A new model for analyzing the effect of fractures on triaxial deformation

Abstract

Rock is porous, with a connected network of cracks and pores. The static and dynamic behaviors of a rock sample under load depend on both the solid mineral matrix and the porous phase. In general, the configuration of the pore phase is complex; thus most studies on the effect of the porous phase on rock deformation are conducted numerically and theoretical analyses of the constitutive relations are scarce. We have studied rock deformation under axially-symmetric loading by analyzing a model where the pore phase is approximated by rough planes, randomly spaced and oriented, extending through the sample. The roughness is caused by asperities, all with the same tip radii, but having heights h with a probability density distribution given by the negative exponential e-h/λ where λ is a length parameter. Slip at contacts under local shear stress is resisted by simple Coulomb friction, with friction coefficient f. Both static and dynamic deformation were analyzed. The effect of porosity on deformation for both modes was found to be given by the non-dimensional parameter λαj, where αj is the total area of the fault planes per unit volume. We demonstrate that stress-induced microfracturing begins as randomly oriented microslip throughout the sample. As axial load increases, microslip occurs along preferred orientations and locations, which finally leads to deformation on a single fault. The model was found to fault under static loading conditions---the axial load at faulting and the angle of the “fracture” plane agree with values of those parameters given by Coulomb’s theory of fracture. Dynamic moduli and Poisson’s ratio are found to be virtually elastic and independent of the friction coefficient acting at contacts. The attenuation for uniaxial dynamic loading is a strong function of the friction coefficient and increases linearly with strain amplitude, in agreement with laboratory measurements.