# A Partitioned Rigid-Element and Interface-Element Method for Rock-Slope-Stability Analysis
## 1 Introduction
To solve such problems as slope instability, concrete cracking, and opening or closing of internal contraction joints in the dam, [PERSON] [26] proposed an interactive method of partitioned finite elements and interface elements (PFE-IE). This method divides the structure into several continuous and locally discontinuous interfaces. Treating nodal displacement as a variable, the elastic deformation of the continuum is solved using PFE, and the rigid displacements in each body and the constraining internal forces on the interface are solved using IE based on the continuous stress condition and the static force equilibrium condition. The PFE-IE method absorbs the advantages of FEM, DEM, and DDA and partitions the large-scale model with structural discontinuity and nonlinear mechanical properties so that each region can be solved independently and the solution speed can be improved. Moreover, the PFE-IE method can conveniently calculate the stability safety factor of rock slopes with the SRM [27]. With PFE-IE method, most of the time is spent solving the stiffness matrix of the elastic body in the slope. However, in practice, when the rock slope is in the limit equilibrium state, the elastic deformation of the rock mass can be ignored compared with the deformation at the structural plane. Therefore, we would like to find a new method to treat the rock mass as a rigid body, which can greatly improve the computational speed with less impact on the calculation accuracy. In this paper, the partitioned rigid elements and interface elements (PFE-IE) method is proposed as an improvement to the existing PFE-IE method: the structure is divided into several rigid bodies and discontinuous structural planes, on which the partitioned rigid element and interface element are established, respectively, so that the contact forces and displacements on the nodes between the rigid elements and the corresponding interface elements can be coupled. By taking the contact force of node pairs and the displacement of the rigid body centroid as mixed variables, the Lagrange multiplier method is used to establish a potential energy functional according to the principle of minimum potential energy. Then, the governing equations of PFE-IE are obtained through variational calculus and solved using the nonlinear contact iterative method and the incremental method. Finally, taking the failure of all contact node pairs as the criterion of slope failure, the stability safety factor of rock slope can be calculated using SRM. PFE-IE method absorbs the advantages of PFE-IE method and only performs nonlinear iteration on possible discontinuous structural planes, which greatly improves the efficiency of numerical calculation. The PFE-IE method can be applied to analyze the dynamic stability of a high steep rock slope [28; 29] and can be coupled with the smoothed particle hydrodynamics (SPH) method to investigate the effects of a landslide-generated wave (LGW) for the the safety of reservoir areas [30]. As an improvement to the PFE-IE method, the PRE-IE method also has the potential to solve these problems. Therefore, future research could focus on using the PRE-IE method to analyze the dynamic behaviors of structures such as slopes, dams, and retaining walls and investigate the coupling of the PRE-IE method with other emerging methods [31; 32] to monitor the stability of reservoir bank slopes and the structural health of dams.