## 3 Characterization of Anchor Cable in FDEM
### The Combined One-Dimensional and Entity Element Models in FDEM  
The number of elements to divide a centimeter-scale anchor bolt model in a slope model with a height of hundreds of meters is huge (the diameter of the bolt has a limited effect on the calculation result of the whole model). At the same time, FDEM is an explicit algorithm, and small mesh sizes mean small time steps, which can lead to a geometric increase in the calculation time for a constant total physical time. In addition, many studies have demonstrated that the anchor cable failure generally occurs at the resin-rock interface or the anchor cable itself breaks (assuming that the free segment of the anchor cable can only bear the axial stress) [39]. Here, the cable, resin, and rock in the anchorage segment can be considered as a whole (i.e., anchorage body), so there is no need to consider the separate modeling of the anchor cable and resin, which can also be significant for studying the evolution law of the landslide-anchorage structure system while ensuring the accuracy and efficiency of the calculations. Therefore, entity modeling of the cable and resin is not desirable in the present study, but entity element modeling is still required to characterize the anchorage body. Finally, after describing the advantages and disadvantages of the anchor bolt characterization methods in the previous section, the combined one-dimensional and entity element model (ODEEM) method for anchor cables in FDEM (Figure 5) is proposed based with the actual needs of this study and is improved as follows:  
1. Simplify the modeling process and optimize the mesh size distribution. During modeling, only the anchorage body and anchor plate need to be established, while the anchor cable in the free segment can be characterized by adding the coordinates of the two endpoints to the input file. As a result, the larger the geometry dimension of the anchorage body, the more uniform the mesh size of the entire model, and the fewer  
Figure 4: Simplified bolt reinforced model [34]. the total number of elements, which greatly improves the efficiency of the dynamics calculations and is beneficial to the application of FDEM at the engineering scale. 2. Realizing prestressing in one-dimensional element model method and simplifying the process. Prestress is pre-considered in the constitutive relation of the bolt triangular element, which can transfer the pre-compressive stress of each segment of the anchor cable to the corresponding rock. Furthermore, the application process is simple: just write the setting value of the prestress in the input file. 3. Optimize the calculation process by adding a simplified constitutive relation of the anchor cable. The constitutive relation of the bolt joint element in the one-dimensional element method is complicated, and the calculation efficiency is low. Moreover, the object of the present study is the anchor cable, which is assumed not to be subjected to shear stresses. Therefore, a simplified anchor cable constitutive relation is added, as detailed below. FDEM divides the mesh into triangular elements and joint elements, where the triangular elements are only capable of linear elastic deformation, while the yielding and failure of the material are characterized by the joint elements. The bolt material in the one-dimensional element method is also applicable to the above principle, where the triangular elements are still subjected to linear deformation only, and the yielding, hardening, and failure phenomena of the bolt all occur in the joint elements. The ODEEM method refers to the bolt's constitutive law proposed by [PERSON] et al. (2019) [PERSON] et al. (2019) and is appropriately simplified based on the anchor cable, which is the object of study (Figure 6), as shown in Equation (6). It is assumed that the free segment of the anchor cable does not bear compression and bending moment, and only axial tensile stress.