# Strata Control by Roof Blasting for Bord and Pillar Mining Method in Mechanized Depillaring Panels
## 4 Numerical Simulation
### Simulation of Proposed Panels
#### 4.1.1 Simulation for Design of Gallery Width, Cut-Out Distance, and Rib/Snook  
A simulation of a single pillar is carried out for estimation of safe split gallery width, cut-out distance, and strength of different sizes of rib/snook in the panel. Taking advantage of the existing symmetry conditions of pillar formation, a single pillar considering only three layers (floor, coal, and roof) is modeled in the simulation software for the estimation of the strength of different sizes of pillars whereas different layers as mentioned in Table 6 are considered for the simulation of safe gallery width and COD. Furthermore, vertical roof displacement is observed over numerical models as per Table 6 to determine a safe gallery width and a cut-out distance based on a safe limiting value of roof sagging of 5 mm. The estimated safe width of the gallery is found to be 5.5 m for the panel (Figure 15). Based on experiences of workings under similar geo-mining conditions in different Indian coal mines, the safe width of the gallery is estimated in the model, considering 5 mm [37] as the limiting value of roof sagging to induces permanent movement (plastic in nature) in the galleries to be widened/split/slice (Figure 15). It is found that the roof of the gallery is stable without a considerable amount of roof deformation after the proposed gallery width of 5.5 m (Figure 15). A pillar size of 34.0 m \(\times\) 29.5 m (corner-to-corner) and a gallery width of 5.5 m are found suitable for panel, respectively, as per the numerical simulation study and found to be validating the results of empirical formulations. The estimated maximum unsupported span, i.e., cut-out- distance (COD) for a 5.5 m wide gallery in the panel is found to be around 11 m (Figure 16). Based on experiences of working in different Indian coal mines, the COD in the model is estimated, considering 5 mm [37] as the limiting value of roof sagging to induce permanent movement (plastic in \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Stra**} & **Thickness** & **Mood** & **Young’s** & **Shear** & **Bulk** & **Poisson’s** & **Density** & **Cohesion** & **Friction** & **Compressive** & **Strength** \\  & **(m)** & **Modulus** & **(GPa)** & **(GPa)** & **Ratio** & **(GPa)** & **Ratio** & **(GPa)** & & **(MPa)** & **(MPa)** & **(MPa)** \\ \hline Layer 3. & 50 & Elastic & 7 & 2.8 & 4.67 & 0.25 & 2500 & 2.43 & - & - & - \\ Layer 2. & 1.8 (BCS) & MCSS & 3.00 & 1.20 & 2.00 & 0.25 & 1400 & 0.181 & 39.59 & 25 & 1.67 \\ Layer 1. & 50 & Elastic & 7 & 2.8 & 4.67 & 0.25 & 2310 & - & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Physico-mechanical properties of strata used in numerical modeling. Figure 15: Contour of vertical displacement for different widths driven in a gallery length of 10 m.  
nature) in the split/original galleries/slice to be driven. It is found that pillars are standing without a considerable amount of roof deformation after the proposed divrage of 11.0 m, which validates the results of empirical formulations. The upper face of the model is fixed for the estimation of the strength of ribs/snooks, with the application of a standard calibrated velocity applied in the vertical direction (Figure 17) after developing galleries. Displacements in the vertical and horizontal directions are fixed at the bottom, and four vertical symmetrical planes of the model are constrained, which are considered boundary conditions during the numerical modeling. The standard size of the model is tested during the numerical modeling, considering the limitations of the computational memory and runtime requirements; 50 m of the roof and 50 m of the floor are modeled with a 1.8 m coal seam in the panel (Figure 17). A coal seam of 1.8 m thickness is considered a strain-softening model, while the roof and floor are treated as elastic constitutive models. In situ stresses are developed in the model before studying the effects of the mining operations.