## 3 Design and Computation of Orthogonal Simulation Experiment
### Design of Simulation Models  
Based on the in-situ conditions from the Bulianta Mine, all models are divided into five rock layers (including the coal seam) and defined using the Mohr-Coulomb constitutive model in the software of FLAC\({}^{3\text{D}}\). The layer thicknesses and the physical and mechanical properties are shown in Table 3. The purpose of this research is to identify the key parameters of the coaface that affect the ground damage. Therefore, these strata conditions should be fixed for all designed simulation models, except the thickness of the coal seam, which is one of the objects of interest.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Levels**} & \multicolumn{4}{c}{**Experiment Factors (Parameters of the Coaface)**} \\ \cline{2-5}  & **Factor A** & **Factor B** & **Factor C** & **Factor D** \\  & **Length in Dip** & **Length in Strike** & **Thickness (m)** & **Mining Speed** \\  & **Direction (m)** & **Direction (m)** & **Direction (m)** & **Direction (m)** \\ \hline Level 1 & 250 & 600 & 2 & 8 \\ Level 2 & 300 & 700 & 4 & 10 \\ Level 3 & 350 & 800 & 6 & 12 \\ Level 4 & 400 & 900 & 8 & 14 \\ Level 5 & 450 & 1000 & 10 & 16 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Selection of factors and levels for the orthogonal experiment.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Test ID**} & \multicolumn{4}{c}{**Experiment Factors (Parameters of The Coaface)**} \\ \cline{2-5}  & **Factor A** & **Factor B** & **Factor C** & **Factor D** \\  & **Length in Dip** & **Length in Strike** & **Thickness (m)** & **Mining Speed** \\  & **Direction (m)** & **Direction (m)** & **Direction (m)** & **Direction (m)** \\ \hline
1 & 400 & 700 & 10 & 8 \\
2 & 400 & 800 & 6 & 10 \\
3 & 300 & 600 & 6 & 14 \\
4 & 250 & 1000 & 6 & 16 \\  
For each model, the horizontal displacement at the four vertical boundaries is restricted. More specifically, as shown in Figure 2, the x-direction displacement in right and left side planes is fixed, as well as the y-direction displacement in front and back side planes. The vertical displacement at the bottom is also restricted, whereas the top surface is free.  
All internal displacements of the model are caused by gravity without any additional external forces. That is, the initial stress of the model only depends on the weight and property of the layers.  
The model after excavation for Test 5 is shown in Figure 2 as an example. To better illustrate the ore body layer, for the 3D model in Figure 2a, the overlying strata are uniformly raised by 1000 m (just for display). The plane size of this model is \(3000\times 3000\) m, which is fixed for all 25 models. The coal thickness is 10 m for this test (from Table 2), while the thicknesses of the other layers are shown in Table 3. This model (before excavation) has a total of 183,618 nodes and 170,000 blocks.  
After the initial model balance, the displacements and velocities are reset to zero. The simulative excavation in the coal layer is then implemented based on the orthogonal experiment scheme given in Table 2. The excavation zone for Test 5 is \(300\times 1000\) m. It is noted that to consider the mining speed, the excavation zone is extracted several times to match the designed size. Each time, the excavated length in the strike direction is set as the designed mining speed times 30 days (e.g., 12 m/day \(\times\) 30 day for Test 5). As illustrated in Figure 2b, to shape the final excavation zone (1000 m in the x-direction), we mined 3 times in the coal layer: 360, 360 and 280 m for the first, second and third time, respectively.