## 4 Numerical Simulation Analysis of Slope Instability
### Analysis of Finite Element Simulation Results
#### 4.4.3 Safety Factor of Slope Stability  
The essence of the sliding failure of the slope is strength failure caused by insufficient shear strength of rock and soil mass or structural plane [8]. Therefore, the strength reduction method is used to recheck the safety factor of slope stability. In the numerical calculation, the non-convergence of the analysis, the inflection points of the relation curve between the displacement of the key points of the slope and the strength reduction coefficient, and the penetration of the shear strain concentration area are used to judge whether the slope has entered the critical state comprehensively.  
The strength reduction method is used to calculate the safety factor of slope stability. The shear strength reduction factor is defined as the ratio of the maximum shear strength provided by the soil in the slope to the actual shear stress generated by the external load when the external load remains unchanged. The strength reduction method is used to calculate the safety factor of slope stability by continuously reducing the \(c\) and \(\varphi\) value of materials. The reduced shear strength parameters can be expressed as:  
\[c_{m}=c/F_{r} \tag{3}\]  
\[\varphi_{m}=\arctan(\tan\varphi/F_{r}) \tag{4}\]  
where \(c_{m}\) and \(\varphi_{m}\) are the shear strength required to maintain equilibrium or exerted by the soil mass. \(F_{r}\) is the strength reduction factor.  
The original model, the first excavation model, and the second excavation model are used to calculate the stability safety factor of the slope. In the calculation of each model, \(F_{r}\) is set to increase linearly from 0.75 to 2.5 until it does not converge and the safety factor is calculated, and the safety factors of slope stability under different working conditions are shown in Table 2.  
Figure 15: Development process of shear strain rate concentration area. (**a**) Distribution of plastic zone in slope during early rainfall. (**b**) Distribution of plastic zone in slope at the end of rainfall.  
According to the analysis results in Table 2, the calculation results show that the safety factor before slope excavation is 1.09; After the bank slope is cut for the first time and the load is reduced, the safety factor is only increased to 1.10. Since bolt support is not considered in the calculation, the safety factor of the slope is low. Compared with the tolerable safety factor, the calculated safety factor of all models is small to meet the safety requirements of slope stability.  
To sum up, for typical structural plane-controlled slopes, excavation unloading deformation is mainly represented by structural plane deformation. The slope deformation is composed chiefly of structural plane dislocation deformation. Structural plane deformation is primarily controlled by the exposure of the structural plane when excavating the free face, excavation unloading scale, etc. Therefore, it is reasonable to adopt \"load reduction\" measures in combination with the block shape of \"wide at the top and narrow at the bottom, top heavy and foot light\".