ESDA2012-82932 finale

Proceedings of the ASME 2012 11th Biennial Conference On Engineering Systems Design And Analysis ESDA2012 July 2-4, 2012, Nantes, France

ESDA2012-82932 MODELLING CHEMICAL PROCESSES IN CEMENT BASED MATERIALS BY MEANS OF MULTIPHASE POROUS MEDIA MECHANICS Francesco Pesavento University of Padova Padova, Italy

Dariusz Gawin Technical University of Lodz Lodz, Poland

Bernhard A. Schrefler University of Padova Padova, Italy

Marcin Koniorczyk Technical University of Lodz Lodz, Poland

ABSTRACT A general approach to modelling chemical degradation processes in cement based materials, due to combined action of hygro-thermal, chemical and mechanical loads, is presented. Mechanics of multiphase porous media and damage mechanics are applied for this purpose. The mass-, energy- and momentum balance equations, and constitutive and physical relations are briefly presented, and then numerically solved with the finite element method. Several examples of the model application for analysing ions transport and degradation processes of concrete due to chemical attack of pure water, salt crystallisation and alkali-silica reaction are presented and discussed. INTRODUCTION A possibly accurate prediction of degradation of concrete structures during their whole life cycle, at normal service conditions and after exposition to chemically aggressive environment, is of great practical importance. Much research has been devoted to this subject in recent decades, and several predictive mathematical models have been developed. At the Technical University of Lodz and the University of Padova research on the modelling of building materials as a multiphase, porous medium has been carried out for many years. Concepts of effective stresses and mechanics of porous media, often used in geomechanics, have been adopted for modelling heat, mass and momentum transport in cement based materials, e.g. [1-4]. This approach has been successfully applied to the numerical analysis of such difficult problems as hygro-thermo-chemical behaviour of concrete at early ages or degradation at high temperature, giving results in good agreement with experimental data, [1-3]. Here, a general approach to modelling degradation processes in a cement based material, due to

combined action of hygro-thermal, chemical and mechanical loads, is presented. Mechanics of multiphase porous media is applied for this purpose [1, 3]. The mass-, energy- and momentum balance equations, and constitutive and physical relations are briefly presented, and then numerically solved with the finite element method. Three examples of the model application for analysing ions transport and degradation processes of concrete due to chemical attack of pure water (calcium leaching), salt crystallisation and expansive alkalisilica reaction, are presented and discussed. MATHEMATICAL MODEL The balance equations are written by considering cement based materials as a multi-phase porous medium, which is assumed to be in hygro-thermal equilibrium state locally. More specifically, in the present case the solid skeleton voids are filled partly by liquid water (the wetting phase) and partly by a gas phase (the non-wetting phase). The liquid phase consists of physically bound water and capillary water, which appears when the degree of water saturation exceeds the upper limit of the hygroscopic region, Sssp. The gas phase is a mixture of dry air and water vapour, which is a condensable gas constituent. In the following, subscripts mean physical quantities related to the whole volume of medium, and upper indices their intrinsic values related to the single phase or constituent only. By constituent we indicate a matter which is uniform throughout in chemical composition, while phase means here different physical state of a matter (solid, liquid or gaseous). Symbols s, w, l, g, gw and ga denote solid skeleton, pure liquid water, the whole liquid phase (i.e. water + ions), gas phase in general, vapour and dry air, respectively. The solid phase is assumed to be in contact with all fluids in the pores. When calcium leaching is modelled, Ca indicates the calcium ions in

1

Copyright © 2012 by ASME

the liquid solution, and Ca-p indicates the calcium precipitated from the liquid solution. When any other chemical degradation processes is analysed, the latter subscript should be substituted by the one indicating the ions involved in the process. The full development of the model equations, starting from the local, microscopic balance equations with successive volume averaging, and further transformations are presented in [1, 4]. The final form of the governing equations, written at microscopic level in terms of the primary variables, i.e. gas pressure, capillary pressure, temperature, calcium concentration in water and displacement vector (pg, pc, T, CCa, u), taking into account the small deformation theory, is: - Dry air mass balance equation (including the solid skeleton mass balance) takes into account both diffusive and advective air flow, as well as variations of porosity caused by leaching processes and deformations of the skeleton. It has the following form:

!!

" #

%$!

!

',

"&

( )

! ! # ! ! ! $' ',

)*+ ! ' +

!

!

',

" #( "&

(

+ $' )*+ ! # +

',

)*+ !$' ! !

'#

)=! !

! )*# #

$' ! " # ! ',

!

',

"&

( !! ) +,- ( ! ( !! )

" #$$

!H vap = H gw ! H w ,!H dis = H s ! H Ca ,!H prec = H Ca ! H Ca! p . (4) - Calcium mass balance equation (leaching case) including the diffusion of ionic species, the advection and the chemical reaction related to the dissolution of the calcium contained in the solid skeleton [3] and precipitation of calcium salt, [4]:

$ "# %

(1)

! "#$ ). the source terms related to the leaching process ( ! - Water species (liquid+vapour) mass balance equation (including the solid skeleton mass balance) considers diffusive and advective flow of water vapour, mass sources related to phase changes of vapour (evaporation/condensation and physical adsorption/desorption), and variations of porosity caused by leaching process and deformations of the skeleton, resulting in the following equation:

!" #

$ % ! !" #$

(! " !

!

)

# $%" #&

(

)

! + ! !"! + ! !"#! ! !"# ! ! ! ! !"#

(

)

(

! "# !$

+

)

(2)

+ !"# ! !" + !"# $%& ! ! ! !" + !"# $%& ! !" ! !" ! !

+ ! !"#!

!! ! ! ) ( ! ) ##" "!" ! !

!

!

!"#

%$! & ! !"#$% $ ! & = ' "#$$ ! !"#! + ! !"! &' &% !! '

(

! "! & "# '(#)* &

! "# '(#)*

" ""#$% ,-. ! & +

and n is the porosity. The term at the right hand side represents

(

= !%!"% + !&!"& + ! '!"' is the thermal capacity of the

(! ! ! ) "

!" phase, "ga is the dry air density, ! ! is the dry air diffusive flux

)

! where ! !"# is the thermal expansion coefficient of the

multiphase system, "gw is the water vapour density, !leach the leaching degree and the water vapour diffusive flux. - Energy balance equation (for the whole system) accounting for the conductive and convective heat flow, heat effects of phase changes, dissolution and precipitation processes, can be written as:

)

(3) !& ! ! ! ()*+% = # . $/ + . $/ + . $/ #$$ -*" -*" +,0 +,0 ")#1 ")#1

multiphase system, while the enthalpy of vaporization, dissolution and precipitation are respectively:

+

$'

( )

+ !'!"' ! ' + ! (!"( ! ( " ()*+% #

where #eff is effective conductivity from experiments,

!

!

!

%

"+

+ !""#

"$% "+

+ !

%$,-. !"# + ,

(

!

where Sw and Sg are the water and gas saturation level respectively, !s is the thermal expansion coefficient of the solid

! ! ! ! ! !"

!%

" #$$

)

,-. ""#!$% ! % ! '& ! %

! ,-& /

!

%

"""# "+

+ (5)

!

! 01() /

!

%

!

! ,-& /

!&

""#

%$where CCa is the calcium concentration in the liquid solution, vls is the velocity of the solution with respect to the solid skeleton, and finally !"# is the diffusion mass flux of the !

Ca2+ ions in the water solution. - Linear momentum balance equation (for the multiphase system) in the rate form:

( )

!"# !! !"!#$ !!! ! = " ,

(6)

where ttotal is the total stress tensor, " is the apparent density of the multiphase material, g is the vector of gravity acceleration. EVOLUTION EQUATIONS The progress of chemical degradation processes (calcium leaching, precipitation or ASR reaction) is described by the evolution equations written in terms of the evolution variables: calcium degree of leaching, saturation degree with precipitated salt, and ASR reaction extent (!leach, Sp, !ASR). - Evolution equation for non-isothermal calcium leaching has the following form, [3]

!" !"#$% !&

=#

'( !

()# *+,"- ! !"#

%$(7)

where chemical affinity of the leaching process is defined as follows

2


(

! !"#

)

!"#

(

)

!" = " ! ! ! !!"#$ !" ! " ! ! ! !!"#$ !" !"#

(

"#$

)

! !"#$% = ! "#$ !! is the characteristic time of the process, Tref is the reference temperature, " is the equilibrium function, ! !"# and !"# are the initial and actual values of solid calcium

content (i.e. the calcium phase being leached from the skeleton). The characteristic time !leach for different phases of solid calcium can be expressed by the following approximate relationship [3]:

( )

()

(

)

! ! ! !"#$% ! ! ! !"#$% !"#$ " !"# $& !! ! # !"#$ ') % (

(9)

where Tref= 298.15 K, A$= -0.0239 K-1, and superscript %= por, etr, CSH means the portlandite, ettringite or CSH phases, respectively. One should underline that non-isothermal calcium leaching is an irreversible process and it is described here by a non-equilibrium model. More details concerning modelling this process can be found in [3]. - Evolution equation for salt precipitation, depending on the super-saturation ratio of the salt concentration, "#$ ! = !!" ! !!" , has the following form, [5]:

!"# !"# !$

(10a)

#$% $ #$% = !!" #!$$% ! !"""# ! & ""# < !"""# ! ' < !" < (

!"# $#% is the maximum porous material and kind of the salt, !!"

calcium concentration at temperature T, K is the rate constant. For primary crystallization the super-saturation parameter A’ # 1, and when first salt crystals appear in the pores further crystallization proceeds at A’ = 1. Equations (10) are also valid for the dissolution of salt crystals. - Evolution equation for non-isothermal ASR reaction has the following form, [6, 7], !!

=

! ! " !"#

(

) (

! ! " !!" ! ! ! !!" !! !"#

(

where ! ! " !!" at

(

temperature

)

and

moisture

content

S w,

while

! ! !!" !! !"# is experimentally determined material function, given by, [6],

(

)

! !"# + !"# !! ! ! ! !

)

(12)

EFFECTIVE STRESS PRINCIPLE Cement based materials are multi-phase porous media, hence analysing the stress state and the deformation of the material it is necessary to consider not only the action of an external load, but also the pressure exerted on the skeleton by fluids present in its voids. The total stress tensor acting in a point of the porous medium may be split into the effective stress tef, which accounts for stress effects due to changes in porosity, spatial variation of porosity and the deformations of the solid matrix, and a part accounting for the solid phase pressure exerted by the pore fluids, Ps, [1],

(

)

! !"! = ! !" ! ! ! "" = ! !" ! ! " ! ! !"! #$ "

(13)

where I is the second order unit tensor, & is the Biot with water. In equation (13) capillary pressure is defined in such a way that it has physical meaning also in the hygroscopic range of moisture content, [1], $ !" ! ! # " ! $ = # % " ! $# & $#

(14)

In this region it takes also into account the effect of disjoining pressure, $f, besides the curvature and surface " tension of the water/gas interface, ! "# and ! !" . At higher

relative humidity, in the capillary moisture range, the effect of disjoining pressure is neglected ($f = 0). STRAIN DEVELOPMENTS RELATED TO THE CHEMICAL DEGRADATION PROCESSES In general, by taking into account the chemical processes under investigation in this work, the total strain of concrete !tot, can be split into the following components:

(11)

)

) is the characteristic time of ASR reaction

T

(

! + !"# !! ! ! ! !

with being the latency time of reaction. The presented formulation combines the three existing models [6, 7] to take into account effect of the temperature, constant and variable moisture content and aging upon the progress of ASR reaction.

(10b)

where the saturation degree with precipitated salt is Sp = 1 – Sw – Sg, p is the process order, depending on the properties of

!" !"#

)

! ! !!" !! !"# =

coefficient, and ! !"! the fraction of skeleton area in contact

#$% $ #$% = !" #!$$% ! !"""# & ' ""# ! !"""#

!$

(

(8)

! tot = ! el + ! cr + ! th + ! ch + ! o

(15)

where !el means elastic strains, caused both by external load and drying process (the second one corresponding to shrinkage strains, which are described here by means of the effective stresses), !cr creep strains, !th thermal strains, !o autogenous strains and !ch chemical strains. In the next subsections the strain components will be described. The chemical strains have different nature depending on the chemical process under consideration, e.g. hydration/aging, leaching or silica-alkali reaction, so they will be particularized for different cases.

3


ASR chemical induced strain The second part of ASR process, i.e. water absorption in the gel and material expansion, is modelled assuming that the ASR induced strains are isotropic and their rate is proportional to the ASR reaction extent rate, as was proposed for materials in constant hygro-thermal conditions by Larive , [8], and Ulm et al. [6], ! ASR ( t ) = " ASR # $! ASR ( t ) I

conditions the ASR induced strains are directly proportional to the reaction extent, as was assumed in [6, 8]. The experiments performed by Larive (see [8]) clearly show that the parameter is dependent upon the water saturation degree Sw and two relations were proposed to describe this dependence: the linear one (see [9]) and the exponential one (see [8]). Larive's experiments, [8], show that due to some intrinsic physicochemical processes a loss of swelling potential of already formed gel is observed. The process can be considered as a material aging, see e.g. [7]. Taking into account this effect on the evolution of ASR strains, Steffens at al. (see [7]) proposed an additional material parameter, called the characteristic time of aging $a, affecting both the ASR expansion rate and the final, asymptotic value of the ASR strains. This parameter characterizes the watercombination process of the already formed gel due to ASR reaction, what can be described by the evolution law of the following form, [7]: 1 " !a !! a = ta

(17)

where !a means the normalized aging process extent (i.e. aging process degree). After integration of equations (11) and (17), and some transformations one obtains, see [7], #

/# a 0

(18)

Considering the effect of aforementioned aging process and assuming validity of relation (17), the following form of the ASR strain evolution law (16) will be used in the present model:

!! ASR ( Sw ) = !! ASR 0 ( A! ASR " Sw + B! ASR ) (20)

Linear form.: Exp. form.:

(16)

where I is the unit tensor of the second order. ! ASR is the material parameter corresponding to the asymptotic linear expansion strain in the stress free experiment at constant temperature and moisture content, i.e. ! ASR = " ASR ,# / 3 . In such

1 ! " a = ( 1 ! " ASR ) r 0

Following experimental results given in [8] and analyses presented in [7,9], we assume for this parameter the same form adopted for ! ASR (i.e. linear or exponential formulation):

!! ASR ( Sw ) = !! ASR 0 " exp ( C! ASR " Sw + D! ASR ) (21)

where !! ASR 0 = !! ASR (Sw = 1) , while A! ASR , B! ASR , C! ASR and

D! ASR are material parameters. Assuming that ASR is irreversible, i.e. !! ASR " 0 , it is obvious from (19) that the ASR induced expansive strains cannot decrease. Creep strain The term !cr in eq. (15) identifies the creep strain component and it is taken into account for all the chemical processes considered. Creep is modelled here by means of the solidification theory, [10], for the description of the basic creep, and microprestress theory, [11], for the description of the longterm creep and the stress induced creep (part of the so called drying creep). In the following, a brief description of the necessary constitutive relationships will be presented. According to the solidification theory proposed by Bazant and Prasannan [10] aging is considered as the result of a solidification process involving basic constituents, which do not have aging properties. Due to cement hydration, new products, in particular calcium silicate hydrates (C-S-H), can precipitate forming new layers of material able to sustain an external load (these layers at the beginning are stress-free). The load-bearing components of concrete exhibit both viscous flow and visco-elastic deformation. The increase of global stiffness of the system is the result of a progressive growth of solidified material fraction. In this manner it is possible to formulate non-aging constitutive laws for these basic constituents, considering a certain micro-compliance function %(t,t’) which can be expanded in Dirichlet series, while all the effects related to aging are described by the solidification process. In view of this theory the total creep strain increment, d!cr, is decomposed in two components, the visco-elastic, and the viscous flow strain increments, d!v and d!f : d ! cr = d !v + d ! f with d !v =

d" 1 and d ! f = G"s t s dt (22) # hydr "

# %! ASR ( t ) I (19)

where " is the visco-elastic microstrain and & is the apparent microscopic viscosity. The matrix G is defined in such

where !! ASR (Sw ) is a material function, which cannot not

a way that ! = E "1Gt , where t and ! are stress and strain vectors, respectively, [11]. The apparent macroscopic viscosity, &, is not constant in time and is defined by means of microprestress theory,

! ASR [ Sw ( t ) ,T ( t ) ] = "" ASR ( Sw ) # ( 1 $ % ASR ) r 0 &

/& a 0

be however identified with the ! ASR function, as shown by Steffens et al., [7].

1 / !(S ) = cpS p "1

4

(23)


where S is the microprestress, while c and p are material constants defined positive. In the current model concrete is treated as a multiphase porous medium, so the stresses in Eqs. (22) should be interpreted as the effective ones, tef , [12], and not the total ones, ttot, as in the original theory of Bazant [10]. In such a way it is possible to couple the free shrinkage with the creep, obtaining creep strains even if the concrete structure is externally unloaded. The capillary forces represent, in fact, an “internal” load for the microstructure of the material skeleton. Similarly to [11] it is possible to define the creep compliance function as follows, [13]:

J (t , t ! ) = q1! + " ( t , t ' ) + cpS p #1

(24)

the wall surface is decreasing progressively in a time span of 1000 days from the initial value of 17.885 mol/m3, corresponding to thermodynamic equilibrium at T=60°C, down to 1 mol/m3. The problem is solved for two different conditions for the thermal field: uniform temperature equal to 60°C (case 1) and with a thermal gradient 25°C/60°C between the surfaces of the wall (case 2). The latter one is obtained by the cooling process on the same side of the wall starting from T0=60°C in the same time interval. For the both cases the calcium mass exchange coefficient equal to 10-5 kg/(m2s) is assumed. The material properties assumed in the simulations are the same as in [3]. The simulations are performed with time step length (t= 0.1 day, for the time span of 1)105 days.

Ca IONS CONCENTRATION [mol/m3]

where !(t , t ') is the visco-elastic micro-compliance function related to the growth of hydration products fraction and defined as in [12-14]. The third term on the RHS derives directly from the microprestress theory, Eq. (23), and is the term related to the so-called aging elasticity (see [12-14]). NUMERICAL EXAMPLES The model equations are discretized in space by means of the finite element method. The unknown variables are expressed in terms of their nodal values and shape functions N' as,

() ( ) ! (# ) ! ! ! (" ) ! ! (# ) ! ! ! (# ) ! ! (! ) ! ! ! (! ) " !" # ! !! !! " ! !"

!"

"

!

!

!"

()

()

! " ! !! ! ! !

!!

11 9 7

!

( )

T= 60°C, t= 8

25°C/60°C, t= 8

T= 60°C, t= 30

25°C/60°C, t= 30

T= 60°C, t= 60

25°C/60°C, t= 60

T= 60°C, t=100

25°C/60°C, t=100

t=0 [10^3 days]

0.02

0.04

0.06

0.08

0.1

0.12

0.14

DISTANCE [m]

{

! = ! ! ! !! ! ! ! "!" !!

}! !

( )

+ ! !" ! !+! ! !+! ! !! ! !+! = !"

(26)

(27)

where superscript i (i= g, c, t, Ca, u) denotes the state variable, n is the time step number and (t is the time step length. The equation set (27) is solved by means of a monolithic Newton-Raphson type iterative procedure using a frontal solver [1, 3]. Non-isothermal calcium leaching The first example deals with a 1-D calcium leaching problem where chemical action of deionized water on the surface of a 16-cm cement paste wall is modelled with convective BCs. Similar diffusion – reaction problem, but for the isothermal case with T=25°C, was previously solved in [3]. The calcium concentration in the liquid solution in contact with

a

16

Ca CONTENT IN SKELETON [kmol/m3]

( )

! !+! ! ! !

13

0

where the non-linear matrix coefficients Cij(x), Kij(x) and fi(x) are defined in detail in [3]. The time discretization is accomplished through a fully implicit finite difference scheme,

!!" ! !+!

15

!

( ) !!!! + ! (!) ! = ! (!) ! !"

17

5

(25)

The discretized form of the model equations was obtained in [3] by means of Galerkin’s method and can be written in the following concise matrix form: !!" !

19

14

t=0 [10^3 days]

12

T= 60°C, t= 8 T= 60°C, t= 30 T= 60°C, t= 60

10

T= 60°C, t=100 25°C/60°C, t= 8 25°C/60°C, t= 30

8

25°C/60°C, t= 60 25°C/60°C, t=100

6 0

0.02

0.04

0.06

0.08

0.1

DISTANCE [m]

0.12

0.14

0.16

b

FIGURE 1 - SPACE DISTRIBUTIONS OF CALCIUM CONCENTRATION (A) AND SOLID CALCIUM CONTENT (B) DURING LEACHING OF A CONCRETE WALL Figure 1 shows a comparison between the results concerning calcium ions concentration in the pore solution (Fig. 1a) and solid calcium content in the skeleton (Fig. 1b) for the two cases considered, highlighting the role played by the temperature gradient. In the case with uniform temperature the liquid solution contains less calcium ions (Fig. 1a), what results in a

5


faster dissolution of calcium from the material skeleton (Fig. 1b) and faster progress of the material chemical degradation process. As can be observed, temperature has an important effect of the calcium leaching in cement based materials. Salt precipitation during drying The second problem deals with drying of a wall containing NaCl in water solution. The 20 cm thick wall is made of cement mortar. The material has intrinsic permeability of 3.0 10-21 m2 and porosity of 12%. Other material parameters are given in [5]. The initial conditions are as follows: pg = 101325 Pa, Sw = 0.69, T = 20 °C, CCa = 15%M. In the evolution equation (10), the rate constant K = 0.05 and the process order are equal to 1, 2 or 4. The drying of the material is triggered by the rapid fall of the ambient air humidity to 3.5 g/m3, while its temperature remains unchanged. On the wall surfaces the convective boundary condition with the heat exchange coefficient of 23 W/m2K and the mass exchange coefficient of 0.023 m/s are assumed.

vicinity of the surface, Fig. 2a. The change of the dissolved salt concentration profiles for the same case is shown in Fig. 2b. For all the analysed cases one can observe the U-like profiles. The lowest value of the dissolved salt concentration on the surface can be noticed for the case with p=1 (CCa=0.26), while the highest one for the case with p=4 (CCa=0.31). The saturation concentration of the salt solution is equal to 0,26 kg/kg. For the comparison, the same experiment is simulated assuming thermodynamic equilibrium between dissolved and precipitated salt. Two types of binding isotherms are assumed, Freundlich’s and Langmuir’s ones. The obtained results are compared in Fig. 3. The profiles of saturation degree with the crystallized salt for the case with p=2 are presented in Fig. 4 indicating that the salt precipitates only close to the wall surface.

a

a

FIGURE 3 - COMPARISON OF RESULTS BETWEEN THE KINETIC AND EQUILIBRIUM APPROACHES

b

b

FIGURE 2 - DEGREE OF SATURATION WITH LIQUID PHASE (A) AND DISSOLVED SALT CONCENTRATION (B)

FIGURE 4 - SATURATION DEGREE WITH THE PRECIPITATED SALT FOR THE SECOND ORDER RATE LAW (p=2).

Figure 2 shows the results of simulation obtained for the second order evolution law (i.e. p=2) for salt precipitation (10), at the beginning and after 20, 40, 60, 80 and 100 hours. One can notice a rapid decrease of the liquid saturation degree in the

Expansion due to ASR reaction The third problem is based on the experimental tests [6] and it deals with a cement mortar specimen exposed to various

6


hygral and thermal conditions. The material contained reactive aggregates hence considerable swelling strains due to the ASR reaction were observed. The simulations are performed for three different values of ambient temperature, 23°C, 38°C and 60°C, at the same relative humidity of 92%, and then for four different values of ambient relative humidity, 100% (in water), 98%RH, 92% and 86% at the same temperature of 38°C. The same materials parameters are used for all the analysed cases. The comparison of the simulation results with the experimental ones [6] is presented in Figures 5 and 6, showing their good agreement. )*+,-./01# !"(!#345,-./01#

)*+,-./2&#

)*+,-./20#

)*+,-./%!!#

345,-./2&#

345,-./20#

345,-./%!!#

,-.%-!.,"/-%&0+

!"'$# !"'!#

ACKNOWLEDGMENTS The work reported here has been partially funded by the project POIG.01.01.02-10-106/09-00 “Innovative means and effective methods to improve the safety and durability of building structures and transportation infrastructures in the strategy of sustainable development”. REFERENCES [1] Pesavento, F., D. Gawin, B.A. Schrefler (2008). “Modeling cementitious materials as multiphase porous media: theoretical framework and applications.” Acta Mechanica, 201(1-4), pp. 313-339.

!"&$# !"&!# !"%$# !"%!# !"!$# !"!!# !

$!

%!!

%$!

&!!

&$!

'!!

'$!

!"#$%&'()*+

FIGURE 5 - COMPARISON OF THE ASR STRAINS OBTAINED FROM SIMULATIONS WITH THE EXPERIMENTAL DATA [6] FOR 4 DIFFERENT VALUES OF RH AT T=38°C

[2] Gawin, D., M. Wyrzykowski, F. Pesavento (2008). “Modeling hygro-thermal performance and strains of cementitious building materials maturing in variable conditions.” Journal of Building Physics, 31(4). pp. 301-318. [3] Gawin, D., F. Pesavento, B.A. Schrefler (2009). “Modeling deterioration of cementitious materials exposed to calcium leaching in non-isothermal conditions.” Computer Methods in Applied Mechanics and Engineering., 198(37-40), pp. 30513083. [4] Koniorczyk, M., D. Gawin (2008). “Heat and moisture transport in porous building materials containing salt.” Journal of Building Physics, 31(4), pp. 279-300.

!"&!#

,-.%-!.,"/-%&0+

multiphase nature, has been presented. It can be adapted to very different types of chemical degradation, e.g. leaching, salt precipitation or expansive chemical reaction. The model is thermodynamically consistent and it has been developed within framework of mechanics of multi-phase porous media. Three applications to concrete leaching, salt transport and precipitation, and expansive ASR reaction show the potentialities of the model.

!"%$# )*+,-./&'01 )*+,-./'201

!"%!#

)*+,-./3!01 456,-./&'01

!"!$#

456,-./'201 456,-./3!01

!"!!# !

%!!

&!!

'!!

!"#$%&'()*+

[5] Koniorczyk, M. (2010). “Modelling the phase change of salt dissolved in pore water – Equilibrium and non-equilibrium approach.” Construction and Building Materials, 24(7), pp. 1119-1128. [6] Ulm, F.-J., O. Coussy, K. Li, C. Larive (2000). “Thermochemo-mechanics of ASR expansion in concrete structures”. Journal of Engineering Mechanics, ASCE, 126(3). pp. 233-242.

(!!

FIGURE 6 - COMPARISON OF THE ASR STRAINS OBTAINED FROM SIMULATIONS WITH THE EXPERIMENTAL DATA [6] FOR 3 DIFFERENT VALUES OF TEMPERATURE AT RH=92% CONCLUSIONS A general model for chemo-thermo-hygro-mechanical behaviour of cement based materials, considering their

[7] Steffens, A., K. Li, O. Coussy (2003). “Aging Approach to Water Effect on Alkali–Silica Reaction Degradation of Structures”. Journal of Engineering Mechanics, ASCE, 129(1). pp. 50-59. [8] Larive, C. (1998). “Apports combinés de l’expérimentation et de la modélisation à la comprehension de l’alcali-reaction et de ses effets mécaniques”. Monograph LPC, OA 28, Laboratoires des Ponts et Chausse´es, Paris.

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