Electrical resistivity of three-phase cracked rock-soil medium and its anisotropic changes caused by crack changes

摘要

Electrical resistivity of sedimentary rock-soil is highly variable and governed mainly by a wide range of properties including resistivities of both solid matrix and fluid, cracks or pores, fluid saturation, and crack fabric (e.g. crack shape and alignment). An anisotropic, three-phase, effective medium resistivity model is proposed in this article to describe the resistivity of cracked rock-soil medium of sediments in macroscale. The resistivities of both solid matrix and fluid are assumed to be isotropic. Anisotropic features are therefore caused by cracks. The model permits both solid and fluid phases to have arbitrary range of resistivity. We derive the differential form between resistivity changes and crack changes. Expressions of the volumetric sensitivity and saturation sensitivity are obtained. An amplification matrix is defined to describe the anisotropic changes in resistivity. The three electrical principle axes have different volumetric sensitivity. Therefore, the resistivity shows anisotropic changes when the cracks change. For water-bearing rock and soil medium, the minimum electrical axis is most sensitive to crack changes. However, the anisotropic changes of anhydrous rocks are not obvious. Apparent resistivity has been continuously monitored at fixed stations in China for more than 50?years, using Schlumberger arrays. Apparent resistivity monitored in the direction perpendicular or nearly perpendicular to the maximum principal stress axis has recorded the maximum magnitude of changes before earthquakes. While the magnitude is minimum when apparent resistivity is monitored in the direction parallel or sub-parallel to the axis. There is an angle difference of π / 2 between the resistivity changes and the apparent resistivity changes for Schlumberger array. The analytic results of anisotropic changes based on the model agree with the field monitoring results.