A COUPLED TRANSPORT-REACTION MODEL FOR SIMULATING AUTOGENOUS SELF-HEALING IN CEMENTITIOUS MATERIALS PART II: VALIDATION

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1 -4 October 4, Beijing, China A COUPLED TRANSPORT-REACTION MODEL FOR SIMULATING AUTOGENOUS SELF-HEALING IN CEMENTITIOUS MATERIALS PART II: VALIDATION Haoliang Huang (), Guang Ye (,) and Denis Damidot (3,4) () Microlab, Department of Civil Engineering and Geoscience, Delft University of Technology, the Netherlands () Magnel Laboratory for Concrete Research, Department of Suctural Engineering, Ghent University, Belgium (3) UniversitéLille Nord de France, France (4) Ecole Nationale Supérieure des Mines de Douai, France Absact In this paper, the coupled ansport-reaction model is validated with the experimental results on autogenous self-healing in Portland cement paste. The parameters are studied for modelling the dissolution of cement, the diffusion of ions between the solution in the crack and in the bulk paste and the precipitation of reaction products in the crack. Simulation results for different parameters are compared with the experimental results. Discussion on the coupled ansport-reaction model is presented.. INTRODUCTION The physico-chemical processes of autogenous self-healing can be described as : dissolution of unhydrated cement, diffusion of ions in the solution in the crack and in the bulk paste and precicitation of solid reaction products in the crack. When water peneates into the crack, the unhydrated cement present at the crack surfaces comes in contact with water and starts to dissolve. At the same time, an exchange of ions takes place between the pore solution in the bulk paste and the solution in the crack. When the concenations of ions in the crack reach the supersaturation level for precipitation of reaction products, solid reaction products are formed in the crack. In the Part I, a coupled ansport-reaction model is developed for simulating the physicochemical processes of autogenous self-healing. In the coupled ansport-reaction model, it is assumed that the crack is filled with water. The dissolution of unhydrated cement, the diffusion of ions in the crack and the precipitation of reaction products in the crack are simulated. The model is a two dimensional (D) model. Different phases, i.e. reactive material, non-reactive material and crack, in the paste are represented with micro-pixels. To simulate the healing process, the period of self-healing is discretized into small time steps and the healing process is calculated iteratively. In each time step, the dissolution of unhydrated 44

2 -4 October 4, Beijing, China cement is described as boundary conditions for simulating ion diffusion. With the information about the dissolution of unhydrated cement and the initial concenations of ions in the solution in the crack, the concenations of ions in each micro-pixel before the formation of reaction products is determined and form input for the thermodynamic model. With the thermodynamic model the amount of reaction products and the remaining ion concenations after chemical reactions are calculated. In the iteration process, the remaining ion concenations after the formation of reaction products form the initial conditions for the next calculation step. In this paper, the validation of the coupled ansport-reaction model with experimental results on autogenous self-healing in Portland cement paste is presented. The parameters for modelling the dissolution of cement, the diffusion of ions between the solution in the crack and in the bulk paste and the precipitation of reaction products in the crack are studied and discussed.. VALIDATION OF THE COUPLED TRANSPORT-REACTION MODEL. Microsucture of Portland cement paste Portland cement paste is prepared with CEM І 4.5N. The mineral composition of CEM І 4.5N is listed in Table. Samples are cracked at the age of 7 days, 4 days and 8 days, respectively, and then cured in water again for self-healing. From the microsucture of cement paste (see Figure (a)) it is found that some unhydrated cement particles are present at the crack surfaces, while others are embedded inside the bulk paste. The unhydrated cement particles at the crack surfaces can directly react with water in the cracks and the reaction products can be formed in the crack. The unhydrated cement particles embedded in the bulk paste are surrounded by hydration products and can not directly react with the water in the crack. This is different from the situation of unhydrated cement particles present at the crack surfaces. In the sample for simulation, the volume fraction of unhydrated cement particles present at the crack surfaces (see Figure (b)) is determined by means of BSE image analysis. The volume fraction of all unhydrated cement particles and capillary porosity of the sample is quantified as well. Detailed information is listed in Table. UHC in the maix UHC present at Crack surfaces, A cr,rm Non-reactive material at the crack surfaces, A cr,se crack UHC existing at crack surfaces UHC embedded in bulk paste Observed surfaces with ESEM (a) BSE image of cement paste with a crack (b) Scheme of the disibution of UHC in 3D view Figure : Disibution of unhydrated cement particles in cement paste (UHC refers to unhydrated cement particles). 45

3 -4 October 4, Beijing, China Table : Mineral composition of Portland cement (CEM І 4.5N) calculated by Bogue equation [] Compound C 3 S C S C 3 A C 4 AF Total Weight (%) Table : Information about microsucture of Portland cement paste determined by means of BSE image analysis, compared to that from modeling with HYMOSTRUC3D (in brackets). The w/c ratio is.3. Age (days) Capillary porosity (-) Fraction of unhydrated cement (%) 7.4 (.4) 9. (8.5) (.4) 7.8 (6.4) (.87) 6.3 (4.7) 3.4 Fraction of unhydrated cement at crack surfaces in the sample for simulation (%). Parameters of the coupled ansport-reaction model.. Basic dissolution rate of cement R As described in the previous study, in the coupled ansport-reaction model for autogenous self-healing the rate of phase-boundary reactions can be described as: R R t () where R [m/s] is the basic dissolution rate of reactive material, which depends on the chemical composition; [-] is the parameter used to describe the induction period of the reaction as affected by the large amount of water in the crack; [-] is the parameter used to described the acceleration of the reaction due to the seeding effect of non-reactive material at the crack surfaces. The rate of diffusion-conolled reaction can be calculated by the formula: R Rt 6 P () P where [m] is the ansition thickness particularly for the reaction of reactive material at crack surfaces. For cement clinker, the basic dissolution rate is related to the chemical composition of the clinker []. To simulate hydration of C 3 S, a good fit of the simulation results with the experimental results is obtained for R =.65 μm/h []. In comparison, to simulate hydration of C S, a good fit of simulation results with the experimental results is obtained for R =. μm/h []. As recommended by van Breugel [], R value ranges from.5 μm/h to.55 μm/h for different types of Portland cement, depending on the percentages of C 3 S and C S. For Portland cement CEM І 4.5N, the basic dissolution rate R in Equation can be assumed to be.45 μm/h []... Diffusion coefficients for ions In the healing process, ion diffusion takes place between the solution in the crack and the solution in the maix. This ion diffusion can be described by Fick s second law [3]: 46

4 -4 October 4, Beijing, China ci ( Di ci) (3) t where c i [mol/m 3 ] is the concenation of the i th ion and D [m /s] is the diffusion coefficient i in the solution in the crack for the i th ion. In this section, the ion diffusion coefficients used in the model are discussed. Before the reaction products are formed in cracks, the diffusion coefficient D i,c of the pixels representing the crack can be assumed to be equal to the ion diffusion coefficients in free water. The ion diffusion coefficients in free water used in the simulation are listed in Table 3. Table 3: Diffusion coefficients of ions in free water at 5 C [4] Species Ca + Al 3+ Mg + OH - SO 4 H SiO 4 Diffusion coefficient ( -9 m /s) When reaction products are formed in cracks, the ion diffusion coefficients inside the crack decrease gradually. Zhang [5] determined the relationship between the diffusion coefficient of cement paste for chloride ions and the effective porosity by using lattice Boltzmann method. The mathematic expression of diffusion coefficient of cement paste as a function of the porosity ( ) could be obtained by fitting the data in [5]. Moreover, the diffusion coefficient almost linearly decreases with the decrease of porosity ranging from.55 to.65 [5]. Based on this, it is assumed that the diffusion coefficient almost linearly decreases with the decrease of porosity for.55. The diffusion coefficient DiC, D i, C in the crack is written as:.8 Di, C Di, C where D [m /s] is the initial diffusion coefficient of the solution in the crack before the ic, healing process. In this case, D ic, is equal to the ion diffusion coefficient in free water; After reaction products are formed in the crack, the crack is partially filled and [-] is the volume fraction of the crack not filled by reaction products. It must be mentioned that in the coupled ansport-reaction model should not be smaller than.5, otherwise Equation 4 is not valid. Regarding the ion diffusion in the bulk paste, the diffusion coefficient D i, B can also be calculated with the capillary porosity of the bulk paste in Table with Equation 4. The results are presented in Table 4. Table 4: Diffusion coefficient D, for Ca +, H SiO 4 and OH - ions in the bulk paste i B Age (days) Diffusion coefficient of Ca + ( - m /s) Diffusion coefficient of H SiO 4 ( - m /s) Diffusion coefficient of OH - ( - m /s) (4) 47

5 -4 October 4, Beijing, China..3 Effect of large amount of water on the induction period of the reaction of reactive material - Regarding the hydration of cement four stages can be considered: pre-induction, induction, acceleration and deceleration [6]. During the induction period, t ind, the reaction rate of cement is almost. Therefore, the parameter used to describe the induction period of the reaction in Equation, can be written as: t t t t ind ind However, for mixture with w/c ratio of 5., there is no induction stage during the hydration, whereas for the mixture with w/c ratio of.5, the induction period lasts for about 5 hours [7]. For self-healing of cracks, there is much water in the crack compared to the volume of cement clinker present at the crack surfaces. Therefore, in case of self-healing in Equation can be written as: t (6)..4 Seeding effect of the crack surfaces on the dissolution kinetics of reactive materials - and Parameter in Equation describes the seeding effect of the crack surfaces on the dissolution of reactive material in the coupled ansport-reaction model. Parameter is the ansition thickness describing the change from a phase-boundary reaction to a diffusionconolled reaction. The simulation results obtained for different values of these two parameters are compared with the experimental results. For simulation of hydration of cement CEM І in bulk paste, the ansition thickness defined in cement hydration model HYMOSTRUC3D approximates.5 μm [8]. No seeding effect is present for the hydration of cement in bulk paste, therefore =.. In case of simulation of self-healing, for =. and =.5 μm, the filling fraction of cracks calculated by the coupled ansport-reaction model is much lower than the experimental results (see Figure ). When and increase to.6 and 4., respectively, the simulated results are in good agreement with the experimental results from [9]. These values of and indicate that the seeding effect of the crack surfaces accelerates the cement hydration and delays the ansition from a phase-boundary reaction to a diffusion-conolled reaction, i.e. taking place at higher degree of hydration of cement...5 Summary of study of parameters in the coupled ansport-reaction model For autogenous self-healing in Portland cement paste (w/c=.3) starting after the age of 7 days, values of the parameter R,, and of the coupled ansport-reaction model are summarized in Table 5. (5) 48

6 Filling fraction of cracks by CH (%) RILEM International Symposium on Concrete Modelling, -4 October 4, Beijing, China 3. PREDICTION OF AUTOGENOUS SELF-HEALING WITH THE COUPLED TRANSPORT-REACTION MODEL In case of self-healing in Portland cement paste, the seeding effect of the crack surfaces depends on the area of the non-reactive material at the crack surfaces (A cr,se in Figure ). 5 =.6, δ = 4. μm 4 3 Series Series7 =.6, δ =.5 μm Series4 =., δ = 4. μm Series5 =., δ =.5 μm Time (h) Figure : Filling fraction of a crack with portlandite for different values of and in Equations and. Self-healing starts at the age of 8 days of the paste. The experimental results from [9] are shown with solid squares in the figure. The crack width is μm. Table 5: Parameters for simulating self-healing in Portland cement paste immersed in water. The w/c ratio is.3. Self-healing starts after the age of 7 days. Parameters R (μm/h) (-) (-) (μm) Values Table shows that for Portland cement paste with w/c ratio of.3 the fraction of unhydrated cement in the cement paste hardly changes after the age of 7 days (from 9.% to 6.3%). Therefore, when cracks occur at any time after the age of 7 days, the ratios A cr,rm /A cr of the crack surfaces can be almost the same (A cr,rm is the area of reactive material at the crack surfaces; A cr is the area of the crack surfaces, see Figure ). Hence, A cr,se /A cr can be assumed to be a constant for the case that cracks occur after the age of 7 days in Portland cement paste with w/c ratio of.3. The same values of and can be used for this particular case. The parameter values of the coupled ansport-reaction model determined above (summarized in Table 5) are used for simulating autogenous self-healing starting at the age of 7 days and 4 days of Portland cement paste. As shown in Figure 3 and Figure 4, the calculated filling fraction of cracks by portlandite is in good agreement with the experimental results from [9]. Moreover, Figures 3 and 4 show that the filling fraction of cracks with C-S-H is much lower than with portlandite. This is consistent with the experimental results in [9], 49

7 Filling fraction of cracks (%) RILEM International Symposium on Concrete Modelling, -4 October 4, Beijing, China demonsating that the fraction of portlandite in the reaction products formed in cracks accounts for about 8% by mass, while C-S-H accounts for less than 5%. For the cement pastes with a higher w/c, there is less cement directly exposed to the crack surfaces. A cr,rm /A cr is lower. A cr,se /A cr, hence, is higher. A larger value of should be used for describing the seeding effect of the crack surfaces in the simulation of autogenous self-healing Exper_Portlandite Simul_Portlandite Simul_C-S-H Time (h) Figure 3: Filling fraction of a crack in Portland cement paste starting at the age of 7 days. Exper_Portlandite refers to the filling fraction of cracks with portlandite determined experimentally in [9]. Simul_Portlandite refers to the calculated filling fraction of cracks with portlandite, while Simul_C-S-H refers to the calculated filling fraction of cracks with C-S-H. The initial crack width is μm. For the cement paste made of coarser cement particles, the degree of hydration of cement is lower than finer cement particles. Hence, more cement will be directly exposed to the crack surfaces. A cr,rm /A cr is higher. A cr,se /A cr, hence, is lower. A smaller value of, therefore, is used for simulating autogenous self-healing. 4. CONCLUSIONS In this paper, the coupled ansport-reaction model is validated with the experimental results on autogenous self-healing in Portland cement paste. The model can be used to predict autogenous self-healing in Portland cement paste. The effect of large amount of water in the crack on the dissolution rate of cement should be taken into account. It is also necessary to consider the seeding effect of the crack surfaces on the rate of self-healing. The reaction products can be formed not only at the surface of unhydrated cement, but also at the seed surface, i.e. non-reactive material at the crack surfaces. Because of the seeding effect of the crack surfaces, the dissolution rate of the cement exposed to the crack surfaces is accelerated. 5

8 Filling fraction of cracks (%) RILEM International Symposium on Concrete Modelling, -4 October 4, Beijing, China The ansition from a phase-boundary reaction to a diffusion-conolled reaction is delayed, i.e. taking place at higher degree of hydration of cement Exper_Portlandite Simul_Portlandite Simul_C-S-H Time (h) Figure 4: Filling fraction of a crack in Portland cement paste starting at the age of 4 days. Exper_Portlandite refers to the filling fraction of cracks with portlandite determined experimentally in [9]. Simul_Portlandite refers to the calculated filling fraction of cracks with portlandite, while Simul_C-S-H refers to the calculated filling fraction of cracks with C-S-H. The initial crack width is μm. ACKNOWLEDGEMENTS The authors would like to thank the National Basic Research Program of China (973 Program: CB38) and the China Scholarship Council (CSC) for the financial support. REFERENCES [] Bogue, R.H., The chemisy of portland cement, ed. nd. 955, New York: Reinhold Pub. Corp. [] van Breugel, K., Simulation of Hydration and Formation of Sucture in Hardening Cement-based Materials. 99, Delft University of Technology. [3] Cussler, E.L., Diffusion : mass ansfer in fluid systems. 997, UK: Cambridge university press. [4] Mills, R. and V.M.M. Lobo, Self-diffusion in elecolyte solutions. 989, Amsterdam: Elsevier. [5] Zhang, M., Multiscale lattice Boltzmann-finite element modelling of ansport properties in cement-based materials. 3, Delft University of Technology. p. 8. [6] Taylor, H.F.W., Cement Chemisy. 997, London: Thomas Telford Publishing. [7] Damidot, D. and A. Nonat C3S hydration in diluted and stirred suspensions: (I) study of the two kinetic steps. Advances in Cement Research, , [8] Van Tuan, N., Rice husk ash as a mineral admixture of ula high performance concrete., Delft University of Technology. [9] Huang, H., G. Ye, and D. Damidot, Characterization and quantification of self-healing behaviors of microcracks due to further hydration in cement paste. Cement and Concrete Research, 3. 5: p