# Slope Failure of Noncohesive Media Modelled with the Combined Finite-Discrete Element Method
## 4 Example II: Landslide Triggered by Chi-Chi Earthquake
Furthermore, for the FDEM modelling, some rock blocks are still on the slope surface and have not fallen, and this phenomenon is not available in both DEM and MPM simulations. However, these differences are minor and can be considered acceptable due to the different methods employed. Figure 10 plots the horizontal travelling distances of the landslide simulated by the FDEM, DEM and MPM. It can be observed that all three curves agree quite well for 0 s \(\leq\) t \(<\) 20 s. Then, major differences appear during 20 s \(\leq\) t \(<\) 60 s, in which the result from the FDEM is between those from the DEM and MPM. Results from the FDEM and MPM converge around t = 60 s, which is much quicker than that from the DEM. Finally, all three curves converge consistently at t = 120 s.  
Figure 9: Evolutions of landslide from DEM and MPM. (**a**) DEM (with \(\Phi\) = 22\({}^{\circ}\), after [7]); (**b**) MPM (with \(\Phi\) = 24\({}^{\circ}\), after [8]). Define the percentage differences \(\eta_{1}\) and \(\eta_{2}\) on the travelling distances between different methods as:  
\[\eta_{1}=\left(\,\left|\,\Omega_{\text{FDEM}}\text{-}\Omega_{\text{DEM}}\,\right| \,/\,\Omega_{\text{FDEM}}\right)\times 100\% \tag{8}\]  
\[\eta_{2}=\left(\,\left|\,\Omega_{\text{FDEM}}\text{-}\Omega_{\text{MPM}}\,\right| \,/\,\Omega_{\text{FDEM}}\right)\times 100\% \tag{9}\]  
where \(\Omega_{\text{FDEM}}\), \(\Omega_{\text{DEM}}\) and \(\Omega_{\text{MPM}}\) are results from the FDEM, DEM and MPM, respectively. Table 4 presents the percentage differences on the travelling distances between different methods. From Table 4, the percentage difference between the FDEM and MPM is quite large at early stage although their travelling distance curves are very close as can be seen in Figure 10. Percentage differences of \(\eta_{1}\) and \(\eta_{2}\) are still quite noticeable between t = 30 s and t = 60 s. This is deemed as acceptable considering the different methods employed. The velocity contour plotting of the landslide is given in Figure 11. It can be observed that initial velocity is passed to individual rock blocks with the motion of mountain (t = 2.5 s). The rock blocks slide gradually along the slope surface, and the toe and tail parts have higher velocities over other parts (see Figure 11b,c). When these blocks are accumulated in the lower basin of the mountain, the velocities almost drop to zero at around t = 60 s. It is worth mentioning that compared with the velocities and movements of individual rock blocks, the motion of the mountain is quite small. This suggests that for unstable mountainous areas, small base motions may result in disastrous landslide consequences. Figure 12 shows the resultant velocity of the toe block. For FDEM modelling, it can be observed that the velocity increases and reaches its peak between t = 20 s and 30 s. Afterwards, the velocity decreases dramatically and actually there is no residual velocity any longer after t = 60 s. This behaviour is in good agreement with DEM results from reference [7] before t = 60 s. In the DEM simulation, the velocity is still oscillating up to t = 120 s and reaches a second peak around t = 80 s, which is not realistic as the toe block has rested. The oscillation behaviour is not observed in the FDEM simulation, \begin{table}
\begin{tabular}{c c c} \hline
**Time (s)** & \(\eta_{1}\) **(\%)** & \(\eta_{2}\) **(\%)** \\ \hline
5 & - & 44.23 \\
10 & - & 15.20 \\
15 & 1.94 & 20.39 \\
30 & 27.73 & 32.56 \\
60 & 18.84 & 1.75 \\
120 & 1.64 & 2.16 \\ \hline \end{tabular}
\end{table} 
Table 4: Differences on the travelling distances between different methods. Figure 10: Comparison on the horizontal travelling distance versus time.