## 5 Effect of Slope Inclination  
This section examines the effect of slope inclination on the seismic behaviour of the slopes, adopting as performance criterion the permanent displacement at the end of shaking. More specifically, Table 6 presents three slope profiles (A, B, and C) corresponding to slope inclinations 2:1, 4:3, and 1:1, respectively, which have been investigated in this study. A common set of soil properties was assumed for the three slopes given in Table 7, in which the soil strength parameters are higher than those in Table 1 to avoid numerical difficulties in the case of steeper slopes. For the case of homogeneous slopes, Table 8 shows the static safety factor FS, the mean horizontal permanent displacement \(u_{x}\), the mean vertical permanent displacement \(u_{y}\), and the total permanent displacement \(u\) for the modified seismic records in Figure 3, matching the Eurocode 8 spectra (for rock sites) with a peak ground acceleration of 0.30 g. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Geometry** & **Inclination (H:V)** & **Height, m** & **Angle** \\ \hline A & 2:1 & 20 & 27\({}^{\circ}\) \\ \hline B & 4:3 & 30 & 37\({}^{\circ}\) \\ \hline C & 1:1 & 30 & 45\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Geometric characteristics of investigated slopes. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Property** & **Mean Value \(\mu\)** & **Coefficient of Variation \(\sigma\)/\(\mu\)** \\ \hline Cohesion \(c\), kPa & 50 & 0.3 \\ \hline Friction angle \(\varphi^{\circ}\), degrees & 30 & 0.2 \\ \hline Dilation angle \(\psi^{\circ}\), degrees & 0\({}^{\circ}\) & 0 \\ \hline Density \(\rho\), kg/m\({}^{3}\) & 2000 & 0.1 \\ \hline Modulus \(E\), MPa & 60 & 0.2 \\ \hline Poisson’s ratio \(v\) & 0.3 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Mean value and standard deviation of soil properties. Figure 9: Probability of exceedance of a given value of total permanent displacement \(u^{\star}\) for different values of \(l_{x}\) and \(l_{y}\) (Weibull distribution). Figure 10 presents the coefficient \(f_{x}=u_{x}/\bar{u}_{x}\) of horizontal permanent displacement \(u_{x}\) of the heterogeneous slope normalized with respect to the horizontal permanent displacement \(\bar{u}_{x}\) of the homogeneous slope for the three slope inclinations. Additionally, Figures 11 and 12 present the coefficients \(f_{y}=u_{y}/\bar{u}_{y}\) and \(f=u/\bar{u}\) of the vertical and total permanent displacement of the heterogeneous slope with respect to the corresponding displacements of the homogeneous slope. As the permanent displacements \(u_{x}\), \(u_{y}\), \(u\), \(\bar{u}_{x}\), \(\bar{u}_{y}\), and \(\bar{u}\) correspond to the same mean soil strength for a given slope, the coefficients \(f_{x}=u_{x}/\bar{u}_{x},f_{y}=u_{y}/\bar{u}_{y}\), and \(f=u/\bar{u}\) mainly express the impact of the spatial variability of soil properties, while the changes of the statistical characteristics of \(f_{x},f_{y}\), and \(f\) express the impact of slope inclination. As expected, it is shown by the results that increasing the slope inclination significantly increases the ratios of \(f_{x},f_{y}\), and \(f\). The mean values of \(f\) for the 2:1, 4:3, and 1:1 slopes are 1.24, 1.54, and 1.90, respectively. It is observed that for the slopes 2:1 and 4:3, some values of \(f\) are less than 1, but for the slope 1:1, all values of \(f\) are larger than 1. Finally, Figure 13 plots the probability of exceedance of a given value \(f^{*}\) of the coefficient \(f=u/\bar{u}\) of total permanent displacement for the three slopes (\(u=\) total permanent displacement, \(\bar{u}=\) total permanent displacement of homogeneous slope). Figure 10: Probability density of the coefficient \(f_{x}=u_{x}/\bar{u}_{x}\) of horizontal permanent displacement for three slopes (\(u_{x}=\) horizontal permanent displacement, \(\bar{u}_{x}=\) horizontal permanent displacement of homogeneous slope). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Geometry** & **Inclination (H:V)** & **FS** & \(