# Slope Failure of Noncohesive Media Modelled with the Combined Finite-Discrete Element Method
## 1 Introduction  
Slope failure, including rock slide and landslide, is particularly detrimental and hazardous to human lives and engineering infrastructures [1]. Therefore, much attention has been paid to the slope stability analysis from geotechnical communities during the past decades. Generally, slope failure is caused by instability triggered by internal or external factors. Among all these factors, earthquake excitation [2] and rainfall [3] have been recognised as major causes. Apart from the triggering of slope instability, the inherent failure mechanism, failure process and postfailure behaviour are also of significance. Methods used to investigate slope instability can be categorised as experimental and numerical. Researchers used to conduct shaking table tests and other experimental approaches to investigate the failure of slopes [4; 5]. Though experimental studies are direct, they are expensive and time-consuming, and it is not easy to perform large-scale parametric studies. Consequently, numerical modelling has become popular in recent decades. There are a number of numerical methods that can be employed to examine the slope instability and the failure process. Since discontinuous and large displacements are involved in slope failure, traditional finite element method (FEM) is not best suited for this sort of analysis. It is argued that thediscrete element method (DEM) is naturally accommodated for discontinuous problems. [PERSON] and [PERSON] [6] analysed the stability of jointed rock slopes using explicit DEM UDEC. In reference [7], [PERSON] et al. employed an implicit discontinuous deformation analysis (DDA) for the dynamic analysis of a slope in the Taiwan Chi-Chi earthquake. Other computational methods contributing to the development of slope stability analysis include the material point method (MPM) [8; 9], the smoothed particle hydrodynamics (SPH) [4; 5], the meshless method [10; 11] and the extended finite element method (XFEM) [12]. In this study, the two-dimensional combined finite-discrete element method (FDEM) is employed. The FDEM is a special branch of the DEM. It aims at solving large-scale transient dynamics where discontinuous entities and multiple contacts are involved. The method has been developed since the 1990s [13; 14]. In the FDEM, each element is a discrete element. Within each discrete element, finite element mesh is embedded and thus more accurate evaluation of contact forces and deformation becomes possible. Details on the FDEM can be referred to in the monographs of [PERSON] and his coworkers [15; 16; 17]. The FDEM has been employed in a variety of brittle and quasi-brittle materials in recent years [18; 19; 20]. Regarding slope failure modelling of noncohesive media with the FDEM, MR contact detection is a very important aspect to determine whether element pairs are in contact or not. Further details on the MR contact detection algorithm can be referred to [16; 21]. Previous work on geotechnical considerations with the FDEM is traceable. A simple rock fall problem under gravity was given in reference [22] for the illustration purpose of the Y-GUI. [PERSON] et al. [23] simulated the instability of a homogeneous slope along a circular sliding surface under gravity with the FDEM. Their results were compared with those from limit equilibrium method (LEM) and FEM, and factor of safety was calculated. [PERSON] et al. [24] performed slope stability analysis using the FDEM, and presented examples including rock fall, toppling failure, cliff recession and planar slide. However, geometries of these given examples were simple and regular. Later, algorithmic developments [25] were included into the Y-Geo code which is based on the FDEM. Examples on cliff recession were presented, and emphasis was given to the fracture and failure of rocks. Recently, [PERSON] et al. [26] examined the stability of an ancient slope in western Beijing, China, under gravity with the FDEM, and compared their results with field surveys.