## 3 Engineering Geological Model  
### Model Setup  
Particle Flow Code (PFC) 5.0 is a common calculation and analysis software based on the discrete element method (DEM), and it is widely utilized in research on rocks and rock-like materials [5]. In PFC 2D, rock samples can be represented by disk-shaped particles, and the interactions between particles are achieved through contact bonds. In particular, the parallel bond model (PBM) can transmit both force and moment between the particles [32], which is extensively used in simulating deformation behaviors and strength characteristics of natural rock or cement mortar materials [5; 33; 34; 35]. The smooth joint model (SJM) is used to simulate the behavior of a planar interface created by a rock joint in a parallel bond model [36]. A linear model (LM) can provide the behavior of an infinitesimal interface that does not resist relative rotation [37]. One crack occurs when a contact bond fractures. Additionally, the mechanical behavior of particles in PFC adheres to [PERSON]'s second law [38]. The deformation and the stress equilibrium state of the sample are calculated by iterative analysis until the end of the simulation tests. In this study, a representative simplified model was utilized based on the true geological conditions of the Fushun West Open-pit Mine in order to investigate the stability and failure process of an anti-dip rock slope with interbedded mudstone-brown shale (Figure 2a). The simulated slope model consists of mudstone and brown shale strata. The thickness of each mudstone stratum is 3 m, and the thickness of each brown shale stratum is 1.5 m. According to this investigation, joints with inclination angles ranging from 70\({}^{\circ}\) to 90\({}^{\circ}\) exist in the strata of mudstone. Therefore, joints with 75\({}^{\circ}\) inclination angles and 3 m length were set inside the mudstone layer. The numerical model was established based on the following procedures. Firstly, the contours of mudstone and brown shale were drawn with multi-segment lines in a certain area using CAD 2014. These contours were later imported into PFC 2D, resulting in the generation of corresponding particles within their respective regions. The height and width of the slope were set to 30 m and 60 m, respectively. To optimize the computational efficiency, the actual mineral particle size was scaled up within the numerical model. The size of the mudstone particles ranged from 0.1 m to 0.15 m randomly, while the size of the brown shale particles followed a random distribution ranging from 0.12 m to 0.18 m.  
Figure 1: Local geological structure and rock stratum distribution of the rock slope. PBM was utilized to simulate the contact between the particles and reproduce the rock behavior within the model. LM was used to act as the interlayer contact between the mudstone and brown shale particles, while SJM was adopted for the simulation of the rock joint. Notably, the designed lines were digitalized in CAD and then imported into the PFC 2D numerical model to act as the joint. Additionally, four measuring circles were strategically arranged on the side of the slope surface to monitor the stress and strain state during the landslide simulation. In this study, three boundaries of the simulation model were constrained by a rigid wall. The excess particles outside the slope wall were directly deleted to simulate the excavation of the mining process. Then, we began to calculate under gravity to reach a new equilibrium. In PFC 2D, the safety factor can be calculated by the gravity increase method, which is defined as the ratio of the gravitational acceleration in the limit state to that in the initial state, according to [39; 40]. This study did not concentrate on the stability analysis by calculating the safety factor and instead focused on the failure process and mechanical damage mechanism. Figure 2: Numerical model.