## 3 Theoretical Foundation and Numerical Model Construction
### Numerical Model  
In this study, the previously established damage constitutive equation is embedded into the COMSOL Multiphysics(r) 6.1 Multiphysics finite element analysis platform in the form of an external material model, and the nonlinear relationship between stress and strain is established by calling a dynamic link library (DLL) written in C language to realize the numerical simulation of slope stability. The model takes the geomechanical response of the slope as the main research object, and takes into account the influence of different water storage conditions on the slope stability. By applying different head boundary conditions, four different water levels, namely, status quo, \(-\)50 m, 0 m, and +50 m, are simulated to systematically analyze their effects on the overall stability of the slope. On the basis of 3D fine geological modeling and high-quality mesh discretization, a massively parallel finite element simulation is carried out with the help of an ASUS high-performance server configured with an Intel Xeon W-3245M CPU (16 cores and 32 threads) and 512 GB of RAM, which can support up to one billion degrees of freedom computational tasks. The  
Figure 3: The elastic damage constitutive law of rock under uniaxial stress conditions [24].  
numerical solution is based on the Strength Reduction Method (SRM), which iteratively calculates the slope damage evolution process under different strength reduction factors (SRFs), and defines intermediate variables to record the SRF values corresponding to the damage of the units, so as to realize the quantitative characterization of the safety reserve of the units. The final results can not only give the overall slope stability evaluation, but also visualize the spatial distribution and damage pattern of potential sliding zones, which can provide high-precision mechanical information support and risk identification basis for open-pit mine slope engineering.  
In this study, the determination of geomechanical parameters takes into account the laboratory test results, the structural characteristics of the rock body, and the actual engineering practice in the field. Firstly, the initial rock strength parameters were obtained based on the indoor mechanical tests of the rock samples; then, by combining the structural features and GSI obtained from the field investigation, the Hoek-Brown Rock Strength Criterion was used to complete the parameter conversion from the experimental scale to the engineering scale, and then to obtain the representative rock strength parameters reflecting the geometric dimensions and structural features of the actual slopes. On this basis, we further refer to a large number of published research results on Fushun West Open-Pit Mine, which is one of the most important large-scale open-pit coal mines in China. Hundreds of related studies have been published to systematically study the geologic conditions and slope stability of this mine, and the mechanical parameters in this paper are also based on the widely accepted research data. In the process of numerical modeling, the simulation results are compared and adjusted with the actual slope stability condition many times, and the parameter combinations with engineering representativeness and field adaptability are finally determined to ensure the accuracy and reliability of the simulation results.