# Research on the Self-Drilling Anchor Pull-Out Test Model and the Stability of an Anchored Slope
## 4 Self-Drilling Anchor Grouting Slope Simulation Analysis
### Slope Model Optimization  
#### 4.2.1 Numerical Model and Calculation Parameters  
A slope reduction scheme was implemented for the original slope to reduce the slope load. The slope reduction design is shown in Figure 21. The design adopts a three-tier slope reduction with a slope ratio of 1:1 and a 2-m-wide platform. Based on the engineering geological profile, the original slope and its reduction were simplified using AutoCAD2020 software, and the schematic diagram was imported into FLAC3D software. The Extrusion module was employed for the preprocessing of the slope model grid. The model's coordinate system was defined such that the direction of horizontal sliding of the slope's geotechnical body was the negative x-axis, and the z-axis positive direction was from the bottom to the top of the slope. The coordinate origin was located at the outer side of the slope's toe. The model grid was divided at 1-m intervals. Boundary constraints were applied to the slope using the fix velocity command, with normal constraints applied to all surfaces of the slope except for the slope face, top, and bottom. The stratigraphy, boundary conditions, and model grid divisions are illustrated in Figure 22a for the original slope calculation model and Figure 22b for the slope calculation model after reduction. Figure 21: Slope design diagram. Figure 20: Site exploration map. In FLAC3D software, the soil is modeled by the Mohr-Coulomb constitutive model, which usually uses the bulk modulus (\(K\)) and shear modulus (\(G\)) instead of [PERSON]'s modulus (\(E\)) and [PERSON]'s ratio (\(\
u\)). The bulk modulus (\(K\)) represents the material's ability to resist volumetric changes, while the shear modulus (\(G\)) represents the material's ability to resist shear strain. Since \(K\) and \(G\) provide a more accurate description of material deformation, \(E\) and \(\
u\) need to be converted into \(K\) and \(G\) for numerical simulation calculations. The conversion formulas are as follows:  
\[K=\frac{E}{3(1-2\
u)} \tag{8}\]  
\[G=\frac{E}{2(1+\
u)} \tag{9}\]  
In the equation:  
\(E\) is the elastic modulus of the geotechnical material,  
\(v\) is the Poisson's ratio of the soil. The model parameters are detailed in Tables 3 and 4. Based on the displacement monitoring results in Figure 23, the maximum horizontal displacement of the original slope was 13.78 cm (along the positive x-axis). After the excavation treatment, this value decreased to 8.19 cm. The spatial distribution of horizontal displacement shows that the maximum displacement occurred at the middle section of the front edge of the slope before and after the excavation, with the displacement decreasing in both directions from the front edge to the rear edge and from the slope surface to the deep part of the slope body. It is noteworthy that the displacement peak at the front edge of the original slope reached 1.68 times that of the post-excavation condition, indicating that the removal of surface soil at the front edge effectively restrained deformation of the surface layer of the slope. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Anchor Bolt Type** & \begin{tabular}{c} **Young’s** \\ **Modulus** \\ **(MPa)** \\ \end{tabular} & \begin{tabular}{c} **Grouting** \\ **Cohesion** \\ **(N/m)** \\ \end{tabular} & \begin{tabular}{c} **Grouting** \\ **(Pa)** \\ \end{tabular} & \
\begin{tabular}{c} **Grouting** \\ **Friction Angle** \\ \end{tabular} &
\begin{tabular}{c} **Drilling** \\ **Diameter (mm)** \\ \end{tabular} \\ \hline Self-drilling anchor bolt & 2.0 \(\times\) 10\({}^{11}\) & 48.2 \(\times\) 10\({}^{3}\) & 11.4 \(\times\) 10\({}^{6}\) & 30 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Anchor parameters of the numerical model. Figure 23: Displacement contour in the X direction. Figure 24: Displacement contour in the Z direction. The vertical displacement analysis in Figure 24 shows that the displacement field before and after excavation has similar spatial distribution characteristics.