# Numerical Modeling of 3D Slopes with Weak Zones by Random Field and Finite Elements
## 4 Results and Discussion  
The stability calculation of the slope is shown in Figure 13. The rotation angle of the weak zone layer inside the slope is one of the main controlling factors for the safety factor of the slope. In the figure, when the weak zone is rotated \(50^{\circ}\) around the \(X\)-axis and \(40^{\circ}\) around the \(Y\)-axis, the slope and the inclination of the weak zone are approximately parallel, while simultaneously resulting in the safety factor of the slope being greatly reduced. Therefore, when the inclination of the weak zone is approximately balanced with the slope, the safety factor of the slope will decrease, and the slope is more prone to landslides.  
Figure 12: Schematic diagram of the distribution of weak zones (red zone represents weathered flint strips dolomite; blue zone represents weak zones). (**a**) Rotation angle of \(30^{\circ}\) around the \(X\)-axis; (**b**) rotation angle of \(30^{\circ}\) around the \(Y\)-axis; (**c**) rotation angle of \(30^{\circ}\) around the \(Z\)-axis; (**d**) rotation angle of \(60^{\circ}\) around the \(X\)-axis; (**e**) rotation angle of \(60^{\circ}\) around the \(Y\)-axis; (**f**) rotation angle of \(60^{\circ}\) around the \(Z\)-axis; (**g**) Rotation angle of \(0^{\circ}\).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Volumetric** & \multirow{2}{*}{**Elastic Modulus**} & **Poisson Ratio** & **Cohesion \(c\)** & **Internal Friction** \\  & **Weight** & \(E\) **(GPa)** & \(v\) & **(kPa)** & **Angle \(\varphi\) (\({}^{\circ}\))** \\ \hline Rock & \multirow{2}{*}{28.0} & \multirow{2}{*}{100} & \multirow{2}{*}{0.2} & \multirow{2}{*}{50} & \multirow{2}{*}{30} \\ (weathered flint strips dolomite) & & & & & \\ Weak zones & & & & & \\ (residual cohesive soil) & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Material mechanical parameters of the slope.  
The plastic strain diagram of the slope is shown in Figures 14-16. It can be seen from the figures that when the slope is in a limit equilibrium state, yield occurs first at the weak zones, and the deformation of the weak zones develops continuously, resulting in an increase in the plastic zone. Therefore, when the weak zone layer is rotated at an angle of 50\({}^{\circ}\) around the \(X\)-axis and a rotation angle of 40\({}^{\circ}\) around the \(Y\)-axis, the safety factor of the slope reaches its lowest value. The figures suggest that the maximum plastic strain zone is likely to be parallel with the slope and the weak structural surfaces, thus decreasing the stability of the slope.  
Figure 14: Plastic strain diagram of the slope with transverse anisotropy of the weak zones (\(FOS=1.98\)).  
Figure 13: \(FOS\) under different rotational angles of the weak zones.  
Figure 15: \(Cont.\)  
Figure 16: _Cont._  
Figure 15: Plastic strain diagram of the slope with 30\({}^{\circ}\) rotation angle of the weak zones. (**a**) Rotation angle of 30\({}^{\circ}\) around the \(X\)-axis (\(FOS=1.87\)); (**b**) rotation angle of 30\({}^{\circ}\) around the \(Y\)-axis (\(FOS=1.89\)); (**c**) rotation angle of 30\({}^{\circ}\) around the \(Z\)-axis (\(FOS=1.94\)).