## 1 Introduction
However, it is obviously inappropriate in some cases, because too many iterations would be superfluous, while too few iterations result in inaccurate calculation results. Much research work has been conducted to address the above problems. For example, the overall displacements were investigated, and vector graphics of the overall displacements were plotted. [PERSON] et al. [32], [PERSON] et al. [33], and [PERSON] et al. [34] suggested that obvious changes in vector graphics could indicate that a slope has been deformed. Although the method is rational, it is only applicable to simple slopes. In other cases, vector graphics would be quite confusing, and the obvious changes in displacements would be difficult to estimate. Displacement characteristics are commonly used to reflect the deformations and failures of slopes. For example, in collapsed landslides [35; 36], the slope is stable at the beginning, compared with the size of the slope, the displacements of rock blocks are quite small. When the slope begins to be unstable, the average displacements around the sliding surface would increase by degrees, and the dispersion degree of the displacements of the rock blocks around the sliding surface would also increase by degrees. In traction landslides [37; 38], with the development of landslides, the mean of slope displacements would gradually increase. However, the rock blocks located around the sliding surface have broadly consistent mean of displacements. This means that the dispersion degree of the displacements gradually decreases. Recently, [PERSON] et al. [22] used the displacement-based discrete element modeling method (DSDM) to investigate the stability of jointed rock slopes. The procedure of the displacement-based method is as follows:  
(1) According to the geological conditions and the geographical location, the potential sliding surface is determined approximately;  
(2) In the established calculation model, the vertices around the determined potential sliding surface are determined before the iterative DEM modeling;  
(3) The iteration interval specified during the DEM calculation (e.g., at the 500 th step, the 1000 th step, etc. ), and the mean, the standard deviation (SD), and mean/SD of the displacements of marked vertices are calculated;  
(4) The authors analyzed the convergence of the mean/SD values. However, in the aforementioned displacement-based method, there is a problem that it needs to determine an obvious potential sliding surface before DEM modeling. In fact, in many cases, it is difficult to effectively determine an obvious potential sliding surface. The position of the sliding surface would directly affect the final results. Moreover, the displacement-based method only considers the displacements of rock blocks around the potential sliding surface, but the weights of blocks around the potential sliding surface are not considered in the displacement-based method. To address the above problems, in this paper, an energy-based discrete element modeling method is proposed for analyzing the deformations and failures of jointed rock slopes, which is combined with time-series analysis. The proposed method is a generalized form of the displacement-based discrete element modeling method. The proposed method considers not only the displacement of each block, but also the weight of each block. Moreover, the computational cost of the proposed method is approximately the same as that of the displacement-based discrete element modeling method. The objective of proposing the energy-based method is to generalize the displacement-based method. As mentioned several times, the most obvious shortcoming of the displacement-based method is that, it needs to previously determine the potential sliding surface before conducting the numerical modeling. In contrast, in the proposed energy-based method, there is no need to determine the potential sliding surface before DEM modeling. In other words, the displacement-based method is only applicable to the cases where the sliding surface can be easily determined.