## 3 Numerical Model
### Model Analysis and Design
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Strat** & & & **Layer** & **Volume** & **Shear** & **Tensile** & **Cohesion** & **Internal** & **Bulk** \\
**Graphic** & **Horizon** & **Lithology** & **Thickness** & **Modulus** & **Modulus** & **Strength** & **(MPa)** & **Criction** & **Density** \\
**Number** & & & **(m)** & **(GPa)** & **(GPa)** & **(MPa)** & **(MPa)** & **Angle (\({}^{\circ}\))** & **(KN-m\({}^{-3}\))** \\ \hline \multirow{2}{*}{GS-No. 01} & Overlying & Sandy & \multirow{2}{*}{2.00} & \multirow{2}{*}{2.81} & \multirow{2}{*}{1.03} & \multirow{2}{*}{1.41} & \multirow{2}{*}{0.722} & \multirow{2}{*}{25.4} & \multirow{2}{*}{26.1} \\  & strata & mudstone & & & & & & & \\ \multirow{2}{*}{GS-No. 02} & Overlying & \multirow{2}{*}{Mudstone} & \multirow{2}{*}{2.15} & \multirow{2}{*}{2.81} & \multirow{2}{*}{1.03} & \multirow{2}{*}{1.41} & \multirow{2}{*}{0.722} & \multirow{2}{*}{25.4} & \multirow{2}{*}{26.1} \\  & strata & mudstone & & & & & & & \\ \multirow{2}{*}{GS-No. 03} & Overlying & Medium & \multirow{2}{*}{5.50} & \multirow{2}{*}{4.07} & \multirow{2}{*}{2.58} & \multirow{2}{*}{1.82} & \multirow{2}{*}{1.410} & \multirow{2}{*}{27.4} & \multirow{2}{*}{27.9} \\  & strata & sandstone & & & & & & & \\ \multirow{2}{*}{GS-No. 04} & Overlying & \multirow{2}{*}{Hudstone} & \multirow{2}{*}{3.85} & \multirow{2}{*}{2.81} & \multirow{2}{*}{1.03} & \multirow{2}{*}{1.41} & \multirow{2}{*}{0.722} & \multirow{2}{*}{25.4} & \multirow{2}{*}{26.1} \\  & strata & mudstone & & & & & & & \\ \multirow{2}{*}{GS-No. 05} & Overlying & \multirow{2}{*}{Fine-grained} & \multirow{2}{*}{1.30} & \multirow{2}{*}{3.87} & \multirow{2}{*}{2.13} & \multirow{2}{*}{1.64} & \multirow{2}{*}{1.260} & \multirow{2}{*}{26.3} & \multirow{2}{*}{26.5} \\  & strata & sandstone & & & & & & & \\ \multirow{2}{*}{GS-No. 06} & Overlying & Sandy & \multirow{2}{*}{1.45} & \multirow{2}{*}{2.81} & \multirow{2}{*}{1.03} & \multirow{2}{*}{1.41} & \multirow{2}{*}{0.722} & \multirow{2}{*}{25.4} & \multirow{2}{*}{26.1} \\  & strata & mudstone & & & & & & & \\ \multirow{2}{*}{GS-No. 07} & Overlying & \multirow{2}{*}{Silstone} & \multirow{2}{*}{1.90} & \multirow{2}{*}{2.82} & \multirow{2}{*}{1.05} & \multirow{2}{*}{1.43} & \multirow{2}{*}{0.736} & \multirow{2}{*}{26.4} & \multirow{2}{*}{27.3} \\  & strata & & & & & & & & \\ \multirow{2}{*}{GS-No. 08} & Main & \multirow{2}{*}{Mudstone} & \multirow{2}{*}{3.55} & \multirow{2}{*}{2.81} & \multirow{2}{*}{1.03} & \multirow{2}{*}{1.41} & \multirow{2}{*}{0.722} & \multirow{2}{*}{25.4} & \multirow{2}{*}{26.1} \\  & inclined shaft & mudstone & & & & & & & \\ \multirow{2}{*}{GS-No. 10} & inclined shaft & \multirow{2}{*}{Mudstone} & \multirow{2}{*}{1.12} & \multirow{2}{*}{2.81} & \multirow{2}{*}{1.03} & \multirow{2}{*}{1.41} & \multirow{2}{*}{0.722} & \multirow{2}{*}{25.4} & \multirow{2}{*}{26.1} \\  & inclined shaft & mudstone & & & & & & & \\ \multirow{2}{*}{GS-No. 10} & Main & Sandy & \multirow{2}{*}{7.75} & \multirow{2}{*}{2.81} & \multirow{2}{*}{1.03} & \multirow{2}{*}{1.41} & \multirow{2}{*}{0.722} & \multirow{2}{*}{25.4} & \multirow{2}{*}{26.1} \\  & inclined shaft & mudstone & & & & & & & \\ \multirow{2}{*}{GS-No. 14} & Underlying & \multirow{2}{*}{Limestone} & \multirow{2}{*}{0.80} & \multirow{2}{*}{2.30} & \multirow{2}{*}{1.94} & \multirow{2}{*}{2.60} & \multirow{2}{*}{3.350} & \multirow{2}{*}{38.7} & \multirow{2}{*}{27.4} \\  & strata & mudstone & & & & & & & \\ \multirow{2}{*}{GS-No. 15} & Underlying & \multirow{2}{*}{Mudstone} & \multirow{2}{*}{7.70} & \multirow{2}{*}{2.81} & \multirow{2}{*}{1.03} & \multirow{2}{*}{1.41} & \multirow{2}{*}{0.722} & \multirow{2}{*}{25.4} & \multirow{2}{*}{26.1} \\  & strata & mudstone & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic parameters of rock strata in shaft, roadway and chamber roof and floor.