## 1 Introduction  
The deformations and failures analysis of slopes is a representative problem in geotechnical engineering [1], which have been widely performed in both scientific and practical research. At present, many numerical simulation methods have been used to analyze the deformations and failures of rock slopes, such as the discrete element method (DEM) [2, 3, 4], finite element method (FEM) [5, 6, 7], finite difference method (FDM) [8], boundary element method (BEM) [9], material point method (MPM) [10, 11, 12], general particle dynamics (GPD) [13, 14], and numerical manifold method (NMM) [15]. These numerical simulation methods are developed from the primitive limit equilibrium method (LEM). In addition, the smoothed particle hydrodynamics (SPH) method [16] and 2-D/3-D finite element code [17] also have been used to evaluate the stability of slopes. The Mohr-Coulomb failure criteria are the most commonly employed in numerical modeling to investigate the stability of slopes in the most research work [18, 19, 20, 21]. When analyzing the deformations and failures of jointed rock slopes, the most commonly used method is the DEM. Because the DEM is a numerical method based on discontinuities, it can be better applied to discontinuous deformations and failures and large displacements. For example, [PERSON] et al. [22] proposed the displacement-based discrete element modeling method (DSDM) to analyze the stability of jointed rock slopes with a potential sliding surface. [PERSON] et al. [23] used the DEM to simulate jointed rock masses and carried out numerical research on the progressive failure of rock slopes with non-permanent joints. [PERSON] et al. [24] evaluated the factors affecting the deformations and failures of a dangerous rock mass and the geological conditions of a highway slope in Yunnan Province using the DEM. In addition, a three-dimensional numerical analysis of the strength reduction of safety factors was carried out. [PERSON] et al. [25] used the discrete element simulation software 3 DEC to capture the basic three-dimensional characteristics of the landslide and form a post-failure structure similar to that observed in the field. In addition, [PERSON] et al. [26] used the DEM to analyze the strata and surface movement and damage caused by open-pit slope mining. [PERSON] et al. [27] carried out DEM numerical simulation by using an equivalent discontinuous model (EDM) to simulate rock movement and failure caused by mining. [PERSON] et al. [28] used the DEM to simulate the failure process of the Xiaogangjian landslide and especially considered the influence of the discrete fracture network (DFN) and rainwater infiltration. [PERSON] et al. [29] used the DEM to simulate the deformation behavior of slate slopes under the long-term influence of gravity and material metamorphism. [PERSON] et al. [30] used the DEM to simulate the deformation and sliding process of highly active slope elements and used the model to predict the slope behavior under the condition of wetting of geotechnical materials. [PERSON] et al. [31] used the discrete element simulation software 3 DEC to study the behavior of Xiandu Mountain rock collapse caused by Typhoon Morakot in 2009. The analysis successfully simulated the wedge failure of the landslide. In addition, the 3 DEC results also illustrate the local rock sliding phenomenon at the boundary of the source area. However, determining when the DEM iterative process can be appropriately terminated is still a difficult problem. The DEM calculations involve an iterative process that needs to terminate appropriately according to specific conditions. The number of iterative steps should be determined appropriately before the DEM modeling. Specifying the maximum number of iterative steps is the most common solution. When the specified maximum number of iterative steps is reached, the iterative process would be terminated. The common solution is very simple.