An Elastic Stress–Strain Relationship for Porous Rock Under Anisotropic Stress Conditions

A stress–strain relationship within porous rock under anisotropic stress conditions is required for modeling coupled hydromechanical processes associated with a number of practical applications. In this study, a three-dimensional stress–strain relationship is proposed for porous rock under elastic and anisotropic stress conditions. This relationship is a macroscopic-scale approximation that uses a natural-strain-based Hooke’s law to describe deformation within a fraction of pores and an engineering-strain-based Hooke’s law to describe deformation within the other part. This new relationship is evaluated using data from a number of uniaxial and triaxial tests published in the literature. Based on this new stress–strain relationship, we also develop constitutive relationships among stress, strain, and related stress-dependent hydraulic/mechanical properties (such as compressibility, shear modulus, and porosity). These relationships are demonstrated to be consistent with experimental observations.