Pressure-dependent joint elastic–electrical properties in brine-saturated artificial sandstones with aligned penny-shaped cracks—Part II: Theoretical modelling

Abstract

SUMMARY Cracks are widely existing in natural rocks, and the effects of cracks on the elastic and electrical properties of rocks make it possible to establish appropriate joint interpretation to detect the crack characteristics more accurately. However, the premise is the knowledge of the joint elastic–electrical properties of cracked rocks. We aim to study theoretically the pressure-dependent joint elastic–electrical properties of porous rocks with aligned penny-shaped cracks. To do so, we developed a model describing the deformation of cracks in a transversely isotropic (TI) background with stress, and combined with existing models for the anisotropic elastic and electrical properties of TI rocks with aligned cracks. The impacts of crack deformation on the anisotropic elastic and electrical properties of cracked rocks, and the effects of crack porosity and crack aspect ratio on the pressure-dependent joint elastic–electrical properties were then studied. We showed that the modelling results compared satisfactorily with experimental data. The modelling results demonstrated that the crack compaction with stress reduced the elastic and electrical anisotropy. We also found that the anisotropic elastic wave velocities and electrical conductivities of cracked rocks exhibited approximately negative linear correlations when linked by the effective stress, and the slopes and intercepts of the linear relationships were shown to be systematically dependent on the porosity and aspect ratio of the aligned cracks. The above knowledge of the pressure-dependent joint elastic–electrical properties of TI rocks with aligned cracks can be employed for quantitative interpretation of the joint elastic and electrical exploration data.