## 4 Numerical Analysis of the Slope Stability of Coarse-Grained Soil Based on COMSOL Multiphysics
### Changes in Slope Soil Stability Under FT Cycles  
In order to fully simulate the changes in the decay of soil strength and the reduction in stiffness of the slope's soil with different moisture contents under continuous FT cycles, the attenuation trends of soil cohesion and internal friction angles with increasing FT cycle counts obtained from laboratory tests were used. Using MATLAB (R2022a) software, the relationship between the cohesion (c), internal friction angle (\(\varphi\)), and number of FT cycles was fitted using the nonlinear least squares method. The fitting results for each moisture content level are shown in Table 3.  
The fitting equations from the above table were input into the soil plasticity section of the slope model to simulate the stability changes of the slope model with increasing FT cycle counts under different moisture content conditions. The equivalent plastic strain contour maps for slopes with different coarse-grained soils are shown in Figures 19-21. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Moisture Content** & **Cohesion \(\boldsymbol{c}\)** & **Internal Friction Angle \(\boldsymbol{\varphi}\) (rad)** \\ \hline
7.6\% & c = 31,728*exp\((-0.002\)*FT) & \(\varphi\) = 0.4206*exp\((-0.002\)*FT) \\ \hline
9.6\% & c = 25,128*exp\((-0.003\)*FT) & \(\varphi\) = 0.4032*exp\((-0.002\)*FT) \\ \hline
11.6\% & c = 17,181*exp\((-0.003\)*FT) & \(\varphi\) = 0.3864*exp\((-0.002\)*FT) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Fitting results of the cohesion and internal friction angle with varying FT cycle counts (FT) under different moisture content conditions. Figure 19: Development trend of equivalent plastic strain in the slope model with a soil moisture content of 7.6%. (**a**) FT = 0, (**b**) FT = 60, (**c**) FT = 150, and (**d**) FT = 176. Figure 20: Development trend of equivalent plastic strain in the slope model with a soil moisture content of 9.6%. (**a**) FT = 0, (**b**) FT = 39, (**c**) FT = 96, and (**d**) FT = 106. Figure 19a shows the distribution of equivalent plastic strain in various parts of the slope model before undergoing any FT cycles. It can be observed that the larger equivalent plastic strain appears as point-like distributions, occurring only at the slope foot, with the maximum value concentrated at 1.89 \(\times\) 10\({}^{-4}\). This indicates that the slope foot is the potential sliding surface's initiation point and an active area for slope shear failure. However, at this stage, the slope is still in a stable state. From Figure 19b, after 60 FT cycles, the equivalent plastic strain is distributed in a star-like pattern, with the maximum value reaching 4.571 \(\times\) 10\({}^{-2}\). At this point, the plastic strain zone starts to show a tendency to expand along the potential sliding surface direction at the slope foot. Due to the increase in pore water pressure and the decrease in effective stress, friction resistance between particles of coarse-grained soil locally fails, triggering small plastic zones. Subsequently, the rate of equivalent plastic strain within the shear zone gradually accelerates. After 150 FT cycles, as shown in Figure 19c, the equivalent plastic strain zone begins to present a continuous band-like distribution (shear band), with the maximum equivalent plastic strain reaching 2.52 \(\times\) 10\({}^{-2}\). As the number of FT cycles increases, the equivalent plastic strain contour map gradually evolves. Finally, after 176 FT cycles, the region with high continuity and high values of equivalent plastic strain appears in Figure 19c, with the maximum value reaching 0.2012. The pore structure of coarse-grained soil is reorganized due to the accumulation of plastic deformation, and the slope enters a critical state of instability. Figures 20 and 21 show a similar trend in the development of equivalent plastic strain in the slope models, as observed in Figure 19. It can be seen that as the moisture content increases, the number of FT cycles required for the slope to reach the critical state of instability significantly decreases.