Shale, like many other sedimentary rocks, is typically heterogeneous and anisotropic with partial alignment of anisotropic clay minerals and naturally formed bedding planes. A numerical method based on the lattice discrete particle model was formulated. Material anisotropy is introduced through an approximated geometric description of shale internal structure and a representation of material properties variation. Calibration was performed by comparing the numerical simulation results with experimental data. A series of simulated experiments, including elastic analysis, Brazilian tensile test and unconfined compression test, were demonstrated. Simulation results shows that the dependence of tested strength and failure modes on sample orientation can be captured successfully. This work will pave the way for the development of reliable hydraulic fracturing models that appropriately account for the mechanical behaviors of heterogeneous and anisotropic shale.
With the rapid growth of the shale gas/oil industry, especially the development of hydraulic fracturing technique, the study to promote deep understanding of the mechanical properties of shale-like rocks is becoming more important. Gas/Oil shale, described as organic rich and fine grained , exhibit significant mechanical anisotropy and heterogeneity due to the organized distribution of platy clay minerals and compliant organic materials . Developing adequate numerical models to capture the heterogeneity and anisotropy of shale leads to a better understanding of the influence of material properties on induced fracture initiation, propagation and fracturing treatment, and therefore provides a powerful tool to predict and optimize the fracturing process.
In a broader sense, the available numerical methods can be classified into continuum- and discontinuum- based methods [3,4]. The continuum approaches, such as finite element method (FEM), finite difference method (FDM) and boundary element method (BEM), treats the computational domain as a single continuous body and captures material failure behaviors through common techniques such as plastic softening and damage models. As the lack of an internal length scale, the standard continuum approaches cannot capture localization of failure, and manifests itself in mesh sensitivity [3,5]. These shortcomings can be overcame by introducing micro-structural effects with second gradient damage models, non-local models  etc. On the contrary, the discontinuum approaches, represented by discrete element method (DEM), treat the materials as an assembly of separate blocks or particles, and is capable of incorporating the length scale automatically. The methods of modeling material anisotropy are often classified into smeared approach and discrete approach . The smeared approach utilizes a smeared representation in which the anisotropy is introduced at the level of constitutive laws by varying material parameters as a function of the relative orientation between elements and the bedding plane orientation . The discrete approach utilizes a discrete representation in which the anisotropy is introduced by a geometric description of layers or joints with varying material parameters [6,8,9]. The discrete approach offers unique advantages when the extended loss of continuity inside the material makes continuum constitutive models inappropriate .