Analytical Method for Evaluating Calcium Diffusion Coefficient of Partially Leached Cement Paste

Abstract

This paper aims at presenting an analytical method for evaluating the calcium diffusion coefficient of partially leached cement paste. The analytical method is developed based on a two-scale model of partially leached cement paste. On the first scale, the solid phase in partially leached cement paste is modeled as a two-phase composite material, composed of a matrix of calcium silicate hydrate (C─S─H) gel and inclusions of unhydrated cement and undissolved calcium hydroxide (CH) crystal. The relative calcium diffusion coefficient is derived analytically by the differential effective medium scheme. On the second scale, partially leached cement paste is treated as a system consisting of the solid phase and spheroidal capillary pores; the percolation behavior of capillary pores near the critical volume fraction is considered. In combination with percolation theory, the effective medium approach is modified to evaluate the calcium diffusion coefficient of partially leached cement paste. The depolarization factor is expressed in terms of the critical volume fraction of capillary pores, and the percolation exponents are calibrated from computer simulation data. Finally, the validity of the analytical method is verified with computer simulation data and experimental results collected from the literature. It is concluded that the proposed analytical method can predict the calcium diffusion coefficient of partially leached cement paste with reasonable accuracy.