## 3 Multi-Scale Numerical Modeling of Rock Failure Process under Compression
### Microscale Simulation
#### 3.1.2 Microscale Numerical Modeling Results  
The spatial distribution of shale minerals at the microscopic scale affects the crack initiation position, propagation path, and final failure pattern. Despite the small amount of pyrite, cracks tend to begin in the organic matter around pyrite. Pyrite has a decisive effect on where cracks emerge. The crack propagates easily along the organic lamina, and the distribution of the organic lamina also determines the failure pattern. The simulation \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Materials** & \(\mathbf{E_{L}(MPa)}\)[43; 44; 45]. & \(\mathbf{P_{L}(MPa)}\) & \(\mathbf{m}\) & \(\mathbf{v}\) & \(\mathbf{\phi}\) (\({}^{\circ}\)) & \(\mathbf{C/T}\) \\ \hline Organic matter & 20,000 & 60 & 2.5 & 0.34 & 35 & 10 \\ Clay & 59,000 & 155 & 2.8 & 0.32 & 35 & 10 \\ Carbonates (calcite) & 70,000 & 190 & 3 & 0.31 & 35 & 15 \\ pyrite & 90,000 & 310 & 5 & 0.19 & 35 & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties of the shale FE model. system can reproduce the typical characteristics of the failure process of microscale multi-mineral rock, and the failure characteristics obtained by the numerical simulation are in reasonable agreement with the physical test results [46]. Figure 6a-f shows the dynamic failure process of microscale organic laminar shale. Referring to the mineral distribution of the sample in Figure 5, it can be seen that at the initial stage of loading (point A), obvious stress concentration occurs at the organic matter lamina and the organic matter around pyrite (Figure 6a). In stages A-B, with the increase in load, the crack first initiates in the organic matter around pyrite (Figure 6b). Before peak point C (including the peak point), there is an obvious displacement discontinuity at the organic lamina (Figure 6c), and a small number of acoustic emission events occur, but there is no obvious macro crack. In stages C-E, with the continuous increase in load, a large number of acoustic emission events are generated, the stress-strain curve decreases in a stepwise pattern, and a small platform appears at point D. The results may be due to the fact that the fracture extension meets the primary fracture, resulting in a sudden increase in strain. In addition, the fracture gradually expands along the organic matter lamina (Figure 6d,e), and the displacement discontinuity gradually increases. Finally, a macro  
Figure 5: Shale microscopic model. (**a,b**) Original FIB-SEM 3D model: (**a**) is a front view, and (**b**) is a back view. (**c,d**) Finite element numerical model, expressed by elastic modulus: (**c**) is a front view, and (**d**) is a back view. (§§organic matter,§ carbonate minerals,§ pyrites). shear plane along the organic matter lamina is formed, and multiple macro cracks are formed along the organic matter lamina. It can be seen that the organic matter lamina plays a decisive role in the final shape of the crack. The macroscopic fracture surface is formed after the peak point, which is also consistent with our general understanding. In E-F, a small number of acoustic emission events occur, the stress-strain curve slowly decreases, and the displacement discontinuity is more pronounced at the main crack (Figure 6f). The strength and modulus of elasticity of the shale were 78.40 MPa and 60,700 MPa, respectively (Figure 6g). Figure 6h depicts the spatial distribution of acoustic emission events in the final damage. A sphere with a specific diameter and color represents an acoustic emission event. The diameter represents the relative magnitude of the released acoustic emission energy. The color represents the type of element failure. Red and blue indicate tensile damage and shear damage, respectively. It can be seen that most of the AE events are caused by tensile damage (red spheres), while only a small number of AE events are caused by sheer damage (blue spheres). Tensile failure is the main cause of rock failure, which is consistent with our general understanding [47].