## 3 Characterization of Anchor Cable in FDEM
### The Existing Characterization of Anchor Bolts in FDEM  
At present, there are two main methods for the characterization of anchor bolts in FDEM: one is the one-dimensional element model proposed by [PERSON] et al. (2013) [35] and [PERSON] et al. (2015) [36], which is mainly used for the simulation of steel bars in reinforced concrete structures and anchor bolts in tunnel engineering; the other is the entity element model proposed by [PERSON] et al. (2019) [37] and [PERSON] et al. (2022) [38] who both applied this method to rock bolt reinforcement in deep-buried tunnels. (a) One-dimensional element model  
In the one-dimensional element model method, the bolt element is considered a one-dimensional, non-thickness line element. The coordinates of the two endpoints of each cable are given in the input file, and the intersections of the two endpoints with the triangular and joint elements are defined as reference points. The reference points are grouped in pairs to form calculation couples, where the calculation couple in the triangular element is called the bolt triangular element, and the one in the joint element is the bolt joint element (Figure 3). The anchor bolt established by the one-dimensional element method has the following shortcomings:  
(1) The calculation process is cumbersome. Considering the complex stress path, the state of the anchor bolt needs to be determined in real-time, and the elastic foundation beam theory requires a large number of initial parameters and inadvertently increases  
Figure 2: Comparison of the reinforcement effect of the slope at the hole of sediment releasing tunnel of Zipingpu Water Conservancy Project. programming costs, which is unfavorable to the calculation efficiency in large-scale numerical implementation. 2. Prestress cannot be applied. At present, prestressed cable bolt is widely used in many geotechnical projects, and the lack of this function dramatically limits the applicability of this technology. 3. The failure criterion of the bolt is doubtful. When a bolt joint element breaks, only this one fails and exits the calculation, while the other bolt triangular and bolt joint elements continue to play a role, which may make the analysis result too conservative. 4. The diameter of the bolt is ignored. At the laboratory test scale, the bolt occupies a specific space, which cannot be ignored relative to the sample size [34]. If the one-dimensional element method is adopted, it will inevitably introduce errors in the calculation results. 5. The interaction and coupling mechanism between the cable and anchorage body, as well as between the rock mass and anchorage body, cannot be reflected. The calculation of the one-dimensional element method is carried out in the background and it applies the results to the corresponding node in the form of force. There is no entity element modeling such as anchor cable and anchor resin to participate in the calculation, and critical physical phenomena when various parts interact are missing. 6. Entity element model The entity element model method focuses on studying the anchor bolt restraint mechanism and the interaction characteristics of the bolt structure with the anchorage body, which requires fine modeling of the anchor bolt and anchorage body [38]. Among them, the anchor bolt and anchorage body are divided into triangular and joint elements, as in the case of rock mass. The resin-bolt and resin-rock interfaces are characterized by the joint element (Figure 4). In specific engineering calculations, the physical and mechanical parameters of the anchor resin and bolt are the same as those of rock mass. They are calculated together until the anchor bolt comes into play. Then, the initial stress of the anchor resin and bolt is reset to zero, and their respective properties are assigned before recalculation [38]. As a metal material, anchor bolt has apparent yield and strain hardening phenomena, and its constitutive modification is required. More details about the constitutive model can be found in [PERSON] et al. (2019) [37].