Stress distribution and failure in anisotropic rock near a bend on a weak fault

Abstract

Large transform faults, thin‐skinned thrust faults, and listric normal faults often contain restraining and releasing bends that can alter the state of stress in the adjacent crust during faulting episodes. Crustal rock commonly has anisotropic mechanical properties due to the presence of sedimentary layering, subsidiary fractures and faults, schistosity, or other foliation. We present an analytical solution for the stress distribution in anisotropic rock produced by sliding on a wavy, frictionless surface. The frictionless surface represents the limiting case of a weak fault. The fault shape treated is either a sinusoid, or a periodic array of isolated restraining and releasing bends. The rheological behavior of the rock is that of an incompressible linear viscous fluid with an orthotropic anisotropy characterized by a greater viscosity for shortening and extension than for shear in the principal directions of anisotropy. Our results illustrate that stress and flow associated with a bend in a fault will extend to much greater distances from the fault when the medium is anisotropic. The magnitude of the stress perturbation increases with degree of anisotropy and decreases with radius of curvature of the fault surface. Principal stress directions tend to align parallel to the principal directions of anisotropy except in the immediate region of the fault bend. Mean stress and maximum shear stress magnitudes vary along the fault in a cellular manner, with multiple maxima near a bend. Stress concentrations emanate from the bend and are elongate in directions parallel to the principal directions of anisotropy. For isotropic rock, locations and orientations of shear failure near restraining bends are distinctly different from those near releasing bends. In contrast, with application of an anisotropic failure criterion, as the magnitude of anisotropy increases, the patterns of shear failure at a restraining and a releasing bend become increasingly similar. The model may help explain field observations from dip‐slip and strike‐slip regimes that indicate a complex stress history and local stress reorientation adjacent to a bend in a fault.