  Geologic shear fractures such as faults and slip surfaces involve marked
friction along the discontinuities as they are subjected to significant
confining pressures. This friction plays a critical role in the growth of these
shear fractures, as revealed by the fracture mechanics theory of Palmer and
Rice decades ago. In this paper, we develop a novel phase-field model of shear
fracture in pressure-sensitive geomaterials, honoring the role of friction in
the fracture propagation mechanism. Building on a recently proposed phase-field
method for frictional interfaces, we formulate a set of governing equations for
different contact conditions (or lack thereof) in which frictional energy
dissipation emerges in the crack driving force during slip. We then derive the
degradation function and the threshold fracture energy of the phase-field model
such that the stress-strain behavior is insensitive to the length parameter for
phase-field regularization. This derivation procedure extends a methodology
used in recent phase-field models of cohesive tensile fracture to shear
fracture in frictional materials in which peak and residual strengths coexist
and evolve by confining pressure. The resulting phase-field formulation is
demonstrably consistent with the theory of Palmer and Rice. Numerical examples
showcase that the proposed phase-field model is a physically sound and
numerically efficient method for simulating shear fracture processes in
geologic materials, such as faulting and slip surface growth.
