Stress-dependence of elastic properties of rock containing finite cracks with contacting surfaces

Abstract

In the present study we examine a modelling of stress-dependence of elastic properties of rocks. We develop a micromechanical theory of changes of the elastic moduli with external loading based on the crack stiffening by contacting asperities. We utilize exact solutions existent for annular crack, welded-area and Hertz contacts. The proposed theory is then used in analysis of experimental results. Parameters of the rock sample recovered from the pressure dependencies of bulk and shear moduli are consistent with each other and physically reasonable. Presented results are based on several simplified assumptions but the theory is ready to incorporate further complexifications (such as contacts interaction and inclusions’ size distribution).