Multiaxial response of a microcrack constitutive model for brittle rock

This paper describes a model that predicts the moduli for brittle rock loaded by compressive principal stresses. All inelastic deformation is assumed due to microcracks that open under local tensile stresses caused by small scale heterogeneities. For axisymmetric loading and an isotropic initial distribution of cracks, the model predicts that crack growth begins in the axial direction and expands to a cone of angle 12-15° as loading continues to peak stress. The macroscopic response evolves from isotropic to transversely isotropic and the elastic moduli decrease with ongoing deformation. For combined axisymmetric compression (a) and torsion (r), axial loading causes the damage surface in r vs. a space, separating stress states causing unloading from those that cause continued damage, to evolve from an ellipse to a surface with a sharp vertex at the current stress point.