# A Partitioned Rigid-Element and Interface-Element Method for Rock-Slope-Stability Analysis
## 1 Introduction  
In recent years, China has planned to establish numerous water conservancy and hydropower projects in the southwest. In these areas, there may be a large number of rock slopes with complex structures and frequent geotectonic movements, which can cause serious consequences for nearby facilities in case of landslides or earthquakes. Therefore, ensuring the stability of rock slopes is crucial for the long-term safe and effective operation of engineering projects. Rock slopes often contain many discontinuous structural planes, such as joints, fissures, and weak interlayers. As a result, the slope can be viewed as consisting of two distinct structures: the rock masses segmented by structural planes, which collectively form a continuous medium, and the discontinuous structural planes themselves, characterized by their irregular shapes, thinness, and vastly different mechanical properties compared to the adjacent rock masses. As such, the structural plane becomes a potential slip surface during slope failure. Therefore, in order to study and analyze the failure mechanism of rock slope, it is necessary to explore innovative methods and conduct in-depth research on the nonlinear and discontinuous characteristics of the structural planes. The commonly used methods for slope-stability analysis are the limit equilibrium method (LEM) [1; 2; 3], limit analysis method (LAM) [4; 5], and other numerical methods. The first two methods are based on the assumption of elastic and perfectly plastic material orrigid and perfectly plastic material, ignoring the loading process and only considering the ultimate load at the time of structural failure. Therefore, they are mostly used for simple two-dimensional problems, are not suitable for solving complex three-dimensional problems, and cannot simulate the process of slope transformation from continuous-medium to discontinuous-medium when slope failure occurs. With the popularization of computers and the improvement in computational efficiency, the use of numerical methods to analyze slope stability has gradually become mainstream [6]. These numerical methods can not only satisfy the mechanical equilibrium conditions while considering the nonlinear constitutive relation of materials, but also demonstrate the development process of the plastic zone during slope failure, which is suitable for solving slope problems with complex conditions. Since [PERSON] [7] proposed the finite-element method-strength-reduction-method (FEM-SRM) in 1975, FEM has gradually become a popular numerical method for slope-stability analysis [8; 9; 10]. [PERSON] et al. [11] constructed a 3D slope model by extending the 2D model longitudinally to study the effects of the dilatancy angle using the PLAXIS 3D FEM with the built-in strength reduction technique. The results showed that the effects of the dilatancy angle on the convergence of 3D and 2D slope models are different. [PERSON] et al. [12] proposed a 2D and 3D slope-stability finite-element limit equilibrium method using elastic finite-element stress fields and indicated that FEM can be applied to solve various slope problems. The FEM also introduces a large number of special elements (such as joint element [13; 14], and thin layer element [15; 16]) to simulate the nonlinear characteristics of the slope structural plane. However, this will put forward a high requirement for meshing, which not only requires the mesh near the discontinuity to be dense enough to ensure the computational accuracy, but also requires the mesh of ordinary elements and special elements to satisfy the compatibility condition on the boundary. Furthermore, in the dynamic case, despite the introduction of special elements, the elastic-plastic constitutive relationship adopted by the finite element makes it difficult to simulate the stick and debonding of discontinuous interfaces. Moreover, in the calculation process, the stiffness matrix of the whole region needs to be updated even if the nonlinear relationship only appears in the local region.