## 5 Stability Analysis of High Slope of Carbonaceous Mudstone Based on Numerical Simulation
### Stability Analysis of Slope After Support  
#### 5.4.1 Selection of Support Scheme  
According to the design specifications, the use of anchor cables and frame beams is an effect support method for high and steep road cut slopes [37]. In response to the support requirements of high cut slopes with carbonaceous mudstone, this study selected prestressed anchor cables and frame beams as the optimal support scheme through comprehensive analysis. This support method is suitable for fractured mudstone slopes with a slope ratio ranging from 1:0.5 to 1:1.5 and can effectively address engineering issues such as rock softening and disintegration. As shown in Figure 15, the support system mainly consists of two key components: prestressed anchor cables provide deep reinforcement, while frame beams form surface protection. By combining the deep anchoring of prestressed anchor cables with the shallow constraint of frame beams, the overall stability of the slope is significantly improved. In the installation of prestressed anchor cable frame beams, the first step is to prepare the construction site, accurately locate the drilling position, and set up the drilling equipment. Subsequently, drilling operations will be carried out according to the design perspective, and grouting treatment will be carried out immediately after the completion of hole cleaning and pre installation of anchor cables. Finally, on-site pouring and curing of reinforced concrete frame beams will be carried out. In this support scheme, the cast-in-place reinforced concrete frame beam mainly undertakes the function of slope protection, while the prestressed anchor cable serves as the core load-bearing component, transmitting tension to the stable rock and soil layer while exerting a suspension effect on the unstable rock mass. During the stress process, the anchoring section forms a whole with the stable bedrock through cement mortar, and the load transmission is achieved through the bonding effect between the slurry and the surrounding rock, thereby improving the stress state of the rock and soil mass, enhancing its resistance to deformation, and effectively suppressing the development of potential sliding surfaces. And the free section is usually deployed within the potential slip zone, mainly responsible for transmitting the anchor head tension to the anchoring section. This segmented design enables the anchor cable system to fully exert its reinforcement effect, significantly improving the overall stability of the slope by coordinating the deformation behavior of the rock and soil mass. Figure 15: Schematic diagram of the composite overall structure of prestressed anchor cable and frame beam support: (**a**) anchor cable + frame beam plan; (**b**) anchor cable + frame beam section. According to the design specifications, the specific design parameters for the support are as follows: The installation angle of prestressed anchor cable is set to 20\({}^{\circ}\), the vertical spacing arrangement adopts a 3 m \(\times\) 3 m equidistant grid, the fixed length of the anchorage section of the anchor cable is 6 m, the free section extends 1.5 m below the potential rupture surface, the prestress is set to 200 kN, and the grouting material is M30 strength grade cement mortar. The frame beam is made of cast-in-place C30 concrete, and the cross-sectional size of the beam body is uniformly designed as 40 cm \(\times\) 30 cm. The detailed technical parameters of the support structure are summarized in Table 5.  
The structural parameters of the support scheme are set as follows: the linear elastic constitutive relationship is used to simulate the mechanical behavior of the slope, where the free section is discretized with truss elements and prestress is applied, and the anchorage section is characterized by a combination of beam elements and interface elements.