## 1 Introduction
The above research results showed that the permeability coefficient will change with time, rainfall intensity and other external factors, which can be verified by the SSD theory (taking the permeability coefficient as a variable) in this study. Second, the SSD coupling method used in this paper needs the coupling of the seepage field and the stress field, which is mainly achieved by solving the seepage field and converting it into an equivalent load acting on the model nodes. Many research on the seepage-stress coupling has been conducted at national and global scales. For example, [PERSON] et al. [12] established a theoretical model of micro-fracture growing seepage based on the fluid-solid coupling between grout seepage and micro-fractures. They studied the fracturing conditions, fractures' spatial distribution, and the variation law of mud seepage distance. Through analysis and comparison, [PERSON] et al. [13] obtained the failure mode and seepage characteristics of unloaded rock with and without water pressure. [PERSON] et al. [14] used finite-difference to analyze the influence of saturated or unsaturated seepage on the slope stability. They obtained the influence of the flow rate on the stability of the slope. [PERSON] et al. [15] analyzed that the external water pressure of the tunnel is related to the basement and seepage of the basement and is the main influencing factor related to safety. [PERSON] [16] used the neural network method to develop the program to combine the seismic load effect and the fluid-solid coupling effect. He analyzed the seepage stability of the earth dam and determined the dangerous sliding surface of the dam slope. [PERSON] [17] gave a method of calculating the safety factor of slope stability considering seepage conditions based on the law of seepage-stress coupling evolution. He estimated that the effect of seepage has a significant impact on slope stability. [PERSON] et al. [18] evaluated the slope stability under rainfall infiltration conditions based on the shear strength reduction technology. They considered the non-coupled conditions of seepage and deformation, combined with statistics and observation methods. [PERSON] et al. [19] studied the factors influencing slope stability under rainfall infiltration conditions. They found that slope instability mainly depends on the rainfall intensity and the nature of the soil, as well as slope type and groundwater level. [PERSON] et al. [20] established saturated and unsaturated transient rainfall infiltration models. Based on correlated groundwater transients, unsaturated infiltration analysis, and groundwater pressure diffusion, the models predicted the time and main source areas of landslides caused by rainfall. [PERSON] et al. [21] considered different groundwater levels, rainfall intensity, and soil properties to analyze the stability of the residual soil slope under rainfall infiltration conditions. The results are in good agreement with the research trend in the parameter study. [PERSON] et al. [22] analyzed the failure laws of shallow slopes under rainfall infiltration conditions based on the Green-Ampt infiltration model and the infinite slope stability model. The proposed model can be used to estimate the first-order approximation of the time when a rainfall-induced shallow landslide occurs and its sliding depth. [PERSON] et al. [23] compared the design plan with actual case data. They investigated the influence of unit weight and the function of unsaturated shear strength and saturation on shallow landslides triggered by rainfall infiltration. [PERSON] et al. [24] established a finite element model that couples solid deformation with fluid pressure in unsaturated soil to evaluate slope stability. However, most of the above research was conducted by using the seepage method or the seepage-stress coupling method. Based on these results, the SSD coupling method was adopted in this paper.