# Three-Dimensional Theoretical Model for Soil Arching with Inclined Slip Surfaces
## 4 Analysis of Parameters on Loose Earth Pressure under 3D Inclined Slip Surface Condition  
In order to study the influence of parameters on loose-earth pressure under a 3D inclined slip surface condition, a series of cases are carried out. The buried depth ratio of the loose zone, the length of the loose zone, the soil parameters and the lateral earth pressure coefficient are taken into account, and corresponding analysis is carried out. The parameters for special cases are shown in Table 1.  
In case 1, the earth pressure under different angles of the slip surface is calculated and the other parameters in case 1 are consistent. It can be seen from the results shown in Figure 6 that the earth pressure at each depth increases with the decrease of the angle of the slip surface. This is mainly because the upward component provided by the shear resistance between slip surfaces decreases when the angle of the slip surface decreases. It also can be found that the maximum earth pressure may not occur at the bottom of the soil when the angle of the slip surface is small. The maximum earth pressure may occur somewhere in the middle of the soil. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Cases** & **H (m)** & **B (m)** & **\(\varphi\) (\%)** & **\(L\) (m)** & **\(\alpha\) (\%)** & **\(c\) (kPa)** & **\(K_{\mathbf{w}}\)** & **\(K_{\mathbf{l}}\)** \\ \hline
2 & 10 & 5 & 30 & variation & variation & 0 & 1 & 1 \\
3 & variation & 5 & 30 & variation & 85 & 0 & 1 & 1 \\
5 & 10 & 5 & variation & variation & 85 & variation & 1 & 1 \\
6 & 10 & 5 & 30 & 10 & 80 & 0 & variation & variation \\
7 & 10 & 5 & 30 & variation & 80 & 0 & variation & variation \\ \hline \end{tabular}
\end{table} 
Table 1: The parameters for different cases. Figure 5: Earth pressure ratio versus depth under different angle of slip surface. The influence of the angle of the slip surface and the aspect ratio of the loose area are studied in case 2. The results are shown in Figure 7. The loose-earth pressure also shows the same trend as mentioned before under different angles of the slip surface. The depth of soil and the aspect ratio of the loose area are studied in case 3. The calculated earth pressure versus the aspect ratio of the loose area under different slip surface angles are shown in Figure 8. It can be seen from results that the earth pressure ratio at the bottom of the loose area is small when the buried depth ratio of the loose area is large. This is because the stress redistribution is more likely to occur due to the increase of the length of the slip surface when the buried depth ratio is larger. The calculation results under different aspect ratios of the loose zone also show the same trend. When \(H/B=1\), the loose earth pressure is 42% to 61% of the total self-weight earth pressure under different aspect ratios. When \(H/B=2\), it will be 25% to 42% of the total self-weight earth pressure. Figure 6: Earth pressure versus depth under different angles of the slip surface. Figure 7: Earth pressure versus aspect ratio of loose area under different angles of the slip surface. When \(H/B=3\), it will be 17% to 31%, and when \(H/B=4\), the loose earth pressure is only 13% to 24% of the total self-weight earth pressure. The influences of soil parameters are studied in cases 4 and 5. Figure 9 shows the influence of the internal friction angle of soil and Figure 10 shows the influence of the cohesion stress of soil. Loose earth pressure is closely related to soil parameters. For frictional soil, the greater the internal friction angle, the more obvious the soil-arching effect and the smaller the soil pressure will be. For cohesive soil, the larger the internal friction angle and cohesion are, the more obvious the soil-arching effect and the smaller the soil pressure will be. The loose-earth pressure when the internal friction angle is 40 degrees is 53% to 65% of that when the internal angle is 25 degrees for different loosing zone aspect ratios.