## 2 Numerical Simulation Scheme
### Boundary Conditions and Loading Conditions  
For numerical simulations, boundary conditions are crucial considerations [29]. Figure 3 displays the boundary conditions of the numerical model used in this investigation. The viscous boundary was positioned at the bottom of the model to lessen the impact of seismic wave reflection on the numerical simulation results, while the free-field boundary was positioned around the model to replicate the semi-infinite space. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{(**a**)} \\ \hline
**Item** & **Density** & **Young Modulus** & **Poisson Ratio** & **Friction Angle** & **Cohesion** (\({}^{\circ}\)) & **(kPa)** \\ \hline Rock mass & 2.50 & 124.46 & 0.12 & 34.8 & 294.0 \\ \hline  & \multicolumn{4}{c}{(**b**)} \\ \hline
**Item** & **Stiffness—Normal** & **Stiffness—Shear** & **Friction Angle** & **Cohesion** (**Pa)** \\ \hline Weak layer & \(2.00\times 10^{10}\) & \(2.00\times 10^{10}\) & 30 & 200.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physical–mechanical parameters in numerical model of the slope. (**a**) Physical and mechanical parameters of rock mass. (**b**) Physical and mechanical parameters of weak layer. Figure 2: Numerical model of the slope. (unit: mm). This study used an integral to convert the seismic wave's acceleration time history to velocity time history, which was subsequently transformed into stress time history using Formulas (5) and (6). To replicate the seismic action, the seismic wave is entered into the model from the bottom as a stress wave. \[\sigma_{n}=-\big{(}2\rho C_{p}\big{)}v_{n}, \tag{5}\]  
\[\sigma_{s}=-(2\rho C_{s})v_{s}, \tag{6}\]  
where \(\sigma_{n}\) is the normal stress (MPa), \(\sigma_{s}\) is the tangential stress (MPa), \(\rho\) is the density of the medium (kg/m\({}^{3}\)), \(v_{n}\) is the vibration velocity in the lead direction of the input mass (m/s), and vs. is the vibration velocity in the horizontal direction of the input mass (m/s). Additionally, \(C_{p}\) and \(C_{s}\) stand for the seismic P and S wave propagation velocities in rock, respectively. Local damping is chosen in the calculation process to better reflect the real response under seismic action, and the local damping coefficient was set to 0.157 [30,31]. Twenty acceleration monitoring points were positioned at different heights within the slope and along the slope surface, as shown in Figure 4, in order to systematically examine the dynamic response law within the slope. The acceleration response law of the internal measurement sites of the slope from low to high along the elevation was examined in this study using a variety of elevation monitoring points (M5, M10, M14, M17, and M19). The monitoring locations (M6, M5, M4, M3, M2, and M1) at the same elevation were selected in order to investigate the acceleration response law of the measurement stations within the slope from the inside to the outside along the slope direction. The acceleration monitoring point M0 was concurrently positioned above the center of the model's bottom to verify the accuracy of the incoming seismic wave. This numerical simulation study uses the Wolong wave as the loading seismic wave, which is consistent with the seismic input wave we employed in our earlier slope shaking table test [20]. The time compression ratio of 1:4 [32] can be computed using the Buckingham similarity relation Formulas (7) and (8). This means that the Wolong wave is compressed four times and used for numerical simulation; Figure 5 displays its time-course curves and spectral curves, and the main frequency of the seismic wave,\(f_{0}\), which is approximately 13 Hz. \[C_{t}=C_{t}\big{(}C_{p}/C_{E}\big{)}^{1/2}, \tag{7}\]  
\[C_{E}=C_{p}C_{l}, \tag{8}\]  
Figure 3: Boundary conditions of numerical simulation. where \(C_{t}\) is the time similarity ratio, \(C_{l}\) is the length ratio, and \(C_{p}\) is the density ratio.