# Enlarged Head Pressure-Dispersed Anchor Cable for Foundation Pit Engineering Purposes
## 4 Numerical Simulation Analysis of the Anchor-Cable Support System
### Selection of Soil Constitutive Model and Calculation Parameters
#### 4.1.1 Calculation of Model Size and Determination of Boundary Conditions  
The basic rules for the shape of the foundation pit in this project are as follows: The upper part of the foundation pit had a slope of 3 m with a slope ratio of 1:1.5. Two-axle mixing piles were set around the foundation pit to block the first layer of the groundwater. The spacing between the supporting piles was 1.2 m. Rotary jet grouting piles were constructed in the spacing between the supporting piles, which jointly blocked the soil between the piles and acted as a water-stop curtain. The pumping well was set between the support pile of the foundation pit and the twin-axle mixing pile to discharge the second layer of groundwater. The horizontal spacing of the anchor cable was 2.4 m. According to the research on the influence range from an earlier study [26], the vertical calculation depth was 2-4 times the excavation depth, and the horizontal calculation length was 3-4 times the excavation depth from the edge of foundation pit outwards.  
The three-dimensional space model was established using the FLAC3D. In Figure 12, the CD section of the foundation pit was selected as a cycle of a support structure, i.e., the distance between two support piles was the width used for the model calculation. The coordinate origin was in the middle of the model top surface; the XY plane was the horizontal plane. The vertical pit wall was the X-axis, the outer pit was 35 m, and the inner pit was 25 m. The vertical direction was the Z-axis, and the model height was 30 m. The Y-axis was along the pit wall, and the width of the foundation pit was 3.6 m.  
When dividing the grid in this study, on the one hand, considering the requirement of the accuracy of calculation and the limitation of computer operation ability, the number of grids selected should not be not too large. On the other hand, for key research areas, the grid needs to be encrypted. The final model was divided into 15,720 zones, and the grid model is shown in Figure 16. The boundary condition constraints are the parallel faces close to the bottom of the anchor cable and are set as free constraints, and the other faces are set as fixed constraints. In this way, in the process of drawing, only the anchor solid will produce displacement, while the anchor head will not, so the displacement of the anchor cable can be used as a judgment of the anchoring effect. The boundary conditions for flow and displacements are shown in Figure 17.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & **Normal Phase** & **Tangential Coupling** & **Friction** & **Cohesion/N** & **Tensile** \\  & **Stiffness/kPa/m** & **Stiffness/kPa** & **Angle/**\({}^{\circ}\)** & **Cohesion/N** & **Strength/kPa** \\ \hline Interface & \(8\times 10^{8}\) & \(8\times 10^{8}\) & 35 & \(6\times 10^{6}\) & \(5\times 10^{3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Grout–soil interface parameters.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & **Density/kg/m3** & **Young’s** & **Compressive** & **Tensile** & **Section Area/m2** \\  & **Modulus/kPa** & **Strength/kPa** & **Strength/kPa** & **Section Area/m2** \\ \hline anchor rope & 7864 & \(1.95\times 10^{8}\) & \(3.90\times 10^{5}\) & \(1.32\times 10^{6}\) & \(5.60\times 10^{-4}\) \\ \hline Parameter & Shear Modulus/kPa & Cohesion/N & Friction Angle/\({}^{\circ}\) & Rigidity/kPa & Perimeter/m \\ anchor rope & \(8.87\times 10^{5}\) & \(4\times 10^{6}/7\times 10^{6}\) & 35 & \(3\times 10^{6}/2.51\times 10^{6}\) & \(1.1/1.885\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Bolt parameters.