Relating unsaturated electrical and hydraulic conductivity of cement-based materials

TL;DR

This paper investigates the relationship between electrical and hydraulic conductivity in cement-based materials, proposing models to predict one from the other, which could improve durability assessments when direct hydraulic measurements are difficult.

Contribution

It develops analytical models linking electrical and hydraulic conductivity using a van Genuchten-Mualem framework, enabling predictions of one property from the other in cement-based materials.

Findings

Models accurately predict $K$ from $\sigma_b$ and vice versa.

Proposed simplified model highlights key microstructural factors affecting conductivity.

Analytical expressions facilitate durability evaluation without extensive hydraulic testing.

Abstract

Unsaturated hydraulic ($K$) and electrical ($\sigma_b$) 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 $\sigma_b$ is rather straight forward. Descriptions of the relationship between $\sigma_b$ 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 $\sigma_b$ -- expressions for diffusivity $D$ are also provided. We then develop analytical expressions relating $K$ and $\sigma_b$ using these models. It is then shown that $K = K(\sigma_b)$ and $\sigma_b = \sigma_b(K)$ 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 $\sigma_b$.