Multi-scale discrete modeling of the mechanical behavior of black shale

With the rapid development of hydraulic fracturing technique, the study to promote deep understanding of the mechanical properties of black shale is becoming more important. Of particular interest is the development of adequate numerical model to capture the mechanical behavior of shales, in order to accurately predict and optimize the fracturing process. Black shale is highly complex and heterogeneous material that can be characterized by several levels of hierarchy. In this work, a micromechanical framework is formulated to capture the mechanical behavior of black shale at the micro-/meso-scopic levels where shale is characterized by partial alignment of anisotropic clay minerals and naturally formed bedding planes. The framework is based on the lattice discrete particle model and is proposed to simulate material heterogeneity and anisotropy. Material anisotropy is introduced through a direct, although approximated, geometric description of shale internal structure that includes representation of material property variation with orientation at micro-scale and explicit simulation of bedding planes at meso-scale. Calibration and validation of the model is pursued by carrying out the numerical simulation of various experimental data, including the ones relevant to elastic properties, splitting tensile strength and unconfined compression test. The simulation results show that the dependence of tested stiffness, strength and failure modes on loading orientation can be captured successfully. To enable macroscale simulations, a mathematical homogenization approach is applied to the upscaling of the proposed micromechanical model. This work will pave the way for the development of reliable hydraulic fracturing models that appropriately account for the correct mechanical behaviors of black shale