic assessment of multi-span masonry ... - Springer Link

Bull Earthquake Eng (2015) 13:2629–2646 DOI 10.1007/s10518-015-9733-2 ORIGINAL RESEARCH PAPER

Simplified seismic assessment of multi-span masonry arch bridges Paolo Zampieri • Mariano Angelo Zanini • Claudio Modena

Received: 8 September 2014 / Accepted: 7 February 2015 / Published online: 15 February 2015 Ó Springer Science+Business Media Dordrecht 2015

Abstract The paper describes a simplified methodology for the evaluation of the seismic retrofit intervention types to be performed on clusters of multi-span masonry arch bridges, on the basis of the main bridges geometrical characteristics. The structural behaviour of the analysed sample bridges has been evaluated in their principal directions highlighting the potential local and global vulnerabilities and the related retrofit intervention typologies that need to be selected. The main aim of this study is to take the form of an useful tool for identify the best retrofit strategies for each masonry bridge structure in function of its geometrical characteristics and thus planning rationally the management of bridges belonging to rail and road networks. Keywords Bridge management Lifeline systems Masonry bridges Seismic retrofit Seismic assessment

1 Introduction Masonry arch bridges are commonly diffused in many quake-prone countries in the Mediterranean area. In last years a growing attention has been emerged due to their great importance for national road and rail networks. In particular referring to European railway networks, the majority of the existing bridges consist of masonry structures (Modena et al. 2014). In Italy, the railway system is relatively old: the first line was built in 1839 and it connected the Royal Palace of Naples to the seaside. The railway system was then characterized by a remarkable expansion after the IInd World War. Nowadays the need to rationally allocate resources for the improvement of the railway system performances and efficiencies of its structures, and in particular of its bridges, is emerging. Damage risk of

P. Zampieri M. A. Zanini (&) C. Modena Department of Civil, Environmental and Architectural Engineering, University of Padova, Via Marzolo 9, 35131 Padua, Italy e-mail: [email protected]

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the most vulnerable bridges should be minimized to avoid significant economical and social losses. These requirements are evident in both road and railway transport networks (SB-ICA 2007). Therefore, their assessment is strongly needed by railway and local administrative authorities. Several procedures have been formulated in last decades in order to predict the behavior of those structures: the difficulty in representing the behavior of the material and the resistant skeleton requires the use of simplified but effective structural models. In particular the assessment could be based commonly on limit analysis (Heyman 1982; Gilbert and Melbourne 1994; Boothby 1995) or nonlinear incremental techniques (Audenaert et al. 2008; Brencich and De Francesco 2004; Molins and Roca 1998). The kinematic method, based on an adaptation of limit design for masonry structures, has proved to be a conceptually simple and robust procedure to verify the safety of masonry arch bridges under vertical loads. The method can also be applied for seismic assessment, providing a limit of bridge capacity under horizontal loads. Since Heyman (1966, 1972) noted that the plastic theory, initially formulated for steel structures, could also be applied to masonry structures, many studies have focused on limit analysis to assess the vertical load-bearing capacity of single- and multi-span masonry arches (Gilbert 2007). Heyman (1982) adopted some simplifying assumptions to perform the above analyses: absence of sliding between voussoirs; infinite compressive strength and no tensile resistance of masonry. With these hypotheses, arch failure occurs when a thrust line can be found, lying wholly within the masonry and representing an equilibrium state for the structure under acting loads, which allows the formation of a sufficient number of plastic hinges to transform the structure into a mechanism. Following Heyman’s assumptions, iterative methods to find the geometric safety factor, related to minimum arch thickness under dead and live loads, were proposed by Clemente et al. (1995). Several authors have incorporated crushing of masonry, which cannot sustain infinite compressive stresses (Gilbert 1998; Clemente et al. 2010). Sliding between adjacent blocks was introduced and evaluated by Gilbert and Melbourne (1994), who successfully modelled multi-span brickwork arch bridges. Cavicchi and Gambarotta (2005, 2007) implemented a finite element limit analysis model, in which infill material was modelled with a special triangular finite element to evaluate the arch-fill effect on the ultimate load-bearing capacity under vertical loads, considering detailed constitutive models (Fanning and Boothby 2001; Fanning et al. 2005). Regarding seismic vulnerability assessment of masonry arch bridges, in literature, many studies focused on local and global assessment methods of existing masonry bridges (Hughes and Blackler 1995; Boothby 1995; Brencich and De Francesco 2004; Rota et al. 2005; Pela` et al. 2009). Relatively recent research has been carried out on the application of limit analysis for assessing masonry arches under horizontal (seismic) loads. In particular, research has focused on the longitudinal behavior of arched structures. Some papers (Clemente 1997, 1998) have studied the dynamic response of a single masonry arch under base motion, providing the horizontal acceleration factor inducing the onset of motion, and analyzing the subsequent first half-cycle of vibration in free and forced conditions according to Heyman’s hypotheses. De Lorenzis et al. (2007) used discrete element modelling to predict the combinations of impulse magnitudes and durations which lead unreinforced masonry arches to collapse, and analysed the impact of rigid blocks over several cycles of motion. De Luca et al. (2004) examined the activation of semi-global and global mechanisms involving not only local arch failure but also the simultaneous formation of hinges in the arch and at the base of piers (or abutments).

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Several studies analyzed also the collapse of spandrel wall, as this represents the most vulnerable out-of plane local failure mechanism (Fanning and Boothby 2001; Boothby and Roberts 2001; Resemini and Lagomarsino 2004; Rota et al. 2005; Junzhe et al. 2013): it may affect structural functionality, but rarely causes bridge global failure. The overall deformed shape at collapse, involving transverse deflection of piers was obtained by Pela` et al. (2009, 2013) with numerical simulations according to non-linear static and non-linear dynamic analyses. In the context of a rational management plan over the years (Morbin et al. 2015), the seismic retrofit of a great number of those existing structures needs simplified and fast procedures for the evaluation of the main fragilities (Pellegrino et al. 2014) referring to bridges’ principal geometrical characteristic, considering also the health state of the structures (Zanini et al. 2013). This kind of approach could be performed by observing the typology of failure mechanism in the main structural directions in relation to the geometrical configuration of masonry arch bridges. In such way, this study aims to reconsider the seismic assessment of masonry arch bridges in an alternative maintenance point of view and to identify homogeneous groups of structures in relation to the tendency to show similar seismic damages and therefore analogous retrofit intervention approaches to be pursued during the rational bridges retrofit management plans. On the basis of these issues, the study explain the outcomes from the analyses carried out on two recurrent structural configurations of multi-span masonry arch bridges: for both configurations a set of sample bridges with different geometrical characteristics have been analysed valuating their structural behavior in presence of ground motion actions. The results have allowed to group the sample bridges into classes of prevailing structural behavior, with the aim of subsequently define standard retrofit applications to be followed in the management plans of significant clusters of bridges belonging to railway and roadway networks for averting the occurrence of local or global failure mechanisms.

2 Structural configurations and modelling techniques Two different structural configurations of multi-span masonry arch bridges have been taken into account in this study: a three-span and a five-span masonry arch bridge. This choice has been justified in the light of a preliminary analysis carried out on the structural behavior of masonry arch structures: in particular, a three-span structural configuration has been considered because it is representative also of the two-span typology, given that their abutments boundary conditions significantly influence the seismic behavior of these bridges. Regarding the other structural configuration, a five-span masonry arch bridge has been considered since its structural behavior should be representative of those masonry bridges characterized by a greater number of spans. This assumption is reinforced by the observation of many railway masonry arch viaducts characterized by a higher number of spans: in those cases, it was commonly diffused in construction practice to insert masonry abutment-piers characterized by sections greater than the other piers and high stiffness values, interposed every three–five (sometimes seven) masonry spans. These abutmentpiers were in fact designed to balance the thrust of the arches in the construction stage and, once in operation, if subjected to the collapse of single arches, to avoid the consecutive failure of the adjacent ones. For these reasons, due to the high stiffness of those structural elements, the assessment of masonry bridges composed by several spans could be lead back to the analysis of each modulus enclosed between two abutment-piers. The results obtained from the five-span structural configuration consider themselves to be therefore

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representative also for bridges characterized by numerous spans. Finally, with regard to a four-span structural configuration, the results can be obtained by interpolating the previous ones derived from the three- and five-span configurations. Figure 1 shows, as example, one of the 3D finite element models used in the analyses. The main distinction between the two considered structural configurations, in fact, is related to the failure mechanisms in both principal directions that could be significantly different for bridges with slender masonry piers due to their lower influence of the abutments’ boundary conditions. The ratios between arch length L and bridge width P often assume values such as the bridge transversal deformability is however reduced for two- and three-span structural configurations due to the deck’ stiffening effect provided by the abutments. In the case of numerous spans this stiffening effect becomes less influent, and consequently masonry piers are subjected to higher seismic actions if compared to the same acting on two- or three-span bridges having analogous geometrical characteristics. For each structural configuration two arch curvatures have been considered (semi-circular arch curvature with f/L = 0.5 and depressed arch curvature with f/L = 0.2, where f is the arch rise), as observed in many recurrent masonry arch bridges in the European railway and roadway networks. Every combination of structural typology and arch curvature values has been analysed considering series of sample bridges characterized by different H/B ratios, where H is the pier height and B is the pier width in longitudinal direction. The whole arches have been characterized with the same s/L ratio, where s represents the arch thickness. Table 1 lists the geometrical characteristics of the tested sample bridges. Sample bridges’ transversal width P has been assumed equal to 5 m, mean width value in the case of single railway line: this is the most vulnerable transversal configuration, characterized by the lowest width values and consequently the highest piers’ transversal slenderness. In the case of double railway lines, bridge transversal width increase up to 8–10 m, and in such geometrical configuration, transversal vulnerability decreases. The structural and geometrical configurations defined have then been modelled using the software MidasFEA (MidasFEA 2009): for masonry structures, the best modelling technique is usually chosen in function of the analysis objective between different modelling strategies and modelling levels (micro-modelling or macro-modelling).

Fig. 1 Representation of a finite element model realized for the structural configuration of the three-span masonry arch bridge

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Table 1 Representation of the main geometrical characteristics considered in the analysed sample bridges Spans No.

L (m)

s/L (–)

B (m)

H/B (–)

P (m)

f/L (–)

Babutment (m)

3

6

0.08

1.8

1–2–4

5

0.2–0.5

3.6

3

12

0.08

2.4

1–2–4

5

0.2–0.5

4.8

3

18

0.08

3.0

1–2–4

5

0.2–0.5

6.0

5

6

0.08

1.8

1–2–4

5

0.2–0.5

3.6

5

12

0.08

2.4

1–2–4

5

0.2–0.5

4.8

5

18

0.08

3.0

1–2–4

5

0.2–0.5

6.0

2D and 3D models implementing a macro-modelling approach have been adopted for finite elements discretization, where masonry was modelled as an homogeneous continuum, using six- and eight-node elements. The Total Strain Crack Model implemented in MidasFEA was used as constitutive law for masonry. More in detail, the Smeared Crack Fixed Model developed from the modified compression field theory proposed in Vecchio and Collins (1986) and later developed in Selby and Vecchio (1993) was used as damage model for cracking. The masonry material exhibits isotropic properties prior to cracking and anisotropic properties after cracking, the cracks being orthogonal to the directions of the main strains. The real construction sequence of the different structural elements (arches, spandrel walls, filling material) was take into account according to Bacigalupo and Gambarotta (2012) through a Construction Stage model implemented in MidasFEA able to simulate the effective dead load construction sequence. The main materials’ mechanical characteristics have been assumed in their mean values, considering masonry compressive strength fc equal to 5 MPa, masonry tensile strength ft equal to 0.1 MPa and elastic modulus EM equal to 5000 MPa. The filling material has been modelled considering Drucker–Prager constitutive law with an elastic modulus EF equal to 500 MPa, internal friction / = 37° and cohesion c = 10 kPa (Cavicchi and Gambarotta 2005). For both materials (masonry and filling material) a specific weight q equal to 18 KN/m3 and a Poisson coefficient m equal to 0.2 have been assumed. The constitutive model used for masonry (Fig. 2a) has been considered elasto-plastic in compression and elastic with linear softening in traction (fracture energy 0.0001 N/mm). This constitutive model allowed to well represent the arches’ failure mode as shown by the damage contour plot of Fig. 2b, where the typical four cracking hinges that arise in masonry arches subjected to longitudinal seismic actions can be clearly observed.

Fig. 2 Stress–strain curve adopted in the finite element models (a) and 2D model crack pattern for longitudinal non-linear static analyses of masonry arch bridges (b)

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3 Vulnerability analysis Once defined the main geometrical characteristics of the sample bridges to be tested, nonlinear pushover analyses have been carried out for the evaluation of the capacity curves in terms of peak ground accelerations (PGA) versus control point displacements. The displacements have been recorded both in longitudinal and transversal directions in correspondence of the top of the masonry arches and of the masonry piers’ summit. Vulnerability analyses have considered all possible global failure mechanisms and local ones such as to involve bridge off-duty (very irksome condition within the railway frameworks). In longitudinal direction the seismic vulnerability of a multi-span masonry arch bridge is influenced by longitudinal piers’ slenderness (H/B ratio) and f/L ratio: for low values of H/B ratio, the arches have an independent structural behavior with respect to piers and abutments giving place to local failure mechanisms, whereas at growing slenderness values the failure mechanism becomes a global collapse mechanism involving also masonry piers. The analysis of the results given from the finite element models have allowed to evaluate when the failure mechanism is local (squat piers) or global (slender piers). This classification, functional to the failure mechanism typology and consequently to piers’ longitudinal slenderness H/B, is besides useful in the transversal direction seismic assessment: also in this case, bridges’ seismic behavior depends on masonry piers transversal slenderness H/P, thus related to bridge transversal width P. The transversal failure mechanisms in the case of seismic actions could be divided in bending or shear failure modes: in the first case longitudinal cracks appear along masonry piers’ height, whereas in the second case inclined cracks split along the transversal width of the piers. In both cases the failure mechanism appears once the equilibrium condition of the structural elements becomes not satisfied and this condition implies the structural collapse. The analyses performed on the sample bridges listed in Table 1 have allowed to group these different structural and geometrical configurations tested in multi-span masonry bridge classes characterized by the same failure consequences, in the case of quake occurrence.

4 Numerical results Pushover analyses performed on 2D and 3D models have led to the assessment of peak ground accelerations (PGA) which turn the structures into global or local failure mechanisms and to the construction of the relative capacity curves. The results obtained from the analyses carried out on the 2D finite element models in longitudinal direction have been plotted in terms of ratios between peak ground accelerations corresponding to the occurrence of a local failure mechanism for the arch (PGAL) and the PGA values related to the creation of a global (arch-piers) mechanism (PGAG) with a consequent global failure mechanism appearance. PGAL and PGAG values have been obtained with N2 method (Fajfar and Gasˇpersˇicˇ 1996) and the spectra type adopted in this work refer to the elastic spectra type 2 (Ground type A) as referred in Eurocode 8 (2005) for the ultimate limit state (10 % exceedance probability during 50 years). PGAL has been assessed with a local arch model whereas PGAG has been estimated by using a global longitudinal 2D model of the entire bridge.

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Figures 3a (three-span) and 3b (five-span) show the PGAL/PGAG trends obtained for the different structural and geometrical configurations tested in this study: when the ratio is greater than 1, the main failure mechanism is the global one involving also masonry piers, whereas if the ratio is lower than 1, the bridge is affected by local failure mechanisms of their arches. The failure mechanism substantially depends from the H/B and f/L ratios, and quite apart from the geometrical dimensions: it has been observed how masonry arches with higher f/L values are more vulnerable than others characterized by lower f/L ratios. The results in terms of PGAL/PGAG ratios are substantially defined by the f/L ratio, whereas masonry piers’ slenderness H/B is less influent ratio under the same f/L conditions. For semi-circular masonry arch bridges, also in the case of slender piers, the four plastic hinges that define the collapse mechanism are generally localized in the arches involving a local failure mode; masonry piers characterized by low H/B values are instead substantially less vulnerable than the slender ones. In transversal direction, failure mechanisms have been identified on the basis of a critical evaluation of the results obtained from the pushover analyses performed on the sample bridges. Referring to their construction, capacity curves have been expressed in the ADRS (Acceleration Displacement Response Spectrum) plane and interpolated with an elastoplastic curve, defined by the yielding displacement dy and the ultimate displacement point represented by the displacement value du and the maximum peak ground acceleration PGAu, in both longitudinal and transversal directions. Figure 4 shows, as example, the results in terms of longitudinal displacements (a), transversal displacements (b) and maximum peak ground accelerations (c) obtained for the structural configuration of threespan semi-circular masonry arch bridges. The whole results obtained are briefly reported in Tables 2, 3, 4 and 5, highlighting how for growing H/B values the ultimate displacement du increases, whereas the maximum peak ground acceleration PGAu decreases. These analytical results should be useful for the design of the retrofit intervention solutions: for masonry arch bridges with squat piers it should be necessary to design a retrofit intervention which lead to increase the structural ductility, like pier jacketing or

Fig. 3 Representation of the PGAL/PGAG ratios in function of the different geometrical values considered for both three- (a) and five-span (b) masonry bridge structural configurations

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80

90

Dy - L=18m

Du - L=6m

60

Du - L=12m

50

70

Du - L=18m

40 30 20

Du - L=6m Du - L=12m

60

Du - L=18m

50 40 30 20 10

0

0 1

Peak Ground Acceleration [g]

Dy - L=12m

Dy - L=18m

10

c

Dy - L=6m

80

Dy - L=12m

70

Displacement [mm]

b

Dy - L=6m

Displacement [mm]

a


2

3

4

1

2

H/B

3

4

H/B

0,9

L=6m - long.

0,8

L=12m - long. L=18m - long.

0,7

L=6m - transv. L=12m - transv.

0,6

L=18m - transv.

0,5 0,4 0,3 0,2 0,1 0,0 1

2

3

4

H/B

Fig. 4 Longitudinal displacements (a), transversal displacements (b) and maximum peak ground accelerations (c) obtained from the capacity curves for the structural configuration of three-span semicircular masonry arch bridges

Table 2 Displacements and maximum peak ground accelerations derived from the capacity curves of the three-span semi-circular masonry arch bridges Longitudinal direction

Transversal direction

H/B

1

2

4

1

2

4

H/B

du (mm)

15.000

14.973

18.787

12.913

21.462

26.161

L=6m

0.769

0.480

0.289

0.642

0.485

0.323

pgau (%g) dy (mm)

3.452

4.220

5.679

2.986

4.430

10.642

du (mm)

18.787

24.425

40.784

16.887

26.421

37.873

0.482

0.378

0.230

0.306

0.242

0.166

pgau (%g) dy (mm)

6.128

7.603

10.787

4.198

7.234

14.346

du (mm)

22.000

28.751

52.469

25.582

38.143

77.042

pgau (%g)

0.357

0.225

0.187

0.191

0.153

0.111

dy (mm)

9.154

12.000

17.552

9.036

12.639

23.238

L = 12 m

L = 18 m

other intervention typologies aimed to achieve higher displacement capacity levels. In the case of masonry arch bridges with slender piers it should instead be reasonable to design retrofit solutions which increase resistances, like the insertion of new resistant structural

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Table 3 Displacements and maximum peak ground accelerations derived from the capacity curves of the three-span depressed masonry arch bridges Longitudinal direction H/B

1

Transversal direction 2

4

1

2

4

H/B L=6m

du (mm)

2.114

15.738

28.152

14.000

19.372

27.849

pgau (%g)

0.850

0.599

0.323

0.769

0.650

0.395

dy (mm)

0.642

3.235

5.556

3.691

5.295

10.236

du (mm)

11.878

21.837

29.323

15.765

21.791

32.008

0.850

0.527

0.276

0.493

0.357

0.213

pgau (%g) dy (mm)

3.140

3.726

6.413

4.134

6.728

11.772

du (mm)

12.084

23.498

30.602

31.828

43.935

58.858

pgau (%g)

0.595

0.378

0.247

0.332

0.238

0.153

dy (mm)

3.865

4.786

11.256

7.792

11.911

14.448

L = 12 m

L = 18 m

Table 4 Displacements and maximum peak ground accelerations derived from the capacity curves of the five-span semi-circular masonry arch bridges Longitudinal direction


H/B

1

2

4

1

2

4

H/B

du (mm)

13.667

30.263

37.155

14.537

42.538

26.433

L=6m

0.748

0.472

0.247

0.612

0.480

0.315

pgau (%g) dy (mm)

3.915

7.818

9.723

3.813

11.416

14.118

du (mm)

20.873

35.587

41.386

22.371

51.641

40.865

0.472

0.368

0.217

0.298

0.238

0.162

pgau (%g) dy (mm)

6.460

9.712

11.744

7.120

13.852

15.000

du (mm)

30.698

39.708

55.735

30.804

52.512

53.530

pgau (%g)

0.340

0.238

0.179

0.183

0.153

0.106

dy (mm)

9.393

9.921

19.798

8.750

14.152

26.951

L = 12 m

L = 18 m

Table 5 Displacements and maximum peak ground accelerations derived from the capacity curves of the five-span depressed masonry arch bridges Longitudinal direction


H/B

1

2

4

1

2

4

H/B

du (mm)

L=6m

11.785

14.895

25.256

14.669

21.702

31.068

pgau (%g)

0.850

0.761

0.285

0.769

0.633

0.387

dy (mm)

3.890

4.689

7.113

4.198

7.894

14.887

du (mm)

4.862

24.225

29.120

22.784

26.357

34.519

pgau (%g)

0.850

0.493

0.255

0.485

0.353

0.208

dy (mm)

2.897

7.235

8.357

6.762

7.156

9.112

du (mm)

13.543

31.833

31.804

56.836

44.065

43.191

pgau (%g)

0.769

0.408

0.230

0.323

0.234

0.145

dy (mm)

6.111

8.914

12.657

13.560

14.679

15.991

L = 12 m

L = 18 m

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Fig. 5 Representation of the strain status at increasing seismic acceleration values for the three-span sample bridge with arch length equal to 18 m, f/L = 0.5 and H/B = 2

elements coupled with the existing masonry structures. In the following two specific sample bridge configurations characterized by different transversal failure mechanisms are shown as example. Strain modes have been evaluated for significant peak ground acceleration values, analysing the relative displacement profiles on both compression and traction sides (Figs. 5, 6), the correlated crack patterns (Figs. 7, 8) at different pier height levels along their width and subsequently evidencing the vectorial main stress trends (Fig. 9) for the masonry piers of the two sample bridges shown. Capacity curve trends have highlighted how seismic vulnerability considerably increases for growing masonry pier slenderness values (H/B ratio), whereas f/L ratio and bridge spans’ number are less influent parameters. The careful valuation of the structural behavior of each sample bridge has led to group them in two different general masonry

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Fig. 6 Representation of the strain status at increasing seismic acceleration values for the five-span sample bridge with arch length equal to 6 m, f/L = 0.2 and H/B = 2

arch bridge classes defined in function of the transversal failure typology prevailing among shear and bending failures. Two different failure mechanisms types have been enquired: shear failure with the apparition of a major diagonal crack or the collapse mechanism is due to a combined bending axial force failure. The observation of the analysis outcomes in terms of crack patterns, principal strains and principal stresses contours has allowed to understand the failure typology for each tested sample bridge. In the case of failure

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Fig. 7 Representation of the crack status at increasing seismic acceleration values for the three-span sample bridge with arch length equal to 18 m, f/L = 0.5 and H/B = 2

mechanisms due to the creation of plastic hinges with cracks at the piers base, the analysis of the principal stress contours highlights how the compressed pier base section part has achieved its maximum capacity so the structure is involved in a collapse mechanism due to combined bending axial force failure (Figs. 5, 7). On the contrary, in the case of shear failure, stresses in the piers base section are lower than the maximum masonry compressive strength (Fig. 6) but the observation of the crack pattern evidences the apparition of an inclined crack along piers transversal width (Fig. 8). These observations are confirmed also analyzing the vectorial stress trends in both the masonry piers reported in Fig. 9. Figure 10 summarizes the results of this study, integrated by analysing some further geometrical configurations characterized by intermediate H/B values (in particular H/B = 1.5–3) with respect to those defined in Table 1, with the aim of

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Fig. 8 Representation of the crack status at increasing seismic acceleration values for the five-span sample bridge with arch length equal to 6 m, f/L = 0.2 and H/B = 2

more clearly demarcate the limit between the two main transversal failure typologies described above. In Fig. 10 the whole cases in which a combined bending axial force failure has been detected are marked with red dots whereas the other ones for which a shear failure has been observed are marked with blue dots. In the diagrams the boundary lines subdividing the two investigated transversal failure modes were represented: the lines and

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Fig. 9 Representation of the vectorial stresses for the three-span sample bridge with arch length equal to 18 m, f/L = 0.5 and H/B = 2 (a) and for the five-span sample bridge with arch length equal to 6 m, f/L = 0.2 and H/B = 2 (b)

their linear trends have qualitative character and are reported for better understanding the transversal behavior of the analyzed bridge configurations. As expected, shear failure appears in presence of low H/B ratios, whereas for higher piers’ slenderness the collapse mechanism is due to a combined bending axial force failure. Growing arch length L values involve instead an increasing probability of bending failure occurrence. Finally, the diagrams confirm how, in presence of analogous geometrical configurations, shear failure range is wider for lower f/L values. In such way, on the basis of the outcomes of the analyses carried out in longitudinal (Fig. 3) and transversal direction (Fig. 10) it is possible to group masonry arch bridge cluster is subclasses characterized by the same failure modes and thus better planning the seismic retrofit measures to be adopted for averting seismic damages in case of quake occurrence.

5 Seismic retrofit management framework for masonry arch bridges On the basis of the results explained above, a proposal of Seismic Retrofit Management Framework (SRMF) for the seismic vulnerability assessment and retrofit of multi-span masonry arch bridges could be structured as shown in Fig. 11. The proposed SRMF is composed by a set of modules which allow to quickly define a preliminary estimation of the direct costs of the retrofit interventions to be performed on clusters of masonry arch

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Fig. 10 Transversal failure mechanism for three-span masonry arch bridges with f/L = 0.5 (a) or f/L = 0.2 (b) and for five-span masonry arch bridges with f/L = 0.5 (c) or f/L = 0.2 (d)

bridges. First, the Geometrical Survey Module requires a geometrical survey of the structures to be assessed for the evaluation of the main geometrical parameters: in particular, arch length L, arch rise f, arch thickness s and longitudinal (H/B) and transversal (H/P) pier slenderness are required. This information is then entered in the Seismic Vulnerability Assessment Module, that allow to identify the main local/global vulnerabilities in both longitudinal and transversal directions—on the basis of the results previously obtained—and the subsequent retrofit interventions typologies to be performed for averting potential failure mechanisms. As described above, a public authority or a private company dealing with the maintenance of bridge structures, should identify a series of typological retrofit interventions (in relation to

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Fig. 11 The seismic retrofit management framework for masonry arch bridges

the specific stock to be managed): for example, masonry arch bridges with squat piers should be strengthened increasing structural ductility, with typological interventions like pier jacketing or other solutions aimed to achieve higher displacement capacity levels. In the case of masonry arch bridges with slender piers it should instead be reasonable to design retrofit solutions which increase resistances, like the insertion of new resistant structural elements coupled with the existing masonry structures. Finally, results obtained from the Vulnerability Assessment Module are used in the final Seismic Retrofit Costs Module for a preliminary cost estimation of the retrofit intervention. In particular, on the basis of the identified typological retrofit intervention and in relation to the main geometrical characteristics, needed for estimating the retrofit intervention quantities (e.g. m2, ml, number of elements, etc.), it is possible to quickly quantify a preliminary cost value for each of the masonry arch structures belonging to a managed asset of bridges.

6 Conclusions This paper describes a simplified methodology for the definition of standard seismic retrofit interventions to be performed on clusters of multi-span masonry arch bridges, in relation of

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their main geometrical characteristics. On the basis of the structural behavior in the two main directions and the potential local or global vulnerabilities, the analysed sample bridges have been grouped in classes characterized by the same prevailing failure mechanisms. In longitudinal direction global or local failure mechanisms were investigated whereas in transversal direction shear collapse with the apparition of a major diagonal crack or the combined bending axial force collapse were considered as main failure mechanisms. In this way, in the case of a rapid screening of a great number of these structures belonging to a railway or roadway network in quake-prone countries, on the basis of the analyses outcomes in longitudinal (Fig. 3) and transversal direction (Fig. 11), known the main geometrical characteristics of each bridge, it is possible to group masonry arch bridge cluster is subclasses characterized by the same failure modes and thus better planning the seismic retrofit measures to be adopted for averting seismic damages in case of quake occurrence. This work reconsiders therefore the seismic assessment of masonry arch bridges in an alternative ‘‘maintenance point of view’’ and allow to identify homogeneous groups of structures in relation to the tendency to show similar seismic damages and therefore analogous retrofit countermeasures to set up. Finally, a proposal of a Seismic Retrofit Management Framework (SRMF) for multispan masonry bridges was described. The proposal aims to create an useful tool in bridge management operations of railway and roadway networks at territorial scale (Carturan et al. 2014), for the results lead to preliminary estimate the seismic retrofit intervention typologies (and thus their costs) to be executed in relation to the potential structural vulnerabilities of the existing bridges.

References Audenaert A, Fanning P, Sobczak L, Peremans H (2008) 2-D analysis of arch bridges using an elasto-plastic material model. Eng Struct 30:845–855 Bacigalupo A, Gambarotta L (2012) Effects of layered accretion on the mechanics of masonry structures. Mech Based Design Struct Mach 40:163–184 Boothby T (1995) Collapse modes of masonry arch bridges. J Bridge Mason Soc 9(2):62–69 Boothby TE, Roberts BJ (2001) Transverse behaviour of masonry arch bridges. Struct Eng 79(9):21–26 Brencich A, De Francesco U (2004) Assessment of multi-span masonry arch bridges. Part I: a simplified approach, part II: examples and applications. J Bridge Eng ASCE 9(6):582–598 Carturan F, Zanini MA, Pellegrino C, Modena C (2014) A unified framework for earthquake risk assessment of transportation networks and gross regional product. Bull Earthq Eng 12(2):795–806 Cavicchi A, Gambarotta L (2005) Collapse analysis of masonry bridges taking into account arch-fill interaction. Eng Struct 27:605–615 Cavicchi A, Gambarotta L (2007) Lower bond limit analysis of masonry bridges including arch-fill interaction. Eng Struct 29:3002–3014 Clemente P (1997) Verifica degli archi a conci lapidei. RT/AMB/97/10, ENEA, Roma (in Italian) Clemente P (1998) Introduction to dynamics of stone arches. Earthq Eng Struct Dynam 27:513–522 Clemente P, Occhiuzzi A, Raithel A (1995) Limit behaviour of stone arch bridges. J Struct Eng ASCE 121(7):1045–1050 Clemente P, Buffarini G, Rinaldis D (2010) Application of limit analysis to stone arch bridges. Proc. 6th Int. conference on arch bridges, ARCH’010, October 11–13, 2010, Fuzhou, Fujian, China De Lorenzis L, DeJong M, Oschendorf J (2007) Failure of masonry arches under impulse base motion. Earthq Struct Dynam 6:2119–2136 De Luca A, Giordano A, Mele E (2004) A simplified procedure for assessing the seismic capacity of masonry arches. Eng Struct 26:1915–1929

123

2646


Eurocode 8—Part 1-1 (2005) Design provisions for earthquake resistance of structures. Part 1-1: general rules—seismic actions and general requirements for structures. ENV 1998-1, CEN: Brussels Fajfar P, Gasˇpersˇicˇ P (1996) The N2 method for the seismic damage analysis of RC buildings. Earthq Eng Struct Dynam 25:23–67 Fanning P, Boothby TE (2001) Three-dimensional modelling and full-scale testing of stone arch bridges. J Comput Struct 79(29–30):2645–2662 Fanning P, Sobczak L, Boothby TE, Salomoni V (2005) Load testing and model simulations for a stona arch bridge. Bridge Struct 1(4):367 Gilbert M (1998) On the analysis of multi-ring brickwork arch bridges. Proc. 2nd Int. conference on arch bridges, arch bridges, October 6–9, 1998, Venice, Italy Gilbert M (2007) Limit analysis applied to masonry arch bridges: state-of-the-art and recent developments, Proc. 6th Int. conference on arch bridges, ARCH’07, September 12–14, Madeira, Portugal Gilbert M, Melbourne C (1994) Rigid-block analysis to masonry arch bridges. Struct Eng 72:356–361 Heyman J (1966) The stone skeleton. Int J Solids Struct 2:249–279 Heyman J (1972) Coulomb’s memoirs on statics. Cambridge University Press, Cambridge Heyman J (1982) The masonry arch. Ellis Horwood, Chichester Hughes TG, Blackler MJ (1995) A review of the UK masonry assessment methods. Proc Inst Civil Eng Struct Build 110(4):373–382 Junzhe W, Heath A, Walker P (2013) Transverse behaviour of masonry arch bridge—investigation of spandrel wall failure. Proceedings of 7th international conference on arch bridges—maintenance, assessment and repair, 2–4 October 2013, Trogir-Split, Croatia MidasFEA (2009) Midas FEA v2.9.6, Nonlinear and detail FE analysis system for civil structures. Midas Information Technology Co. Ltd Modena C, Tecchio G, Pellegrino C, da Porto F, Dona M, Zampieri P, Zanini MA (2014) Reinforced concrete and masonry arch bridges in seismic areas: typical deficiencies and retrofitting strategies. Struct Infrastruct Eng. doi:10.1080/15732479.2014.951859 Molins C, Roca P (1998) Capacity of masonry arches and spatial frames. J Struct Eng 124:653–663 Morbin R, Zanini MA, Pellegrino C, Zhang H, Modena C (2015) A probabilistic strategy for seismic assessment and FRP retrofitting of existing bridges. Bull Earthq Eng. doi:10.1007/s10518-015-9725-2 Pela` L, Aprile A, Benedetti A (2009) Seismic assessment of masonry arch bridges. Eng Struct 31(8):1777–1778 Pela` L, Aprile A, Benedetti A (2013) Comparison of seismic assessment procedures for masonry arch bridges. Constr Build Mater 38:381–394 Pellegrino C, Zanini MA, Zampieri P, Modena C (2014) Contribution of in situ and laboratory investigations for assessing seismic vulnerability of existing bridges. Struct Infrastruct Eng. doi:10.1080/15732479. 2014.938661 Resemini S, Lagomarsino S (2004) Sulla vulnerabilita` sismica di ponti ad arco in muratura, Proc. 11th Italian Conference on Earthquake Engineering-ANIDIS, L’ingegneria sismica in Italia, 25–29 January 2004, Genova, Italy Rota M, Pecker A, Bolognini D, Pinho R (2005) A methodology for seismic vulnerability of masonry arch bridge walls. J Earthq Eng 9(2):331–353 SB-ICA (2007) Guideline for inspection and condition assessment of railway bridges. Prepared by sustainable bridges—a project within EU FP6. (http://www.sustainablebridges.net) Selby RG, Vecchio FJ (1993) Three-dimensional Constitutive Relations for Reinforced Concrete. Technical Report 93-02, University of Toronto, dept. Civil Eng., Canada Vecchio FJ, Collins MP (1986) The modified compression field theory for reinforced concrete elements subjected to shear. ACI J 83(22):219–231 Zanini MA, Pellegrino C, Morbin R, Modena C (2013) Seismic vulnerability of bridges in transport networks subjected to environmental deterioration. Bull Earthq Eng 11(2):561–579

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