## 4 Numerical Calculation of Slopes Based on Weibull Parameter Random Distribution Model  
### Random Distribution Model of Rock Mass Parameters  
Based on the results from the geodetic radar and ultrasonic tests, the platform between elevations of 1195 m and 1240 m was divided into three zones: left, center, and right, for modeling calculations. As shown in Figure 7, the calculation model was further subdivided into three sub-zones: Zone I, Zone II, and Zone III for zonal modeling. The model dimensions are 492 m in the X-direction, 80 m in the Y-direction, and 349 m in the Z-direction, with a slope height of 148 m. The simulation follows the Mohr-Coulomb failure criterion, with the building acting as a stress load applied to the top of the slope. The physical and mechanical parameters of the rock mass are provided in Table 2, excluding the experimentally measured parameters for the platforms between 1195 m and 1240 m.  
The calculation steps are as follows:  
1. Establish the slope numerical calculation model.
2. Fix the boundaries on the four sides and the bottom of the model.
3. Achieve initial geostatic stress equilibrium.
4. Use Fish script to write the code for calculating dissipated energy.
5. Extend downward by one step and record the results.
6. Repeat the previous step until the excavation reaches the 13 th step.  
Due to the presence of numerous joints, fractures, and other defects in the rock mass, which belong to nonlinear units, it is difficult to define the initial condition of the units.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Rock Layer** & **Young/kPa** & **Poisson** & **Cohesion/kPa** & **Friction Angle\({}^{c}\)** & **Tension/kPa** & **Density/(KN/m\({}^{3}\))** \\ \hline Coarse-Grained & \(6.9\times 10^{6}\) & 0.26 & \(0.88\times 10^{3}\) & 37 & \(0.96\times 10^{3}\) & 3.1 \\ Diorite & \(6.5\times 10^{6}\) & 0.28 & \(0.65\times 10^{3}\) & 36 & \(0.87\times 10^{3}\) & 3.1 \\ Ore & \(7.5\times 10^{6}\) & 0.26 & \(0.704\times 10^{3}\) & 37 & \(0.95\times 10^{3}\) & 3.4 \\ Weak Layers & \(0.8\times 10^{6}\) & 0.33 & \(0.02\times 10^{3}\) & 24 & \(0.032\times 10^{3}\) & 2.5 \\ Zone I & \(7.01\times 10^{6}\) & 0.26 & \(0.72\times 10^{3}\) & 36.12 & \(0.26\times 10^{3}\) & 3.6 \\ Zone II & \(2.81\times 10^{6}\) & 0.33 & \(0.56\times 10^{3}\) & 32.92 & \(0.04\times 10^{3}\) & 3.2 \\ Zone III & \(6.17\times 10^{6}\) & 0.27 & \(0.64\times 10^{3}\) & 34.89 & \(0.15\times 10^{3}\) & 3.22 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Physical and mechanical parameters of the rock mass.  
Figure 7: Numerically calculated 3D model and distribution of stochastic parameters.  
Therefore, the Weibull distribution is used for definition. The Weibull probability density function [41; 42; 43; 44; 45] is given by  
\[\mathrm{f(u)}=\begin{cases}\frac{\mathrm{m}}{\mathrm{u}_{0}}(\frac{u}{\mathrm{u }_{0}})^{m-1}\exp(-(\frac{u}{\mathrm{u}_{0}})^{m}&u\geq 0\\ 0&u<0\end{cases} \tag{22}\]  
In the equation, \(u\) represents the value of the random variable. \(u_{0}\) is a scale parameter related to the average value of all unit parameters. m is the shape parameter, which defines the shape of the Weibull probability density function.