Relating unsaturated electrical and hydraulic conductivity of cement-based materials

Unsaturated hydraulic (K) and electrical (σb) conductivity are often considered durability indicators of cement-based materials. However, K is difficult to measure experimentally. This is due to the large pressure requirements at low degrees of saturation resulting from the fine pore-size distribution of cement-based materials. As a result, the commonly-used analytical models, requiring calibration of K from experimental data, are often inaccurate at low degrees of saturation. On the other hand, measuring σb is rather straight forward. Descriptions of the relationship between σb and K may therefore be particularly valuable when K is required. In this work, we use experimental data from previous works to determine the feasibility of models employing a van Genuchten-Mualem based framework to predict K and σb – expressions for diffusivity D are also provided. We then develop analytical expressions relating K and σb using these models. It is then shown that K = K(σb) and σb = σb(K) may be determined when either parameter is fully described. Lastly, we propose a simplified model and discuss the roles of pore-size distribution, saturation, pore connectivity and tortuosity in characterizing the relationship between K and σb.