A rheological model for fractured rock

We propose a rheological model for rock deforming in plane strain by slip on two sets of intersecting, weak surfaces. We assume that the normals to the surfaces lie within the deformation plane, and that the surfaces are unbounded and experience noninterfering slip. Where slip rate is linearly proportional to resolved shear stress, the rock behaves as an incompressible, anisotropic fluid. For the simplest case - where the intrinsic slip behavior along the two sets is identical - the principal axes of anisotropy are parallel and perpendicular to the bisectors of the intersurface angles. For deformation rates parallel and perpendicular to these axes, three behaviors may occur depending on the magnitude of the intersurface angle (2φ). If 0° ≤ 2φ < 45° or 135° < 2φ ≤ 180° the rock is weaker in shear than in shortening or extension. If 45° < 2⇌ < 135° it is stronger in shear than in shortening or extension. Finally, if 2φ = 45° or 135°, the rock behaves isotropically. As applications, we use the derived constitutive relations to examine the response of a fractured layer to two commonly modeled types of folding: forced folding above a vertical fault and buckling of a layer embedded in an isotropic medium undergoing shortening.