## 5 Wet-Dry Cycling Effects on Slope Stability
### Model Construction  
SRM was first proposed by [PERSON] et al. in 1975 [44]. Its basic principle involves gradually reducing the cohesion and internal friction angle of the material through a strength reduction coefficient. When the stress and strength of a given soil unit are no longer in equilibrium, the excessive stress is transferred to the surrounding units of the soil mass. Once the large yield points connect to form a continuous failure surface, the soil mass becomes destabilized. The expression for strength reduction is as follows:  
\[c_{\mathrm{m}}=\frac{\xi}{F_{r}} \tag{5}\]  
\[\varphi_{\mathrm{m}}=\arctan(\frac{\tan\varphi}{F_{r}}) \tag{6}\]  
where \(c\) and \(\varphi\) are the soil cohesion and angle of internal friction determined through the direct shear test; while \(c_{m}\) and \(\varphi_{m}\) denote the corresponding values of cohesion and angle of internal friction after accounting for strength discounting; \(F_{r}\) is the discount factor, defined as the ratio of the strength before and after discounting; \(F_{v}\) is the slope safety factor, whose value is equal to that of the \(F_{r}\) in the ultimate equilibrium state of the slope. The three common methods used to assess slope failure are as follows: (i) if the calculation results show no convergence, it can be concluded that the slope has failed [45]; (ii) if a distinct inflection point appears in the displacement of a characteristic point on the slope, it can be concluded that the slope has failed [46]; and (iii) if a continuous plastic zone emerges, it can be interpreted as an indication that the slope has failed [47]. The SRM can automatically identify the most critical sliding surfaces and calculate the corresponding safety factors without the need for a priori assumptions regarding the size, shape, or location of the failure surfaces. Based on the strength parameters obtained from the tests, the SRM is applied within numerical simulation software to investigate the stability of the slope model, and this method has been widely used by numerous researchers [48,49]. A typical homogeneous soil slope is used as a case study to investigate the impact of multiple dry and wet cyclic actions on slope stability, with the model geometry illustrated in Figure 10a. In a slope stability analysis, the influence of external environmental factors on soil strength is limited to a certain depth [50,51]. Consequently, the model is divided into two zones: the upper zone (Zone I), representing the affected area, and the lower zone (Zone II), representing the unaffected area. Zone I and Zone II constitute distinct regions within the same homogeneous soil body, delineated solely by the \"Partition\" function of the software. The disparity between these two zones manifests solely in the variation in material parameters, specifically cohesion (\(c\)) and angle of internal friction (\(\varphi\)), as a function of the number of \(N\). No contact interface is established between the two zones. This approach circumvents the computational complexity associated with the contact algorithm, thereby reducing the computational workload, and precisely captures the progressive degradation effect of wet-dry cycles on the topsoil. The physical parameters of the soil used in the model are provided in Table 2. In Zone I, which is subjected to wet and dry cyclic actions, the shear strength is reduced, and the cohesion and angle of internal friction under varying cyclic conditions are determined based on the experimental results detailed in Section 3.4 of this study. In contrast, Zone II is not subjected to wet and dry cyclic actions, and its cohesion and angle of internal friction are taken as the values obtained from tests under natural moisture content, prior to any cyclic exposure. The boundary conditions include constrained horizontal displacement on both the left and right sides, a fixed bottom edge, and free boundaries on all other sides. The mesh consists of CPE4 four-node plane strain elements, it can effectively balance calculation accuracy and efficiency.