MODELLING AUTOGENOUS SHRINKAGE OF HYDRATING CEMENT PASTE

Transcription

1 MODELLING AUTOGENOUS SHRINKAGE OF HYDRATING CEMENT PASTE Ines Jaouadi (1), Amor Guidoum (2) and Karen Scrivener (3) (1) Laboratory of Construction Materials, EPFL, Switzerland (2) Laboratory of Construction Materials, EPFL, Switzerland (3) Laboratory of Construction Materials, EPFL, Switzerland Abstract Autogenous deformation is the self-created deformation of a cement paste, mortar or concrete during the hydration process. In ordinary concretes autogenous deformation is negligible if compared to drying shrinkage. On the contrary, in HPC the low water/cement ratio causes a significant drop of the internal relative humidity (RH) in the cement paste during sealed hydration under sealed conditions. Since autogenous shrinkage is closely related to autogenous RH change, it generally results in tensile stresses in the cement paste due to aggregate restraint. Autogenous shrinkage should be limited since it may induce microcracking and may damage the concrete quality. The main objectives of this paper are to determine the evolution of mechanical properties and volume change of cement paste. To predict the mechanical properties of hydrating cement paste at early age, based on its microstructure and the characteristics of constituents, homogenisation process will be made on a computer-generated microstructure obtained by an existing continuum hydration model developed in our laboratory. In the second step, the capillary pressure of the capillary water will be determined numerically at each step of hydration. By knowing the evolution of the porosity of the cement paste during hydration, the critical radius of gaseous pore can be determined. By knowing all this characteristics, the effective autogenous shrinkage as function of time and the water to cement ratio are calculated. All these numerical results are compared to the experimental ones. Key words: autogenous shrinkage, mechanical properties, microstructure, validation. 1. INTRODUCTION Cement paste is a composite material formed of solid phases and pores. The mechanical behavior such as strength, creep and shrinkage are controlled by these phases and their spatial arrangements. The autogenous shrinkage is a consequence of the hydration process of the microstructure. Because of the complexity of the problems, there were only a few attempts in the literature were done where the microstructure is taken into account. 63

2 Hua [1], at the macro-scale, assumes that the liquid phase is continuous. In the equilibrium state, the capillary tension is therefore uniform. The cement paste is assumed macroscopically homogeneous and isotropic; the capillary tension produces therefore a hydrostatic macroscopic stress equal to product of the capillary tension and the total porosity. In this model, the capillary tension is regarded as a time function during hydration. Its determination is undertaken using MIP (Mercury Intrusion porosimetry). At the micro-scale, i.e the grain cement level, Hua assumes that -in periodic distribution - all the anhydrous grains are spherical and have the same size. At each step, the hydration process is simulated as the superposition of successive stress-free layers of hydrated product; the previous layer being subjected to capillary tension which also undertaken by MIP. The two approaches give a relatively good agreement with the experiment but there still a strong dependence upon the experimental data such as the pore size distribution, mechanical properties, degree of hydration. On another side, Koenders [2] used the HOMOSTRUC model to simulate the hydrating cement past in order to get the pore size distribution and the degree of hydration. In this approach, the pore volume is mathematically described by a logarithmic distribution whose parameters can be evaluated from the HYMOSTRUC model. The autogenous shrinkage of then is calculated according to Bangham s model which relates the volumetric changes of the microstructure ant the surface tension in the adsorption layer. The number of adsorption layers in terms of the RH (relative Humidity) is simply fitted from the Hagymassy (1986) experimental results while the elastic modulus is derived from a lattice model. This modeling approach is more closed to phenomenological model than to the numerical one since there is no real mechanical response of the microstructure to the driving force. From those limitations of existing models, this paper has the objective of determine the evolution of autogenous shrinkage by independent numerical and experimental techniques. The numerical simulation is based on the microstructural model called ic (pronounced MIKE), which derives its basics from the Pignat and Navi model [6]. The numerical simulation is performed on a hydrating C3S paste. To achieve this goal, the intrinsic elastic properties of the anhydrates and the hydrates are given. By knowing the evolution of porosity at each step of hydration, the capillary pressure of capillary water is calculated by determination of the critical radius of pore. By knowing all these characteristics, the contraction of solid phase is determined. Both simulated autogeneous deformation and overall mechanical properties are compared to the experimental results where the mechanical properties, the microstructure of the sample and the distribution of the pores under sealed conditions are also determined for a hydrating white cement paste. 2. AUTOGENOUS SHRINKAGE OF EARLY AGE HYDRATED CEMENT PASTE 2.1 Experimental study Material The experimental study has been performed for a period of about 7 days on white cement paste. Three different w/c ratios will be considered. A white Portland cement with Blaine fineness of 397 m 2 /kg and density of 3135 kg/m 3 was used. The Bogue-calculated phase composition (in wt. %) was: C 3 S: 67.5, C 2 S: 23.6, C 3 A:

3 The cement paste was mixed in a Hobart mixer for 7 minutes. Demineralized water was added first to the bowl and followed by the powder. The temperature of the ingredients was approximately 2 C Elastic properties In order to follow the evolution of the properties of cement paste at early ages, non destructive ultrasonic wave propagation technique is used. This technique permits us to evaluate the velocity of both longitudinal and transverse waves by measuring the propagation time through the cement paste at early ages. By considering the cement paste as isotropic and the wavelength larger than the size of the largest inhomogeneity, the Young s modulus E can be determined. White cement pastes with different water/cement ratios were investigated in this study. The compressional and shear wave signals are recorded every 1 minutes for 48 hours. The Young s for different water-cement ratios are plotted in Fig.1. These moduli increase strongly at early ages and become more slowly after. The w/c ratio affect the development of Young s modulus as it is shown in this figure Porosity The knowledge of the development of the pore volume and pore size distribution, of the state of water in the capillary pores (free or adsorbed), as hydration proceeds is needed. Pore size distribution using MIP is determined for different age of hydration for w/c=.36. Fig2 shows that the total pore volume intruded by mercury decreased with increasing the time of hydration. Young's modulus [GPa] w/c=.3 w/c=.36 w/c= Time [h] Figure1: Evolution of Young s modulus for different water to cement ratios. Cumulative volume [mm 3 /g] d 1d 1 2d 1d Pores diameter [µm] Figure2: Pore size distribution for w/c = Measure of autogenous deformation To determine the evolution of autogenous shrinkage, the cement paste was poured under vibration in special corrugated plastic moulds. Then, the specimen was placed in a special dilatometer composed of two bars allowing it to glide freely. The change in length of the specimen was measured by two transducers placed at the ends of the specimens. Figure 3 shows the autogenous deformation for different w/c ratios. The deformations were zeroed when the temperature in the sample was constant, which happened a few hours after the hydration peaks registered in the calorimeter. The autogenous shrinkage increases with 65

4 decreasing w/c ratio, it is about 58 µm/m for w/c =.36 versus 69 µm/m for w/c =.3. These results correspond to those found in the literature [4]; the lower the w/c ratio the larger the autogenous shrinkage. Autogenous shrinkage [µm/m] 2.2 Numerical study Mechanical properties w/c =.3 w/c = Time [h] Figure3: Autogenous deformation for the different w/c ratio. As an intermediary step towards the prediction of the autogeneous shrinkage, the effective elastic properties of of hydrating C3S are first performed on the microstructure generated by the hydration mode [3]. In this model, the anhydrous C 3 S particles are considered spherical and they are placed randomly in a periodic volume according to a particle size distribution and a water-cement ratio chosen. Three different mechanisms; nucleation and growth, phase boundary reaction and diffusion; controlled the evolution of hydration of C 3 S. At the start of the hydration process there are two phases: C 3 S and water. After hydration, we have fourth phases witch represent three solid phases (C 3 S, C-S-H, and CH) and the porosity. The material properties of the three solid phases adopted for the calculation are given in table1. The homogenisation process is made on a microstructure with w/c =.36. The diameter of particles varies from.4 to 4 µm and the total number was Fig.4 shows the mesh of 3D image at early and later age of C 3 S in a computational volume of 1 x 1 x 1 µm. C 3 S CH CSH Porosity E (GPa) ν [-] Table 1: Intrinsic elastic properties of anhydrated and hydrated phases [5]. 66

5 C 3 S C-S-H CH porosity Figure 4: mesh of the microstructure, initial (left; α =.12), right (α =.8). The estimation of effective properties of heterogeneous materials is made through the submission of a percolated specimen to periodic boundary conditions. For each step of hydration, the Young s modulus versus the degree of hydration is determined (Fig.5). A preliminary computation performed under kinematic and static uniform boundary conditions showed that computational volume is closed to the RVE. 3 Young's modulus [GPa] unpercolated percolated Degree of hydration [-] Figure 5: Young s modulus, un/percolated microstructure, under KBC Numerical evaluation of Autogenous shrinkage of hydrating C 3 S paste To be fully predictive, a numerical model has to depend as little as possible on experimental data. For this reason, the calculation of autogenous shrinkage by numerical techniques was done without using any information from experiment except the intrinsic elastic properties of phases taken from the literature. 67

6 By knowing - at each step of hydration- the pore structure (pore volume and pore size distribution) of the hydrating C 3 S paste (Fig. 6) and the evolution of volume fraction of liquid and gas, the critical radius (r c ) of pores at the liquid-gas interface is then calculated at each degree of hydration. The capillary pressure in the paste was computed by using Laplace law (Eq.1). Then, uniform hydrostatic macroscopic stress was calculated (Eq.2) which corresponds to the calculated capillary pressure weighted by the total porosity is applied on the outer boundaries of the computational volume. The autogenous deformation is then computed as the average hydrostatic apparent strain. Even this type of loading and without the effect of creep, the obtained results (Fig. 7) are qualitatively and quantitatively in good agreement with experimental data of ordinary Portland cement. 2σ p = cos θ (1) rc Where p [Pa] the capillary depression, σ [N.m -1 ] is the surface tension of water, θ [rad] is the wetting angle of the solid with water.θ = and σ =.73 N/m [1]. = p φ : is the total porosity for a given degree of hydration. (2) volume fraction of pores deg =.29 deg =.4 deg = R(µm) Sutogenous deformation [µm/m] Time [h] numerical experimental Figure 6: Simulated pore size distribution of C3S paste for various hydration degrees Figure 7: Numerical and experimental results for autogenous shrinkage (W/C =.36). 4. CONCLUSION Despite the fact the numerical simulation was performed on a hydrating C3S paste and the overall deformation was supposed uniform at the level of RVE, the numerical results are in good agreement with the experimental ones. These preliminary results are encouraging to pursue this work in order to predict correctly the autogenous shrinkage. In the further work, the capillary depression will be applied as a uniform stress applied just in the interface between liquid and gas that means in the pores starting to be empty of water. 68

7 REFERENCES [1] Hua, C., Acker, P. Ehrlacher, A., [1995], 'Analyses and models of the autogenous shrinkage of hardening cement paste'. Cement and Concrete Research, Vol.25, No.7, pp [2] Koenders, E., Van Breugel, K., [1997], 'Numerical modelling of autogenous shrinkage of hardening cement paste'. Cement and Concrete Research vol. 27, n 1, p [3] Bishnoi, S. and Scrivener, K., ' Micro-Structural Modelling of Cementitious materials using Continuum Approach', ICC, 27. [4] Tazawa, E.I., Miyazawa, S. [1995] 'Influence of cement and admixture on autogenous shrinkage of cement paste'. Cement and Concrete Research vol. 25, n 2, p [5] Constantinides, G., Ulm,F., [24]' The effect of two types of C-S-H on the elasticity of cement-based materials: Results from nanoindentation and micromechanical modeling'. Cement and Concrete Research vol. 34, p [6] P. Navi, and C. Pignat, "Simulation of cement hydration and the connectivity of the capillary pore space", Advances in Cement Based Materials, Vol. 4, 1996, pp