2001, Novak and Colville. 1989). During the ..... Samson, E., Marchand, J., Robert, J.L. and Bournazel, J.P. (1999B) Modeling the mechanisms of ion diffusion ...
2e Conférence spécialisée en génie des matériaux de la Société canadienne de génie civil
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Montréal, Québec, /.Canada 0 1 2$33 5-8 juin 2002 / , -
PREDICTING THE PERFORMANCE OF CONCRETE STRUCTURES EXPOSED TO CHEMICALLY AGGRESSIVE ENVIRONMENTS - FIELD VALIDATION A,B
A,B
A,B
C
J. Marchand , E. Samson , Y. Maltais , R.J. Lee A CRIB - Department of Civil Engineering, Laval University, Canada, G1K 7P4 B SIMCO Technologies Inc., 1400 boul. du Parc Technologique, Québec, Canada, G1P 4R7 C R.J. Lee Group, 350 Hochberg Road, Monroeville PA 15146, USA
$%675$&7 The behavior of six concrete slabs exposed to sulfate-bearing soils was investigated by a numerical model called STADIUM. In addition to the diffusion of ions and moisture, the model also accounts for the effects of dissolution/precipitation reactions on the transport mechanisms. The simulations yielded by the model were compared to the actual degradation of the slabs after 7.5 years of exposure. The microstructural alterations of concrete resulting from the penetration of magnesium, chloride and sulfate ions were studied by backscatter mode scanning electron microscope observations and energy-dispersive X-ray analyses. The comparison of both series of data indicates that the model can reliably predict the various features of the microstructural alterations of concrete.
,1752'8&7,21
Plain and reinforced concrete structures are often exposed in service to various types of chemical degradation. In most cases, deterioration mechanisms involve the transport of moisture and/or ionic species within the pore structure of the material (St-John et al. 1998, Taylor 1990, Ramachandran et al. 1981). The transport of matter usually modifies the chemical equilibrium within the porous solid and leads to a significant reorganization of the microstructure of concrete. These microstructural alterations often have a detrimental influence on the engineering properties of the material and can even markedly reduce the service-life of the structure (Skalny et al. 2001). The assessment of the resistance of concrete to chemical attack by laboratory or in-situ tests is often difficult and generally time-consuming (Taylor 1990, Ramachandran et al. 1981, Skalny et al. 2001). Furthermore, since dissolution/precipitation phenomena readily affect the pore structure of the material, the kinetics of degradation quickly become non-linear, and a reliable prediction of the evolution of the concrete properties upon leaching can hardly be made on the sole basis of experimental results. For this reason, a great deal of effort has been made towards developing microstructure-based models that can reliably predict the behavior of concrete exposed to chemically aggressive environments. A few years ago, SIMCO Technologies Inc., in collaboration with Laval University, developed a numerical model, called STADIUM, for the prediction of ionic transport in unsaturated porous media. In addition to the diffusion of ions and moisture, the model also accounts for the effects of dissolution/precipitation
1
reactions on the transport mechanisms. The main features of STADIUM have been extensively described elsewhere (Marchand 2000, Marchand et al. 2002). During the course of its development, the numerical results yielded by STADIUM were systematically validated with laboratory test results (Marchand 2000, Marchand et al. 2001, Maltais 2002). The model was also used to predict the behavior of existing structures exposed to various forms of chemical degradation phenomena. After a brief description of its mathematical formulation, the application of STADIUM to the prediction of the behavior of slabs-on-grade exposed to chemically aggressive soils (containing chloride, sulfate and magnesium ions) is presented. The results of the model are compared to the actual degradation of concrete after approximately 7.5 years of exposure.
2. MATHEMATICAL DESCRIPTION OF THE MODEL
The algorithm at the basis of the model is built in such a way that each time step involves two consecutive series of calculations. The concentration profiles of the various ionic species present in the system are first calculated using a series of transport equations without taking into account any chemical reactions. At the conclusion of this first series of calculations, the concentrations at each node of the domain are verified to see if they violate the local chemical equilibrium between the pore solution and the various solid phases considered by the model. If required, the various concentrations are brought back to equilibrium using a separate chemical code. If dissolution or precipitation occurs, the local concentrations in solid phases are modified appropriately. Following that operation, the modified concentration profiles serve as a starting point for the calculation of the next time step. The movement of ions during the transport step is described by the volume-averaged version of the extended Nernst-Planck equation to which is added an advection term (Marchand 2000, Marchand et al. 2002):
[1]
∂& ∂ ln γ ∂ (θ& ) ∂ ' ] ) ∂Ψ − θ' +θ & + θ' & −&9 = 0 ∂W ∂[ ∂[ 57 ∂[ ∂[
where & is the concentration of the species L in the aqueous phase, θ is the volumetric water content 3 3 (expressed in m /m of material), ' is the diffusion coefficient, ] is the valence number of the species, ) is the Faraday constant, 5 is the ideal gas constant, 7 is the temperature of the liquid, Ψ is the diffusion potential, γ is the chemical activity coefficient and 9 is the velocity of the fluid.
Equation 1 has to be written for each ionic species present in the system. The chemical activity coefficients appearing in the equation can be calculated using a modified version of the Davies equation (Samson et al. 1999A):
[2]
ln γ = −
$]
2
,
1+ D
%
,
+
(0.2 − 4.17H − 5, ) $] 2 ,
1000
where , is the ionic strength of the solution, and $ and % are temperature dependent parameters. The parameter D in equation 2 varies with the ionic species considered. More information on this approach can be found in reference (Samson et al. 1999A).
2
The diffusion potential Ψ appearing in equation 1 is given by the Poisson equation, which relates the electrical potential that arises in solution to the concentration of each ionic species (Samson et al. 1999B). The Poisson equation is given here in its averaged form:
[3]
∂ ∂Ψ ) θτ +θ ε ∂[ ∂[
∑
] &
=0
=1
where 1 is the total number of ionic species, ε is the dielectric permittivity of the medium, in this case water, and τ is the tortuosity of the porous network. The velocity of the fluid, appearing in equation 1 as 9, can be described by a diffusion equation when the transport of water is induced by capillary forces (Pel 1995):
[4]
9
= −'
∂θ ∂[
where ' is the non-linear water diffusion coefficient. The value of where ' varies with the water content of the material (Pel 1995). To complete the model, the mass conservation of the liquid phase must be taken into account:
[5]
∂θ ∂ ∂θ − ' =0 ∂W ∂[ ∂[
The transport of ions and water in unsaturated cement systems can be fully described on the basis of equations 1 to 5. This relatively complex system of non-linear equations must be solved numerically. The treatment of the transport equations is based on the work of (Samson et al. 1999B). According to this approach, all equations are solved simultaneously. The spatial discretization of this coupled system is performed using the finite element method according to the standard Galerkin procedure. An Euler implicit scheme is used to discretize the transient part of the model (Zienkiewicz and Taylor 1989). The non-linear set of equations is solved using a Newton-Raphson algorithm (Zienkiewicz and Taylor 1989). This second order algorithm gives a good convergence rate and is robust enough to handle the electrical coupling between the ionic species as well as the non-linearities arising from the transport of water and ions. As previously mentioned, after the transport step, the concentration profiles (of the various ionic species in solution) might not be in chemical equilibrium with the various solid phases present in the system. At each node, the concentrations in ions are corrected with a chemical equilibrium code. It should be noted that this approach assumes the existence of a ORFDOFKHPLFDOHTXLOLEULXP throughout the system. According to this hypothesis, the rate of dissolution/precipitation of the various species in solution is intrinsically much faster than the rate of transport. -
+
+
The actual version of STADIUM accounts for the transport of eight different ionic species (OH , Na , K , 22+ 2+ SO4 , Ca , Al(OH)4 , Mg and Cl ) and the presence of nine solid phases (CH, C-S-H, ettringite, hydrogarnet, gypsum, Friedel’s salt, brucite, mirabilite and halite). Information of the various solid phases is given in Table 1. The curly brackets {...} in Table 1 refer to the chemical activity of each species, which can be calculated using equation 2. As can be seen, the actual version of the model does not account for carbonation effects. The transport of CO2 and its interaction with the cement paste hydration products will be included in a future version of STADIUM.
3
Table 1: Chemical equilibrium expression for each solid phase Phase
Chemical composition
Chemical equilibrium expression
CH C-S-H Ettringite Hydrogarnet Gypsum Friedel’s salt Brucite Mirabilite Halite
Ca(OH)2 (1.65)CaO.SiO2.(2.45)H2O 3CaO.3CaSO4.Al2O3.32H2O 3CaO.Al2O3.6H2O CaSO4.2H2O 3CaO.CaCl2.Al2O3.10H2O Mg(OH)2 Na2SO4.10H2O NaCl
Ksp = {Ca}{OH} 2* Ksp = {Ca}{OH} 6 4 3 2 Ksp = {Ca} {OH} {SO4} {Al(OH)4} 3 4 2 Ksp = {Ca} {OH} {Al(OH)4} Ksp = {Ca}{SO4} 4 4 2 2 Ksp = {Ca} {OH} {Cl} {Al(OH)4} 2 Ksp = {Mg}{OH} 2 Ksp = {Na} {SO4} Ksp = {Na}{Cl}
2
log Ksp
-5.2 -5.6 -44.0 -23.1 -4.6 -29.1 -10.9 -1.2 1.6
*C-S-H is assumed to decalcify like CH with a lower solubility constant
At the end of each time step, the model yields the concentration profile for each ionic species, the distribution of all solid phases and the water content and porosity at each location within the material. In addition to their influence on the concentration of the various ionic species, precipitation/dissolution reactions usually contribute to the modification of the pore structure of the solid. These microstructural alterations are likely to affect the transport properties of the material. In the model, chemical damage effects are taken into account through local variations in the porosity of the material. More information on the subject can be found elsewhere (Marchand 2000, Marchand et al. 2001, Maltais 2002). The input data required to run the model include the initial composition of the material (i.e. its initial content in CH, ettringite, ...), the characteristics of the concrete mixture, the initial composition of the pore solution and the porosity of the material. Informations on the ionic and moisture transport properties of the material are also required.
3. FIELD CONCRETE CHARACTERISTICS AND EXPOSURE CONDITIONS
In order to validate the model, six post-tensioned concrete slabs exposed to sulfate-laden soils in Southern California were sampled and tested. All the six slabs originated from a large residential project of over 80 different units. The slabs had a nominal thickness of 11.5 cm and were cast on a thin layer of sand spread over the soil. Systematic inspections of the slabs indicated that no plastic membrane had been placed between the garage slabs and the soil. On the basis of existing delivery tickets, it was established that a single concrete mixture had been used to build the six slabs. Information on the mixture design is given in Table 2. As can be seen, the concrete was made of ASTM Type V cement and produced at an average (and relatively high) water/cement ratio of 0.65. During the inspection of the slabs after approximately 7.5 years of exposure, various signs of degradation could be visually observed. For instance, many slabs were cracked and significant spalling could also be seen at the leading edge of the slabs. These observations are in good agreement with previous reports on the distress of similar structures exposed to sulfate-bearing soils (Skalny et al. 2001, Novak and Colville 1989). During the inspection of the slabs, signs of efflorescence could also be easily observed. Samples were collected and brought back to the laboratory to be analyzed.
4
Table 2: Information on the field concrete Properties Concrete mixture Cement Water Aggregate Compressive strength 28 days (cylinders) 7.5 years (dry cores) Exposure conditions* Sulfate Chloride Magnesium *Mean values for the entire
Values (kg/m3) 270 175 1920 (MPa) 22.5 37.0 (mmol/L) 22 – 176 4 – 90 ≈ 55
project
Information collected on the project reveals that a minimal compressive strength of 17.5 MPa had been specified for the concrete used to build the slabs. Tests performed on cylinders taken during construction indicate that the concrete had an average compressive strength of 21.0 MPa∗ after 28 days of moist curing. Cores (diameter = 100 mm and nominal height = 115 mm) extracted from the slabs after 7.5 years of exposure and tested in a dry condition had an average compressive strength of 37 MPa*. ASTM C 642 tests carried out on companion cores show that the concrete had a mean porosity of 15.5%*. The site conditions (to which the concrete was exposed) were investigated using various techniques. Numerous soil samples were taken at the vicinity of the six slabs. The analyses reveal that the soil was made of a mixture of clay (mainly montmorillonite), silt and sand. Measurements performed according to ASTM D 1557 indicate that the average degree of saturation of the soil samples was approximately 86%. ¶
The soluble sulfate content of the various soil samples was determined according to the prescriptions of the California Department of Transportation Procedure 417 (1986). According to this procedure, the sample of soil is first immersed in distilled water. After several hours, the sulfate content of the test solution is analyzed by a barium chloride turbidity method. Test results indicate that the soluble sulfate content ranged from 2473 to 4430 mg of SO4 per kg of dry soil for a mean value (for the six slabs) of 3626 mg/kg. It should be emphasized that these sulfate concentrations are considered by the Uniform Building Code (UBC 1985) as severe. According to the specifications of the UBC, concrete exposed to such high sulfate levels should have a maximum water/cement ratio of 0.45 and be prepared with an ASTM Type V cement. In order to get additional information on the severity of the exposure conditions, another series of soil samples were taken at various locations throughout the project. Each soil sample was divided into two parts. The soluble sulfate content of the first part was determined according to California Procedure 417. The second sample was centrifuged, and the extracted pore solution analyzed by ion chromatography. Test results show that the sulfate concentration of the pore solution ranged from 22 to 115 mmol/L. In addition, a good correlation between the soluble sulfate concentration (expressed in mg of SO4 per kg of
∗ ¶
These results are average values obtained for the samples originating from the entire project. For each lot, at least three (and up to six) different soil samples were analyzed.
5
§
SO4 - In soil (by extraction) (mg/kg)
dry soil) and the sulfate concentration of the pore water (expressed here in mg of SO4 per kg of solution) was found (see Figure 1). Analyses indicate that the pore water of the soil samples also contained significant amounts of chloride (from 4 to 90 mmol/L), sodium (from 4 to 178 mmol/L), calcium (≈ 10 mmol/L on average) and magnesium (≈ 50 mmol/L on average). Note that the chloride and magnesium concentrations were quite variable from one sample to another.
20000
15000
10000
5000 Linear regression 0 0
5000
10000
15000
20000
SO4 - Pore water (mg/kg)
Figure 1: Relationship between the sulfate concentration of the soil (as determined by the extraction method) and that of the pore water (obtained by centrifugation)
For each of the six garage slabs, a vertical core was examined using backscatter mode scanning electron microscope (SEM) and energy-dispersive X-ray analyses (EDXA). Three vertical polished thin sections (from the top, middle and bottom parts of each core) were prepared. Each thin section was approximately 30-mm wide and 35-mm high. Microstructural alterations resulting from the exposure to the sulfatebearing soils were systematically analyzed. For each core, a diagram indicating the location of the ettringite formation layer, calcium hydroxide (portlandite) dissolution “front”, C-S-H decalcification zone and gypsum precipitation layer was prepared. One of these diagrams is shown in Figure 2. More information on the SEM observations can be found elsewhere (Diamond and Lee 1999).
§
For the SO4 concentration of the pore solution: 1mg/kg = 96 mmol/L
6
3 1 = Gypsum precipitation zone 2 = Portlandite dissolution zone 3 = Carbonation zone 4 = Ettringite precipitation zone 5 = C-S-H decalcification zone
4 2 1 5 Figure 2: Schematic representation of the degradation observed during the SEM examinations
/$%25$725 75%) meaning that relatively large variations in the degree of saturation do not have significant impact on the relative humidity of the system (Fredlund, D.G. and Rahardjo 1993, Gillott 1987). Additional information on the boundary conditions considered for the three series of simulations is given in Table 4. As can be seen, a first series of simulations was performed assuming that the soil was partially saturated with a sodium sulfate/sodium chloride solution. In the second series of simulations, the sodium chloride content of the solution was raised from 28.2 mmol/L to 84.6 mmol/L. In the third series of simulations, the concentration in magnesium ions was fixed at 55.8 mmol/L. The sulfate concentration assumed in all three series of simulations corresponds to the mean value measured for all the soil samples (over 200) tested throughout the entire project. Ionic concentrations were assumed to remain constant during the entire exposure period considered for the simulations (i.e. 7.5 years).
Table 4: Boundary conditions for the numerical simulations Simulation Ions Soil concentration series (mmol/L)
A
B
C
+
111.6 41.7 28.2 0.0
+
168.0 41.7 84.6 0.0
+
0.0 41.7 28.2 55.8
Na 2SO4 Cl 2+ Mg Na 2SO4 Cl 2+ Mg Na 2SO4 Cl 2+ Mg
5(68/76
SEM observations and EDX analyses of the cores revealed that concrete was characterized by a succession of layers (or zones) starting from the outer surface of the specimens. Each zone was found to be the result of a series of reactions between the external (mainly sulfate) ions and the aluminate and calcium-bearing phases initially present within the material. Furthermore, a layer of carbonation (from 5 to 17-mm thick) was systematically observed near the top surface of all cores (see Figure 2). Deposits of crystalline sulfates were also detected on the upper portion of the cores. As previously mentioned, efflorescence materials collected on the surface of the slabs were analyzed by X-ray
9
diffraction. The analyses revealed that the powder was predominantly composed of anhydrous crystalline sodium sulfate (thenardite). Zones of degradation and reaction fronts were also systematically observed in the bottom portion of the slabs in contact with the soil. In two cases, the analyses revealed the presence of gypsum at the vicinity of the lower surface of the cores. A second zone with extensive ettringite formation was routinely found to lie above the layer of gypsum (see Figure 2). Although the precipitation of sulfate-bearing phases in these porous systems had apparently not resulted in significant macroscopic expansion, it had clearly contributed to the formation of microcracks. As illustrated in Figure 2, a layer of decalcified C-S-H (a few millimeters thick) was observed near the bottom surface of all cores. This zone was immediately followed by another layer of material totally depleted of calcium hydroxide (portlandite) crystals. The presence of Friedel’s salt crystals is usually harder to observe during SEM examinations. However, presence of chloride-bearing phases could be detected in the middle portion of the cores. Similarly, zones enriched in magnesium could also be detected throughout the cores. A summary of the SEM observations and EDX analyses is given in Table 5.
Table 5: Comparison between the SEM observations and the numerical results Depth of penetration (mm) SEM observations
Simulation Series A Simulation Series B Simulation Series C
Ca(OH)2 dissolution
From 12 to 35
20
19
25
C-S-H decal.
From 6 to 12
11
10
14
Ettringite formation
From 12 to 35
32
32
From 12 to 28
Gypsum formation
From 0 to 12
20
18
From 2 to 20
Brucite formation
_
_
_
18
Carbonation*
From 5 to 17
_
_
_
*Not predicted by the actual version of the model
A typical example of the distribution in solid phases predicted by the model is given in Figures 3 and 4. The figures illustrate the numerical results obtained from simulations A and B, respectively. In these figures, the bottom surface of the core (in contact with the soil) is located at the origin of the x-axis while the top of the slab corresponds to x = 0.115 m. The numerical results obtained for a period of exposure of 7.5 years can be compared to the SEM observations made on the various concrete cores. The two series of data are given in Table 5. As can be seen, the numerical simulations tend to reliably describe the extent of the degradation process. For instance, the model correctly predicts the depth of penetration of the ettringite precipitation layer and the thickness of the portlandite-depleted zone. The analyses of the distribution of ions in solution (not shown) also indicate a build-up in sodium and sulfate near the top portion of the slab in good agreement with the presence of sodium sulfate efflorescence detected during the site inspection. The numerical results obtained for a period of exposure of 7.5 years can be compared to the SEM observations made on the various concrete cores. The two series of data are given in Table 5. As can be seen, the numerical simulations tend to reliably describe the extent of the degradation process. For instance, the model correctly predicts the depth of penetration of the ettringite precipitation layer and the thickness of the portlandite-depleted zone. The analyses of the distribution of ions in solution (not shown) also indicate a build-up in sodium and sulfate near the top portion of the slab in good agreement with the presence of sodium sulfate efflorescence detected during the site inspection.
10
Note that the model appears to reliably describe the transport of moisture throughout the slabs. Hence, the model predicts that the flux of moisture going out of the top surface of the slab should be a little less 2 than 9 ml/d/m . Moisture emission measurements made according to ASTM E 1907 on similar slabs gave 2 values slightly above 11 ml/d/ m .
100 90 80
+
70
'(
60
#& #
%$50
!"
40
*) (
68C DEC ;
.0/1 32 , -
30
4 5
?3 @-3 A B
20 10 0 0.00
687:9= 0.02
0.04
0.06
0.08
0.10
Figure 3: Numerical results – Boundary conditions A
100 90 80
d
70
` aY
60
cb a \_ X
50
YZ[
40
\ ]^Y WX
o8p qEp r
ghi HjQ ePO I T JK fG I M
30
kI I O G K lG I M mO G M fMT n HBH JT I
20
o8s:turEv
10 0 0.00
0.02
0.04
0.06
0.08
FG HI JK L M N O PQIR MS PI I PQPNI RM HT JS U Q V
Figure 4: Numerical results – Boundary conditions B
11
0.10
It should be emphasized that the predictions yielded by the model are solely based on the mathematical equations previously described, and that no fitting parameters are included in the model. In that respect, the good correlation between the predicted values and the experimental results further confirms the validity of the numerical model. The good correlation between the values predicted by the model and the SEM observations also confirms that the mechanisms of sulfate attack yield to a major reorganization of the hydrated cement paste microstructure. In addition to the formation of the new sulfate, chloride and magnesium-bearing products, the penetration of external ions markedly accentuates the dissolution of calcium hydroxide (portlandite) and the decalcification of C-S-H. Both phenomena contribute to significantly increase the porosity of the material. Such an increase has numerous severe consequences on the concrete properties. First of all, it reduces the ability of the material to act as an effective barrier and favors the penetration of moisture and aggressive ions. The significant increase in porosity also affects the mechanical properties of the concrete. Considering that the degradation process progresses from the external surfaces to the core of the slab, the pore structure alterations should be particularly detrimental for the flexural resistance of the material. As can be seen, all three series of simulations predict the formation of gypsum near the bottom surface of the concrete core. Gypsum was however observed in only two of the six garage slab cores. Many reasons can explain the fact that gypsum was not systematically detected in all samples. Thermodynamic calculations indicate that the presence of chloride ions often contributes to increase the solubility of gypsum in solution (Damidot and Glasser 1993, Damidot and Glasser 1997). It is possible that the chloride concentration in the soil solution right next to the four remaining slabs was high enough to prevent the precipitation of gypsum. It is worth noting that the influence of the chloride concentration on the solubility of gypsum was well described by the model. As can be seen by comparing Figure 3 to Figure 4, an increase of the external chloride concentration from 28.2 to 84.6 mmol/L has led to a significant reduction of the amount of gypsum predicted by the model. The analysis of Figures 3 and 4 also indicate that the precipitation of Friedel’s salts in the central portion of the cores is in good agreement with the SEM observations and the EDX analyses. It should also be emphasized that a previous investigation of the microstructural features of concrete samples originating from the same project confirmed the frequent presence of gypsum layers near the bottom portion of the slabs (Diamond and Lee 1999). During their examinations, Diamond and Lee also found massive deposits of brucite (Mg(OH)2) at the bottom of a few cores. Their observations are in good agreement with the results of simulation C. As previously mentioned, analyses of pore solutions of the soil samples indicated that the magnesium concentration was quite variable from one location to another. The absence of brucite deposits in the six slabs can probably be explained by the negligible concentrations in magnesium ions in these areas of the project.
&21&/8',1*5(0$5.6
The numerical model can be used to predict with a good reliability the extent of the degradation process. Penetration depths predicted by the model after 7.5 years of exposure are well within the range of values observed for actual garage slab cores. Numerical simulations confirm that the sulfate attack yields to a major reorganization of the hydrated cement paste microstructure. In addition to the formation of the new sulfate and magnesium-bearing products, the penetration of external ions markedly accentuates the dissolution of portlandite and the decalcification of C-S-H.
12
5()(5(1&(6
Damidot, D. and Glasser, F.P. (1997) Thermodynamic investigation of the CaO-Al2O3-CaSO4-CaCl2-H2O system and the influence of Na2O, &RQJUHVVRQWKH&KHPLVWU\RI&HPHQW, Göthenburg, Sweden. Damidot, D. and Glasser, F.P. (1993) Thermodynamic investigation of the CaO-Al2O3-CaSO4-H2O system at 25° C and the influence of Na2O, &HPHQWDQG&RQFUHWH5HVHDUFK, 23: 221-238. Diamond, S. (1981) Effects of two Danish fly ashes on alkali contents of pore solutions of cement fly ash pastes, &HPHQWDQG&RQFUHWH5HVHDUFK, 11:383-390. Diamond, S. and Lee, R.J. (1999) Microstructural alterations associated with sulfate attack in permeable concretes, in 0DWHULDOV6FLHQFHRI&RQFUHWH6SHFLDO9ROXPH 6XOIDWH$WWDFN0HFKDQLVPV,The American Ceramic Society, 123-173. Fredlund, D.G. and Rahardjo, H. (1993) 6RLOPHFKDQLFVIRUXQVDWXUDWHGVRLOV, J. Wiley & Sons, New York, U.S.A. Gillott, J.E. (1987) &OD\LQHQJLQHHULQJJHRORJ\, Elsevier, Amsterdam, The Netherlands. Jacobsen, S., Marchand, J., Boisvert, L. (1996) Effect of cracking and healing on chloride transport in OPC concrete, &HPHQW&RQFUHWH5HVHDUFK, 26:869-882. Marchand, J. (2000) Modeling the behavior of unsaturated cement systems exposed to aggressive chemical environments 0DWHULDOVDQG6WUXFWXUHV, 34:195-200. Marchand, J., Samson, E. and Beaudoin, J.J. (2002) Modeling ion transport mechanisms in unsaturated porous media, (QF\FORSHGLDRI6XUIDFH &ROORLG6FLHQFH, M. Dekker Publisher, New York, USA. Marchand, J., Bentz, D.P., Samson, E. and Maltais, Y. (2001) Influence of calcium hydroxide dissolution on the transport properties of hydrated cement systems, in 0DWHULDOV6FLHQFHRI&RQFUHWH6SHFLDO 9ROXPH &DOFLXP+\GUR[LGHLQ&RQFUHWH, 113-130. Maltais, Y. (2002) Contribution to the study of ionic transport mechanisms and chemical degradation phenomena of fully or partially saturated cement systems, 3K'7KHVLV, Dept. of Civil Engineering, Laval University, (in preparation). Mills, R.H., (1985) Mass transfert of water vapor through concrete, &HPHQWDQG&RQFUHWH5HVHDUFK, 15: 74-82. Noorany, I. and Stanley, J.F. (1994) Settlement of compacted fills caused by wetting, Proceedings of Settlement’ 94, Geotechnical Engineering Division, American Society for Civil Engineering, 1516-1530. Novak, G.A. and Colville, A.A. (1989) Effloresence mineral assemblages associated with cracked and degraded residential concrete Foundation in Southern California, &HPHQWDQG&RQFUHWH5HVHDUFK, 19:1-6. Pel, L. (1995) Moisture transport in porous building materials, 3K'7KHVLV, Eindhoven University of Technology, The Netherlands, 125 p. Ramachandran, V.S., Feldman, R.F., Beaudoin, J.J. (1981) &RQFUHWH6FLHQFH, Heydon & Sons, London, U.K. Samson, E., Lemaire, G., Marchand, J. and Beaudoin, J.J., (1999A) Modeling chemical activity effects in strong ionic solutions, &RPSXWDWLRQDO0DWHULDOV6FLHQFH, 15:285-294. Samson, E., Marchand, J., Robert, J.L. and Bournazel, J.P. (1999B) Modeling the mechanisms of ion diffusion transport in porous media, ,QWHUQDWLRQDO-RXUQDORI1XPHULFDO0HWKRGVLQ(QJLQHHULQJ, 46:2043-2060. Skalny, J., Marchand, J., Odler, I. (2001) 6XOIDWHDWWDFNRIFRQFUHWH, E & FN Spon, London, UK. St-John, D.A., Poole, A.W. and Sims, I. (1998) &RQFUHWHSHWURJUDSK\$KDQGERRNRILQYHVWLJDWLYH WHFKQLTXHV, Arnold, London, UK. Taylor, H.F.W.(1990) &HPHQWFKHPLVWU\, Academic Press Inc., San Diego, USA. Zienkiewicz O.C. and Taylor R.L. (1989) 7KH)LQLWH(OHPHQW0HWKRG, 4th Edn, McGraw-Hill, USA.
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