  Phase-field modeling -- a continuous approach to discontinuities -- is
gaining popularity for simulating rock fractures due to its ability to handle
complex, discontinuous geometry without an explicit surface tracking algorithm.
None of the existing phase-field models, however, incorporates the impact of
surface roughness on the mechanical response of fractures -- such as elastic
deformability and shear-induced dilation -- despite the importance of this
behavior for subsurface systems. To fill this gap, here we introduce the first
framework for phase-field modeling of rough rock fractures. The framework
transforms a displacement-jump-based discrete constitutive model for
discontinuities into a strain-based continuous model, without any additional
parameter, and then casts it into a phase-field formulation for frictional
interfaces. We illustrate the framework by constructing a particular
phase-field form employing a rock joint model originally formulated for
discrete modeling. The results obtained by the new formulation show excellent
agreement with those of a well-established discrete method for a variety of
problems ranging from shearing of a single discontinuity to compression of
fractured rocks. It is further demonstrated that the phase-field formulation
can well simulate complex crack growth from rough discontinuities.
Consequently, our phase-field framework provides an unprecedented bridge
between a discrete constitutive model for rough discontinuities -- common in
rock mechanics -- and the continuous finite element method -- standard in
computational mechanics -- without any algorithm to explicitly represent
discontinuity geometry.
