LIQUID WATER PERMEABILITY OF PARTIALLY SATURATED CEMENT PASTE ASSESSED BY DEM-BASED METHODOLOGY

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1 121 Proc. Int. Symp. Brittle Matrix Composites 11 A.M.Brandt, J.Olek, M.A.Glinicki, C.K.Y.Leung, J.Lis, eds. Warsaw, September 28-30, 2015 Institute of Fundamental Technological Research LIQUID WATER PERMEABILITY OF PARTIALLY SATURATED CEMENT PASTE ASSESSED BY DEM-BASED METHODOLOGY Kai LI*, Piet STROEVEN, Martijn STROEVEN, Lambertus J. SLUYS Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg CN Delft, the Netherlands, * K.Li-1@tudelft.nl ABSTRACT Permeability of virtual cement seems to exceed experimental data by several orders of magnitude. The differences may actually not be that dramatic, since experimental samples are in practice not always fully saturated as generally assumed. This paper demonstrates that this has enormous effects on permeability. A numerical study is conducted on water permeability of partially saturated cement paste based on simulated microstructures. During drying, larger pores empty first according to the Kelvin-Laplace law, leading to a significant decline in water permeability. The results in terms of relative water permeability have been validated against lattice Boltzmann simulations and experimental data, respectively. A satisfactory agreement is found. Both the pore size distribution and pore connectivity are shown to have an important influence on the overall permeability. The effects of technological parameters, such as hydration age and water-to-cement ratio, have also been discussed. Keywords Cement paste, water permeability, water saturation degree, pore network, DEM, particle simulation INTRODUCTION The durability of concrete depends on its ability to prevent the ingress of aggressive agents, such as carbon dioxide (CO 2 ) or chlorides. Permeability, defined as the movement of the agent (liquid or gas) through the porous cement paste under an applied pressure, is therefore the most important property of concrete governing its long-term behaviour [1]. However, permeability values obtained from numerical analyses differ significantly from values in experimental tests. The origin for those differences could be found in the commonly neglected humidity level. Although the specimens used for these experiments were assumed to be fully saturated in order to compare them with numerical experiments, the reality is that humidity fluctuations in the cement paste are unavoidable. Full saturation is difficult if not virtually impossible to establish and maintain. In fact, air pockets are inherent features and have a significant effect on the local transport properties as will demonstrated. Thus, the saturation degree should not be ignored when measuring the intrinsic permeability especially when comparing numerical results with experimental ones. In fact, a series of publications deal with experimental studies on the impact of the degree of saturation on permeability [2-6]. Hereby, the degree of water saturation is defined as the volume fraction of the pores filled with water. Unfortunately, experimental approaches are usually laborious, time-consuming and thus expensive. The modelling of fluid flow through a realistic virtual representation of the cement

2 122 Kai LI, Piet STROEVEN, Martijn STROEVEN, Lambertus J. SLUYS paste s microstructure can therefore be considered an attractive alternative. For that purpose, network models [7-9] and discrete models [10-12] can be used. The latter, voxel-based ones pursue solving the equations of flow by numerical methods such as the lattice Boltzmann method. Although the lattice Boltzmann method became recently quite popular due to its low demand for computing resources, the actual pore structure is not considered, which can be considered a significant disadvantage. The permeability by methods in the first category is determined from a network of cylindrical tubes that are derived from the underlying actual pore network. Each tube represents a local pore. Next, the equations of laminar flow inside this tube network are solved to obtain the intrinsic permeability. Network models heavily depend on the proper description of the pore structure, which determines the permeability. Since we are interested in the relationship between pore structure and permeability, this method is selected in this paper. Pignat et al. [7], Ye et al. [9] and Nghi et al. [13] have conducted earlier studies following this approach. However, these earlier studies only addressed the case of fully saturated porosity conditions and cannot be compared to waterbased experiments with saturation levels lower than 100%. In this paper, the methodology is outlined for simulating the permeability of a partially saturated pore structure of hydrated cement. Discrete element method (DEM) is used instead of random sequential addition (RSA) to realistically distribute the individual cement grains in the container. For more details on DEM versus RSA, see [14-16]. The pore microstructure is obtained after hydration simulation. Thereupon, pore characteristics in the fully and partly saturated specimens are assessed by a novel methodology and associated water permeability values can be determined. As the saturation degree is reduced, the calculated water permeability decreases significantly, spanning the major part of the experimental range of data. Our simulation results, in terms of relative permeability (defined as the ratio of intrinsic water permeability at a certain degree of saturation to the intrinsic water permeability measured in the fully saturated state), are compared with estimates obtained by a lattice Boltzmann approach and with physical experiments. A satisfactory agreement is observed, validating the presented methodology. Pore size distribution and pore connectivity are investigated to explain the changes of permeability data at various degrees of saturation. Moreover, the influences of hydration age and water-to-cement ratio (w/c) on the estimated permeability are also discussed. METHODOLOGY The complete methodology of our computational technique consists of four stages. In the first stage, cement grains packing is modelled by a DEM simulation. Then, the packed structure is an input for hydration simulation by XIPKM (extended Integrated Particle Kinetics Method). Once the hydration simulation is done, porosimetry of hydrated paste can be assessed by DRaMuTS (Double Random Multiple Tree Structuring system) and SVM (Star Volume Measuring). Finally, the tube network model is used for permeability estimation. Interested readers can find all relevant details in [13]. The method as described in [13] only applies to fully saturated specimens. Therefore, a new empty algorithm for modelling the microstructure of a partially saturated paste and thus to calculate permeability has been developed and will be outlined in this paper. In general, the pore space of mature paste for permeability estimation is assumed 100% water-filled. This hypothesis is equivalent to the ideal underwater curing whereby the sample is supposedly fully saturated, and thus the water saturation degree is 100%. As the relative humidity declines, the structure starts loosing water by evaporation from the pores. An empty pore acts as a barrier for water transport; this phenomenon is mimicked in our simulation by positioning solid objects in the presumed

3 Liquid water permeability of partially saturated cement paste assessed empty pores, as illustrated in Fig. 1. According to the Kelvin-Laplace equation [17], larger pores easier loose water and become empty first. Thus, the empty algorithm starts from the largest pores in our simulation. Once the pore structure is determined, water is sequentially removed by positioning solid sphere at the calculated centre of the pore to represent the partially saturated state. (a) (b) (c) Fig. 1. Illustration of the empty algorithm in 2D; (a) fully saturated state; (b) positioning of a solid circle in water-filled pore; (c) partially saturated sate. The position and size of the virtual red circle (in 3D: solid sphere) is obtained by DRaMuTS. A network structure consisting of cylindrical tubes was thereupon constructed to represent the pore channels. The main trunks represent the direct paths through pore space from the bottom to the top of the sample. In contrast to isolated paths and dead-end branches, the main trunks play a key role in the transport process. They can be extracted from the system and then used for permeability calculations, while the other pores are neglected. The diameters of the tubes along the main trunks were taken equal to the size of the underlying pore structure. For the estimation of the pore size, a star volume method (SVM) was used. A pressure gradient is applied between inlet and outlet nodes located at the bottom and top surfaces of the specimen. The intrinsic permeability ĸ, in m 2, can be calculated by Darcy s equation [18], (1)

4 124 Kai LI, Piet STROEVEN, Martijn STROEVEN, Lambertus J. SLUYS where L (m) and A (m 2 ) are the length and cross sectional area of a test sample through which a fluid flow Q (m 3 /s) is driven by applying an external pressure gradient P (Pa). The parameter µ (Pa s) represents the dynamic viscosity of the fluid. The influence of the actual shape of the pores on conductivity is explicitly taken care of, whereby reference [13] gives all details. Virtual cement pastes were generated in a cube (100 µm in size) with an initial w/c of 0.4. The phase composition of the cement clinker was 61% C 3 S, 20% C 2 S, 8% C 3 A, 11% C 4 AF by volume. The Rosin Rammler function represented the particle size distribution, ranging from 1 to 30 µm. The samples were at an age of 28 days subjected to the earlier sketched methodology. The results will be discussed in the next section. RESULTS AND DISCUSSION Evolution of water permeability with the degree of saturation As a first result, the evolution of the measured intrinsic water permeability with the degree of saturation obtained by our numerical simulation approach is shown in Fig. 2. To avoid systematic bias due to the computation, multiple structures (8 samples) were analysed. The standard deviations of our simulation data are also displayed in Fig. 2. As the small standard deviation suggests, reliable results at any given saturation degree can be obtained from a single structure. In general, as the water saturation degree decreases, the number of connected pores filled by water declines, resulting in a reduction of the available paths for water transport in the system. Hence, the system is de-percolating. Moreover, the large pores dry-up first, additionally contributing to a lower permeability. When the water saturation degree reaches a value around 0.25, the remaining fully water-filled pores is mostly disconnected, thus, leading to a permeability approaching to zero. Although a limited number of experimental studies on liquid water permeability of partially saturated cement paste are available, Kameche et al. [19] recently published a paper in this field that is focusing on concrete. This is the latest and according to our knowledge probably also the only available data dealing with water permeability in partially saturated cementitious samples. Even though the experiments concern concrete, the tendency should be similar between concrete and cement paste since both belong to cement-based materials. The relative permeability (instead of intrinsic permeability) allow direct comparison between different cementitious materials, such as concrete and cement paste in this case. In addition to the experimental data, the permeability results of cement paste from the 3D Lattice- Boltzmann (LB) modelling by Zalzale et al. [17] are also used for comparison reasons. The outcomes are shown in Fig. 3. A satisfactory agreement is observed between our simulation data and both other results, validating our methodology.

5 Liquid water permeability of partially saturated cement paste assessed Fig. 2. Standard deviation of water permeability data pertaining to virtual cement pastes. Fig. 3. Validation of our simulation results by comparing them with experimental data and the values obtained by the LB method. Porosimetry analysis Pore size distribution (PoSD) and connected pore fraction are two of the key factors affecting the transport process in cementitious materials. In this paper, these two parameters were investigated to link the variations in water permeability of cement paste at five different water saturation levels (100%, 75%, 61%, 54%, 39%) to its internal structural changes. In Fig. 4, we can see that the volume-based pore size distribution curve of water-filled pores shifts to the left as the capillary water saturation decreases. Note that empty pores are no longer considered on the pore size distribution estimation. As water was progressively removed from the largest pores according to the Kelvin-Laplace equation, this causes the PoSD to shift to the left for lower degrees of saturation. Fig. 5 reveals an almost linear decline in median pore size with diminishing degree of water saturation in the pores. The calculated median pore size

6 126 Kai LI, Piet STROEVEN, Martijn STROEVEN, Lambertus J. SLUYS is also volume-based instead of number-based, as already shown in Fig. 4. So, the PoSD of water filled pores and hence its related permeability is very sensitive to the degree of water saturation. The other important parameter, pore connectivity in mature cement paste, was studied as well. DRaMuTS is based on a system of randomly distributed points, so the accuracy of the method depends strongly on the number of points. A large number of points increases accuracy, but makes the computations more expensive. Although the PoSD also depends on these numbers, the sensitivity is larger with structure-sensitive parameters such as the connectivity. Therefore, a sensitivity analysis of the connected pore fraction (= number of pores directly related to the pore path connecting the top and bottom of the specimen divided by the total number of pores) at various degrees of water saturation was carried out first. The results are plotted in Fig. 6. It shows the connected pore fraction to increase sharply as the number of points distributed in the remaining water-filled pores increases. The curves seem to gradually approach a plateau value indicating the measurement to approach the real value. The number of points used in the remainder of the examples was set to 10 5 to limit the computation time without a significant loss of accuracy. Fig. 4. Pore size distribution of samples at various degrees of water saturation. Fig. 5. Almost linear reduction in volume-based median pore size with declining degree of water saturation in the capillary pore network structure.

7 Liquid water permeability of partially saturated cement paste assessed Fig. 6. Sensitivity analysis of connected pore fraction by the number of measurement points distributed in the pore volume for a variety of water saturation degrees. Fig. 7. Connected pore fraction as a function of capillary water saturation. The connected pore fraction as a function of the capillary water saturation is plotted in Fig. 7. With a decreasing capillary water saturation, the initially fully water-filled pores gradually become empty, leading to a reduced fraction of connected pores. A smaller number of connected pores involves a lower water permeability. The reductions in pore size and pore connectivity explain the structural changes of cement paste under different water saturation degrees. Both factors play a key role in interpreting the decrease of water permeability at lower saturation degrees. Influence of technological parameters on permeability The influence of two technological parameters (hydration age and w/c) on permeability have been studied as well. Firstly, specimens at four different hydration ages (3 days, 7 days, 28 days and 4 months) but identical w/c of 0.4 were selected to study the influence of this parameter on water permeability of samples with various degrees of water saturation. The results are plotted in Fig. 8. For the different hydration ages, a pattern of slightly curved almost parallel lines is

8 128 Kai LI, Piet STROEVEN, Martijn STROEVEN, Lambertus J. SLUYS obtained for water saturation versus intrinsic water permeability. This can easily be explained by the increasing density in the hydrate structure and as a result reduced pore space. The latter involves both smaller pores and more advanced pore depercolation, both leading to reduced permeability. Secondly, specimens with w/c = 0.3, 0.4 and 0.5 at 28 days of hydration were selected for the permeability analysis. The results are illustrated in Fig. 9. For different values of w/c, a pattern of slightly curved almost parallel lines is obtained for water saturation versus intrinsic water permeability. An increasing w/c actually means that the volume of cement in the container space is declining, leading to a lower packing density and thus to higher porosities. This, in turn, leads to an increased permeability. Fig. 8. Influence of hydration age on water permeability of partially saturated cement pastes. Fig. 9. Influence of w/c on water permeability of partially saturated cement pastes.

9 Liquid water permeability of partially saturated cement paste assessed CONCLUSIONS In this paper, a new methodology (XIPKM-DRaMuTS-SVM-Empty algorithm-tube network modelling) has been developed to determine the permeability of partially saturated pastes, reference [20] gives all details. It is found that the intrinsic water permeability strongly depends on the degree of water saturation. In general, water permeability reduces with decreasing water saturation. Pore size distribution and pore connectivity are investigated to understand the underlying modification related to pore structure. Specifically, large pores are blocked in the empty procedure leading to a leftwards shift of the pore size distribution curve. This also reduces the pore connectivity in the structures since the transport paths for water are blocked. Both factors result in lower permeability data. The effects on permeability of two technological parameters, i.e., hydration age and w/c, have been discussed as well. As hydration age increases, the structure of hydrated paste becomes denser since pore space is gradually filled up with hydration products. Therefore, the calculated permeability declines at prolonged hydration duration. An upward trend can be observed in the permeability curves by increasing w/c. This is because at higher w/c the density of the hydrate structure is reduced, yielding lager pore space for water transport, and thus higher permeability. Moreover, the curves almost remain parallel in Fig. 8 and Fig. 9 which is an interesting observation. The influence of the investigated parameters seems to just shift the curves to a certain extent. ACKNOWLEDGEMENTS The first author would like to thank the China Scholarship Council (CSC) for the financial support to this work. REFERENCES 1. Banthia, N., Biparva, A., Mindess, S., Permeability of concrete under stress. Cement and Concrete Research, 35, 2005, Villain, G., Baroghel-Bouny, V., Kounkou, C., Hua, C., Measuring the gas permeability as a function of saturation rate of concretes. French J. of Civil Engineering, 5, 2001, Abbas, A., Carcasses, M., Ollivier, J.P., Gas permeability of concrete in relation to its degree of saturation. Materials and Structures, 32, 1999, Baroghel-Bouny, V., Thiery, M., Wang, X., Modelling of isothermal coupled moisture-ion transport in cementitious materials. Cement and Concrete Research, 41, 2011, Sercombe, J., Vidal, R., Galle, C., Adenot, F., Experimental study of gas diffusion in cement paste. Cement and Concrete Research, 37, 2007, Monlouis-Bonnaire, J.P., Verdier, J., Perrin, B., Prediction of the relative permeability to gas flow of cement-based materials. Cement and Concrete Research, 34, 2004, Pignat, C., Navi, P., Scrivener, K.L., Simulation of cement paste microstructure hydration, pore space characterization and permeability determination. Materials and Structures, 38, 2005, Koster, M., Hannawald, J., Brameshuber, W., Simulation of water permeability and water vapour diffusion through hardened cement paste. Computational Mechanics, 37, 2006, Ye, G., Lura, P., Breugel, K.V., Modelling of water permeability in cementitious materials. Materials and Structures, 39, 2006,

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