  A three-dimensional Multiphysics Lattice Discrete Particle Model (M-LDPM)
framework is formulated to investigate the fracture permeability behavior of
shale. The framework features a dual lattice system mimicking the mesostructure
of the material and simulates coupled mechanical and flow behavior. The
mechanical lattice model simulates the granular internal structure of shale and
describes heterogeneous deformation by means of discrete compatibility and
equilibrium equations. The network of flow lattice elements constitutes a dual
graph of the mechanical lattice system. A discrete formulation of mass balance
for the flow elements is formulated to model fluid flow along cracks. The
overall computational framework is implemented with a mixed explicit-implicit
integration scheme and a staggered coupling method that makes use of the dual
lattice topology enabling the seamless two-way coupling of the mechanical and
flow behaviors. The proposed model is used for the computational analysis of
shale fracture permeability behavior by simulating triaxial direct shear tests
on Marcellus shale specimens under various confining pressures. The simulated
mechanical response is calibrated against the experimental data, and the
predicted permeability values are also compared with the experimental
measurements. Furthermore, the paper presents the scaling analysis of both the
mechanical response and permeability measurements based on simulations
performed on geometrically similar specimens with increasing size. The
simulated stress-strain curves show a significant size effect in the post-peak
due to the presence of localized fractures. The scaling analysis of
permeability measurements enables prediction of permeability for large
specimens by extrapolating the numerical results of small ones.
