# A Partitioned Rigid-Element and Interface-Element Method for Rock-Slope-Stability Analysis
## 1 Introduction
Therefore, the conventional FEM is inefficient in solving complicated discontinuity issues. In 1999, [PERSON] [17] proposed a minimal remeshing finite-element method for crack growth. This method allows the crack to be arbitrarily aligned within the mesh. For severely curved cracks, remeshing may be needed, but only away from the crack tip, where remeshing is much easier. Then it evolved into a novel method called the extended finite element method (XFEM) and has subsequently been developed quickly worldwide. XFEM can be used to simulate heterogeneous materials with voids and inclusions, interfaces of bimaterial, and two-phase, so it is a possible computational alternative to treat slope instability, concrete cracking, and interfacial problems [18]. With the in-depth study of numerical methods, the numerical methods based on the continuous medium hypothesis can hardly meet the requirements of researchers for calculation accuracy, and the numerical simulation of complex structural planes in the rock slope has gradually developed into discontinuous medium methods. The continuum medium method is dominated by FEM, and the discontinuous medium method is dominated by the discrete element method (DEM) [19] and discontinuous deformation analysis (DDA) [20]. [PERSON] et al. [21] presented a numerical investigation into the rainfall-induced instability mechanism of a jointed rock slope with two joint inclinations of dipping 45\({}^{\circ}\) and 60\({}^{\circ}\) and the corresponding safety factor using the two-dimensional DEM, where the non-uniform strength reduction approach is employed. The results show that the proposed DEM strength reduction provides a feasible approach to analyze the rainfall-triggered instability of the jointed rock slope. [PERSON] et al. [22] took an anti-dip layered rock slope supported with anchor cables that failed owing to flexural toppling as an example, and took the DDA as the main analytical tool. The rationality of DDA was verified by correctly simulating the failure state of the anti-layered rock slope, and the underlying failure mechanism was studied. In recent years, the coupled FEM-DEM approach [23] has been widely used. In this method, DEM is used in the discontinuous medium region and FEM is used in the continuous medium region, and the two regions are connected by defining a special transition layer, which can be used to simulate the failure process of local discontinuous and heterogeneous structures. However, DEM and DDA have the following limitations in practical use: DEM and DDA can usually only simulate two-dimensional models or simple three-dimensional models; these two methods require many mechanical and kinematic parameters to be determined before calculation, but the relationship between these parameters and the macroscopic properties of object is not clear; and most importantly, the DEM and DDA have high requirements for computer performance and are time-consuming when solving large and complex slope stability problems. The rigid element method (REM) [24; 25] is another numerical method that can simulate structural planes in rock slopes. The REM regards the system as a mass of rigid elements connected by springs distributed on contact surfaces, and the strain energy of the structure is only stored at the interface between the rigid elements. Compared with FEM, REM can solve the problems of cracking, dislocation, and sliding between elements. Compared with DEM and DDA, the computational efficiency is greatly improved. However, since the displacement interpolation function of REM is first-order, the displacement has only first-order approximation. In addition, the node stress cannot be obtained directly by REM, but only indirectly by the surface force on the interface. Therefore, the accuracy of displacement and stress solved by REM is low, which makes it difficult apply to practical slope stability analysis.