## 3 Methodology
### Numerical Evaluation
#### 3.2.4 Factors Inducing Slope Instability  
The inverse analyses are focused on single-factor effects. Previous research has shown the main triggers for landslides are rainfall infiltration [51; 52; 53] and earthquakes [54; 55; 56]. Additionally, when engineering slopes are reinforced with anchorage materials, the stability changes as the anchorage force evolves [57; 58]. Forward analysis, on the other hand, needs to consider multi-factor effects, which are more useful for engineering assessments. This study will take into account the effects of these single factors (rainfall, earthquakes, and anchorage force) and establish eight working conditions (see Table 4).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Factors** & **W0** & **W1** & **W2** & **W3** & **W4** & **W5** & **W6** & **W7** \\ \hline Prestressing loss & \(\surd\) & & & \(\surd\) & \(\surd\) & & \(\surd\) \\ Rainfall & & \(\surd\) & & \(\surd\) & & \(\surd\) & \(\surd\) \\ Earthquake & & & & \(\surd\) & & \(\surd\) & \(\surd\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Working conditions.  
The consideration for each factor in modeling is summarized as follow:  
1. Many previous studies have reported that the anchoring force attenuates [59, 60, 61]. Field monitoring data reported by [PERSON], et al. [62] show that the prestressing loss of anchorage cables can reach approximately 20% in 120 days. Furthermore, the corrosive environment also reduces the anchoring force. Prestressing loss caused by corrosion occurs after 120 days and reaches 4.3% [31]. Longer-term monitoring data show that the prestressing loss can reach 28.48% after more than ten years [59]. Together, these studies indicate that the prestressing loss occurs in phases. To simulate the prestressing loss, we set prestressing at three gradients: 80%, 75%, and 70% (Table 5).
2. The weakening effects caused by the interaction of water and rock will decrease the stability of a rock slope. The pore pressure will increase, and the strength will decrease under this effect. The weakening effect caused by rainfall does not include the pore pressure increasing in the present study, considering the additional complexity and computational cost involved. To better understand the mechanisms of softening, [PERSON], et al. [63] analyzed the triaxial shear test data of 30 groups of dry and saturated rocks. They proposed the cohesion (C) of the saturated sample is reduced by 31.8%, and the friction angle (\(\varphi\)) is almost unchanged. In the present study, we set C to three gradients, as 90%, 80%, and 70%, to simulate the softening of rock materials at different saturations, listed in Table 5.
3. The pseudo-static approach is a common method to analyze the slope stability subject to seismic disturbance [64]. This method simplified the problem by treating the earthquake load as a static load: \[F=kW\] (5) where \[F\] is the earthquake load, \[W\] is the gravity of the sliding mass, and \[k\] is a seismic coefficient representing the size of the effect induced by the earthquake. The seismic coefficient of the study area is 0.5 g. The present study set earthquake influence coefficient gradients to reflect the slope response to different intensities (Table 5).  
After modeling the weak interlayers and setting the parameters, we used a built-in strength reduction method (SRM) to compute the FOS.