## 6 Limit Equilibrium Model with Cemented Paste Backfill
### Simulation Slope with a Different Cement Paste Backfilling Body  
Simulated slope stability with a different cement paste backfilling body was a crucial aspect of understanding the behavior of cemented paste backfill (CPB) structures in underground mines. The strength development and distribution of CPB structures are influenced by various factors, including the backfilling strategy, the inclination angle of the slope, and the filling rate. By using this model, the changes in CPB strength were investigated under various factors influencing the cement ratio. This study did not explicitly model the contact behavior between individual layers of the cemented paste backfill, which can significantly influence the overall mechanical response and stability of the backfill system. Limit equilibrium on the slope was used with different cement paste backfilling to calculate the factor of safety for each cement percentage after 1 day, 3 days, 7 days, and 28 days of curing time (CT) to obtain the optimum compressive strength and shear straight of cemented paste backfill with high paste fill shear strength on the slope. For the cement paste backfill with 6% cement for 3 days and 28 days, the paste fill density (\(\gamma\)) = 34,333.3 and 33,428.6 kg\(\cdot\)m\({}^{-3}\), UCS (\(\sigma\)) = 0.97 and 5.18 MPa, shear strength (\(\sigma\)) = 0.311 and 2.909 MPa, cohesion (\(c\)) = 0.071 and 0.070 MPa, and internal friction angle of paste fill (\(\varnothing\)) = 13.910\({}^{\circ}\) and 28.730\({}^{\circ}\), respectively. With these parameter values, the safety factor was calculated as 1.10 and 1.99. See Figure 18a,b. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number** & **Lithology** & **Thickness (m)** & **Density (kg\(\cdot\)m\({}^{-3}\))** & **Cohesion (MPa)** & **Internal Friction Angle (\({}^{\circ}\))** \\ \hline
1 & Silstone Sandstone & 50.71 & 2460 & 2.45 & 40 \\
2 & Coal Silstone & 1.24 & 2050 & 2.45 & 40 \\
3 & Thin Variable & 0.97 & 2470 & 2.45 & 40 \\
4 & Coal & 0.90 & 2050 & 3.5 & 24 \\
5 & Backfilling Body & Variable & Variable & Variable & Variable \\
6 & Silstone/Tillite & 0.97 & 2590 & 2.45 & 40 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Input mechanical parameters for the model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Type of Paste Fill** & **Density** & **UCS (MPa)** & **Strain** & **Shear Strength** & **Cohesion** & **Internal Friction** \\
**Specimen** & **(kg\(\cdot\)m\({}^{-3}\))** & **UCS (MPa)** & **Strain** & **(MPa)** & **(MPa)** & **Angle (\({}^{\circ}\))** \\ \hline
6\% Cement D1 = S1 & 34,571.4 & 0.62 & 0.023 & 0.194 & 0.073 & 11.040 \\
6\% Cement D3 = S8 & 34,333.3 & 0.97 & 0.018 & 0.311 & 0.071 & 13.910 \\
6\% Cement D7 = S11 & 34,523.8 & 2.51 & 0.014 & 1.125 & 0.012 & 23.920 \\
6\% Cement D28 = S14 & 33,428.6 & 5.18 & 0.028 & 2.909 & 0.070 & 28.730 \\
8\% Cement D1 = S2 & 34,095.2 & 1.16 & 0.032 & 0.358 & 0.071 & 13.910 \\
8\% Cement D3 = S5 & 33,142.9 & 1.93 & 0.036 & 0.868 & 0.012 & 23.920 \\
8\% Cement D7 = S12 & 33,571.4 & 5.60 & 0.030 & 3.140 & 0.070 & 28.730 \\
8\% Cement D8 = 15 & 33,714.3 & 12.22 & 0.022 & 7.362 & 0.253 & 30.190 \\
10\% Cement D1 = S3 & 34,095.2 & 2.81 & 0.015 & 1.258 & 0.012 & 23.920 \\
10\% Cement D3 = S6 & 31,619.0 & 3.95 & 0.028 & 2.492 & 0.115 & 31.040 \\
10\% Cement D7 = S9 & 33,571.4 & 7.39 & 0.034 & 4.623 & 0.087 & 31.540 \\
10\% Cement D28 = S16 & 30,552.4 & 9.56 & 0.025 & 6.487 & 0.102 & 33.740 \\
12\% Cement D1 = S4 & 33,619.0 & 4.89 & 0.019 & 3.058 & 0.115 & 31.040 \\
12\% Cement D3 = S7 & 32,095.2 & 7.36 & 0.016 & 4.982 & 0.324 & 32.330 \\
12\% Cement D7 = S10 & 30,904.8 & 7.44 & 0.019 & 5.071 & 0.102 & 33.740 \\
12\% Cement D28 = S13 & 31,333.3 & 13.48 & 0.017 & 9.860 & 0.337 & 35.240 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Input parameters of cement paste backfill.