# Study on the Distribution Law of Crustal Stress in Fault Fracture Area
## 2 Model Establishment  
To consider the influence of crushed rocks on stress, it is crucial to take into account the varying degrees of fault fracturing commonly observed in fault zones as a result of strata extrusion [21; 22; 23]. Within the fault zone, crushed rocks can manifest in different forms, including fragmented structures and block structures. In this study, different crushed rock conditions are incorporated to represent distinct fracture degrees of faults, with content ranging from 0% to 15%, as depicted in Figure 1. The model employed in this research has dimensions of 90 m in length and 30 m in width, with the fault situated at the center spanning 10 m in width and 30 m in length, aligned vertically. The fragmented rock mass within the fault is generated randomly, adhering to specific requirements using the macro language in ABAQUS. The model is simulated using planar strain elements with a mesh size of 1 m.  
To focus solely on the effects of material property variations on stress distribution, a Mohr-Coulomb elastoplastic model with mechanical parameters (shown in Table 1) is employed for each material in this article [24; 25]. The elastic modulus of the ordinary formation model is set to four different working conditions to investigate the impact of different \(E_{r}/E_{f}\) ratios on stress changes.  
To simplify the calculation, it is assumed that the maximum principal stress acting on the model area \(\sigma_{1}\) is 30 MPa, and the minimum principal stress \(\sigma_{3}\) is 10 MPa. Under different working conditions, \(\sigma_{1}\) acts on the model boundary from different angles. The  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material** & **Density** & **Elastic Modulus** & **Poisson’s Ratio** & **Cohesion c (MPa)** & **Angle of Internal Friction (\({}^{\circ}\))** \\ \hline Ordinary stratigraphic area & 2.7 & 30, 60, 90, 120 & 0.27 & 2 & 56 \\ fault & 2.63 & 30 & 0.35 & 1.5 & 45 \\ Crushed rock & 2.8 & 100 & 0.26 & 1.8 & 50 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mechanical Parameters of Model Materials.  
Figure 1: Stratigraphic Model under Different Crushing Conditions of Faults.  
model constrains normal displacement on all sides, with a free interface at the top and all degrees of freedom constrained at the bottom boundary [26; 27], as shown in Figure 2.  
Several different principal stress directions are designed, including \(\alpha=0^{\circ}\), \(30^{\circ}\), \(60^{\circ}\), and \(90^{\circ}\), where \(\alpha\) represents the angle between the maximum principal stress direction and the \(x\)-axis direction. To apply the model boundary conditions of \(\sigma_{x}\), \(\sigma_{y}\), and \(\tau_{xy}\), it is required to convert the coordinates using Equations (1)-(3).  
\[\sigma_{x}=\frac{\sigma_{1}+\sigma_{3}}{2}+\frac{\sigma_{1}-\sigma_{3}}{2} \cdot\cos 2\alpha \tag{1}\]  
\[\sigma_{y}=\frac{\sigma_{1}+\sigma_{3}}{2}-\frac{\sigma_{1}-\sigma_{3}}{2} \cdot\cos 2\alpha \tag{2}\]  
\[\tau_{xy}=\frac{\sigma_{1}-\sigma_{3}}{2}\cdot\sin 2\alpha \tag{3}\]  
To summarize, this article's model considers three factors: the degree of fault fragmentation \(P\), the ratio of elastic modulus between strata and faults \(E_{r}/E_{f}\), and the angle \(\alpha\) between the fault inclination and the direction of horizontal principal stress in the strata. Each factor has four situations, resulting in 64 operating conditions, as shown in Table 2.