## 3 Finite Element Stability Analysis of the Slope Based on Strength Reduction Method  
To identify specific monitoring locations and obtain effective monitoring results, a two-dimensional geometric model was established to analyze the displacement and strain characteristics of the slope using ANSYS numerical analysis software (Ansys 2021 R2). Based on slope characteristics, the simplified 2D finite element meshing model of the slope is shown in Figure 8. The stability analysis of the north profile of the slope was carried out using the strength reduction method. The basic idea of the strength reduction method is reducing the shear strength parameter of the slope geotechnical body and then bringing it into the model for calculation until the numerical calculation does not converge and the slope reaches the limit of the damage state. Ansys embedded program automatically obtains the potential slip surface of the slope based on the results of elastoplastic finite element calculations, and the safety factor of the slope is also obtained. To carry out slope stability analysis and calculation, select the initial discount factor \(F\) (generally take \(F=1\)), and then the slope soil material strength coefficient is discounted, and the cohesion and internal friction angle after the discount with the formula are expressed as:  
\[C^{\prime}=\frac{C}{F} \tag{1}\]  
\[\tan\varphi^{\prime}=\frac{\tan\varphi}{F} \tag{2}\]  
\(C\) and \(\varphi\) are the initial cohesion and the angle of internal friction of the soil body of the slope, \(C^{\prime}\) and \(\varphi^{\prime}\) are the discounted cohesion and angle of internal friction, respectively. The calculation adopted displacement boundary conditions: the model was set up with horizontal and vertical fixed constraints at the bottom of the model, horizontal fixed constraints at the left and right boundaries, and no constraints at the top of the slope. According to the analysis of engineering survey data, the selected rock layer's physical and mechanical parameters are in Table 1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Name of the Soil**} & **Internal Friction Angle (\({}^{*}\))** & \multirow{2}{*}{**Cohesion**} & **Modulus of Elasticity** & **Poisson’s Ratio** & **Natural Density (KN/cm\({}^{3}\))** \\ \hline Sand clay (with gravel) & 20.45 & 13.6 Kpa & 0.64 Gpa & 0.32 & 17.9 \\ Diorite & — & — & 80 Gpa & 0.25 & 28.5 \\ Mudstone & 36.4 & 0.13 Mpa & 6 Gpa & 0.232 & 26.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Soil and rock parameters selected in numerical analysis. The model is divided into three zones according to the material characteristics of profile E3 from top to bottom. The upper part is the Quaternary (\(Q_{4}^{fl+el}\)) slope residual layer, the lower part is mudstone, and the middle part of the model is Diorite. Figure 9 shows the x-direction displacement diagrams of the slope profile E3 with different reduction factors. Observing Figure 9a, under the effect of natural gravity, the deformation of the slope in the horizontal direction is mainly concentrated at the top and foot of the slope. In these two areas, there is a regular layering phenomenon in the vertical direction, the displacement value gradually decreases from the surface layer to the deeper layer, and the maximum displacement of the slope occurs at the trailing edge of the slope. In addition, at the time of site investigation, tensile cracks had already appeared at the rear edge of the slope, but the width was not wide, which is consistent with the deformation trend of numerical analysis. Meanwhile, in the plastic strain map in Figure 10a, the plastic strain has been generated inside the slope body under natural conditions, and the plastic strain area extends from the rock interface to the upper slope residual layer but does not penetrate the slope. In addition, the numerical calculation results converge, indicating that the slope is stable under natural conditions.