## 3 Methodology
### Numerical Evaluation
#### 3.2.2 Model Assumptions, Mesh Generation, Boundary Conditions, and Validation  
Before modeling, we validated the numerical method in this study by reproducing a the results from a study. Please refer to Appendix A. Some assumptions were made for model operation:  
1. The pit is excavated in layers. 2. Anchor construction and the prestressing are completed instantly with no loss of prestress. 3. The anchors are considered by cable elements in the numerical model. Each cable element is defined by its geometric, material, and grout properties. The cable behaves as an elastic, perfectly plastic material that can yield in tension and compression but cannot resist a bending moment. A cable is grouted such that force develops along its length in response to relative motion between the cable and the grid. The grout behaves as an elastic, perfectly plastic material, with its peak strength being confining stress dependent and with no loss of strength after failure. First, a pyramid-dominant mesh was generated with a specified min angle (15\({}^{\circ}\)) and min edge length (3 m). In this mesh, each boundary extended 150 m (Figure 6a), while the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Material** \\ **Properties** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Density** \\ **(kN/m\({}^{3}\))** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Cohesion** \\ **C (MPa)** \\ \end{tabular} } & \multicolumn{2}{c}{**Internal**} & \multicolumn{2}{c}{**Uniaxial Compressive Strengths**} & \multicolumn{2}{c}{**Modulus**} & \multirow{2}{*}{\begin{tabular}{c} **Tensile** \\ **Strength** \\ **(MPa)** \\ \end{tabular} } \\ \cline{3-3} \cline{5-10}  & & & & & & & & \\ \hline \begin{tabular}{c} Intact rock \\ Rock mass \\ Bedding \\ plane \\ \end{tabular} & 27 & 14.7 & 31.3 & 63 & — & 44.1 & — & 5.9 \\ \
\begin{tabular}{c} Rock mass \\ Bedding \\ plane \\ \end{tabular} & 24.7 & 0.5 & 30.7 & — & 1.4 & — & 4.0 & 0.14 \\
\begin{tabular}{c} Bedding \\ plane \\ \end{tabular} & 27 & 0.09 & 27 & — & — & — & — & — \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mechanical properties of rock. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Types of** \\ **Anchorage** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Cross-** \\ **Sectional** \\ **Area (m\({}^{2}\))** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Young’s** \\ **Modulus** \\ **(GPa)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Tensile** \\ **Yield** \\ **Strength** \\ **(kN)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Grout** \\ **Cohesive** \\ **Strength** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Grout** \\ **Stiffness** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Pre-** \\ **Exposed** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Inclination** \\ **(C)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Anchoring** \\ **Length** \\ **(m)** \\ \end{tabular} } \\ \hline
1 & 5.8 \(\times\) 10\({}^{-5}\) & 20 & 1260 & 1000 & 20 & 0.2512 & 1050 & 30 & 10.3 \\
2 & 5.8 \(\times\) 10\({}^{-5}\) & 20 & 1620 & 1000 & 20 & 0.1884 & 1350 & 30 & 10.3 \\
\begin{tabular}{c} Cables \\ \end{tabular} & 1 \(\times\) 10\({}^{-4}\) & 20 & 1620 & 1000 & 20 & 0.2512 & — & 30 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mechanical properties of anchorage structure. bottom extended 80 m. For the boundary conditions, horizontal motion (X and Y directions) is constrained at the four vertical boundaries, while both horizontal and vertical motions (X, Y and Z directions) are constrained at the bottom boundary. Then, the bedding planes forming two unstable blocks (Section 4.1) were inserted into the mesh and generated two models (Figure 6b is Model 1 for Block 8, and Figure 6c is Model 2 for Block 9). The mesh numbers of the two models are 33,312 (Model 1) and 34,877 (Model 2).