Reliable prediction of fracture process in shale-gas rocks remains one of the most significant challenges for establishing sustained economic oil and gas production. This paper presents a modeling framework for simulation of crack propagation in heterogeneous shale rocks. The framework is on the basis of a variational approach, consistent with Griffith’s theory. The modeling framework is used to reproduce the fracture propagation process in shale rock samples under standard Brazilian disk test conditions. Data collected from the experiments are employed to determine the testing specimens’ tensile strength and fracture toughness. To incorporate the effects of shale formation heterogeneity in the simulation of crack paths, fracture properties of the specimens are defined as spatially random fields. A computational strategy on the basis of stochastic finite element theory is developed that allows to incorporate the effects of heterogeneity of shale rocks on the fracture evolution. A parametric study has been carried out to better understand how anisotropy and heterogeneity of the mechanical properties affect both direction of cracks and rock strength.

A simplified multiscale damage model is proposed for the transversely isotropic shale rocks under tensile loading. In this framework, the multiscale representations for the shale rocks are presented by introducing the microcrack-weakened equivalent solid with hierarchical microstructures, whose transversely isotropic properties are obtained by performing multilevel homogenization procedures. To simplify the calculation process for the damage-induced properties, the equivalent isotropic medium is attained by applying the Voigt–Reuss–Hill averaging process to the transversely isotropic solid. Subsequently, the microcrack-induced inelastic compliances are approximately derived in terms of microcrack opening displacements in the equivalent isotropic medium of the shale rock under tensile loading. The sizes and orientations of microcracks are taken as random variables. Both stationary and evolutionary damage models are considered. Microcrack kinetic equations are characterized through the use of a fracture mechanics-based stability criterion and microcrack geometry within a representative volume element. Numerical examples including experimental validations and comparisons with existing micromechanical models are presented to verify the proposed multiscale damage model. Finally, the influences of the silt inclusions and porosity on the material intrinsic and damage-induced properties are discussed.