Numerical Test Study of the Microscale Failure Modes and Fractal Analysis of Lower Cambrian Shale Based on Digital Images

To reveal the effect of confining pressure on the mechanical properties and rupture modes of quartz-bearing shale, the shale core of the no. 3 block of Fenggang, Guizhou Province, China, was analyzed by nuclear magnetic resonance, polarized light microscope thin section observation and identification, and core X-ray whole-rock minerals diffraction analysis to determine the distribution of shale minerals in the Niutitang Formation. On the microscale, based on digital image processing technology, this paper characterizes the nonuniformity of minerals in shale, a numerical model that can reflect the true microstructure of shale. Then, the failure process of shale under different confining pressures was simulated. The results show that when the shale is loaded with vertical displacement under different confining pressures, the compressive strength and elastic modulus of the sample change significantly. The failure mode can be roughly divided into three types: the inverted V-shaped (0 MPa, 2 MPa, and 4 MPa), V-shaped (6 MPa and 8 MPa), and inverted Z-shaped (10 MPa). Since the development of fractal theory provides a new space for studying the damage and fracture of rocks, the damage evolution and failure process of shale can also be regarded as the fractal process of cracks, in which the fractal dimension is the core parameter. The calculation is different under different stress levels. The fractal dimension under the condition of confining pressure shows that the value of the fractal dimension is greatly affected by the effect of confining pressure. When the fractal dimension is higher, the fracture mode is more complicated, and the internal damage degree is more serious. The research results provide important theoretical guidance for shale gas fracturing production.