# Dynamic Stability Finite Difference Time Domain Analysis of Landfill Based on Hypergravity Test
## 5 Analysis of Dynamic Stability
### Analysis of the Seismic Stability of a Landfill using Safety Factor Time History  
According to the abovementioned method, the safety factor time history of each modeling scenario has been obtained. The time history curves of the safety factor are presented in Figures 8 and 9. The vertical dashed lines depicted in the two figures signify the end of earthquake activities. The four different time history curves of the safety factor, corresponding to four different earthquakes (\(k_{h}=0.13\), \(k_{h}=0.25\), \(k_{h}=0.34\), and \(k_{h}=0.46\)), of landfills with low water levels are shown in Figure 8. Under the scenarios of \(k_{h}=0.13\), \(k_{h}=0.25\), and \(k_{h}=0.34\), landfills are considered to be stable, with a safety factor value of about 2.0 when the excess pore pressure has nearly dissipated, indicating the good stability of landfills during weak earthquakes. However, when the earthquake intensity is high (\(k_{h}=0.46\)), the safety factor fluctuates significantly, with a minimum value of 1.49. It is noticed that, in the time history of pore pressure response, the negative excess pore pressure within the landfill dissipates considerably by the time the post-earthquake safety factor suddenly decreases, while the pore pressure of the landfill continues to rise. There are three main reasons for the occurrence of this phenomenon: firstly, the increase in pore pressure leads to a decrease in effective stress; secondly, the softening of the MSW during seismic activities; and last, the deformation of the landfill increases during the recovery of pore pressure, resulting in a decrease in the safety factor. Overall, landfills with low water levels can maintain good stability under different earthquake intensities. Yet, attention should also be paid to the impacts of deformation induced by strong earthquakes on the stability of the landfill mass. The time history curves of the safety factor, corresponding to four different earthquake intensities (\(k_{h}=0.13\), \(k_{h}=0.25\), \(k_{h}=0.34\), and \(k_{h}=0.46\)), of landfills with high water levels are depicted in Figure 9. During the same seismic activity, there is an obvious reduction in the safety factor of a high-water-level landfill compared to the one with a low water level, suggesting the adverse impact of rising water levels on the stability of a landfill. When the seismic intensity is relatively low (\(k_{h}=0.13\), \(k_{h}=0.25\)), the landfill with a high water level can maintain good stability during the earthquake process. This stability is reflected in the time history curve of the safety factor, as the curve remains near the stable value throughout the earthquake process with minor fluctuations. During moderate or high-intensity earthquakes (\(k_{h}=0.34\) and \(0.46\)), the safety factor of the landfill with high water initially experiences a slight increase. However, it gradually decreases as the negative excess pore pressure reaches its peak and starts to rebound. The safety factor of the landfill closely correlates with the development trend of negative excess pore pressure. As the negative excess pore pressure approaches complete dissipation and the effective stress of the landfill returns to the pre-earthquake state, significant changes occur in the stiffness and damping characteristics of the solid waste itself during the earthquake process. Additionally, volume expansion occurs under tension. Therefore, although the effective stress remains higher than before the earthquake, instability has already occurred in the landfill. At the same time, it can be clearly seen that, during the earthquake process, due to the negative excess pore pressure response of the high-water-level landfill, the safety factor actually increases to a certain extent during the period of pore pressure decrease. The minimum safety factor values of the high-water-level landfills under the four intensities of an earthquake are 1.59, 1.60, 0.31, and 0.35, respectively.