Numerical simulation and fractal analysis of mesoscopic scale failure in shale using digital images

Shale rock formations often contain calcite, which is a mineral that plays an important role in the failure of shale and in fracturing the reservoir volume. This study uses digital images to characterise the mesoscopic-scale non-uniformity of shale resulting from the shape, size and distribution of calcite in the shale. The geometry of the calcite is mapped to a finite element mesh based on the meso-scale structure of the rock. The numerical failure analysis model RFPA2D-DIP, which can accurately represent the meso-scale structure of shale, is used to simulate uniaxial compression. The influence of the meso-scale structure on the compressive strength and the failure process under various loading conditions are studied. The simulation results show that the meso-scale structure has an important influence on the compressive strength and the ultimate failure mode of samples loaded in various directions α. Furthermore, the results show that the compressive strength varies significantly with the direction of the load, indicating anisotropy. Depending on the direction, the failure mode can take the form of an inverted V (α=0°, 30°, 45°), an inverted Z (α=15°), a line (α=75°), or a V (α=60°, 90°). The spatial distribution of the acoustic emissions (AE) we observed is similar to those observed in macroscopic failure modes. The fractal dimension (D) of the shale fractures under various loading conditions is calculated using the box-counting method. The fractal dimension is an effective indicator of the failure mode. The value of D corresponding to the various failure modes is as follows: for the inverted Z the maximum value is 1.688016, for the line the minimum value is 1.481904, and for both the inverted V and the V, the value is between 1.688016 and 1.481904. Therefore, the failure mode is more complex for larger values of D.