# Performance Analysis of an Improved Gravity Anchor Bold Expanded Foundation
## 3 Finite Element Model
### Finite Element Model in ABAQUS
#### 3.3.2 Loading Method and Analysis Steps  
The model is subjected to a variety of forces including gravity, prestress, overburden pressure, vertical force \(V\), horizontal force \(H\), torque \(T\), and bending moment \(M\). The load used in the simulation is the extreme condition data in the existing project. The model is simplified, and the upper soil of the foundation is not modeled. The calculated uniform earth pressure is applied to the top of the foundation. The bending moment and concentrated force are applied to the center point of the top of the flange. The center point is coupled with the top surface of the flange. Figure 9 shows the details of the load application. Table 6 shows the specific value of the above load. The negative sign indicates the negative direction of the coordinate axis.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Gravity (m/s\({}^{2}\))**} & **Uniform Distributed Soil** & \multirow{2}{*}{\(V\) (kN)} & \multirow{2}{*}{\(H\) (kN)} & \multirow{2}{*}{\(T\) (kN\(\cdot\)m)} & \multirow{2}{*}{\(M\) (kN\(\cdot\)m)} \\  & **Pressure (USP) (Pa)** & & & \\ \hline \(-9.8\) & \(-49\),\(371.4\) & \(-4779.86\) & \(-917.19\) & \(-7254.68\) & \(100\),\(560.8\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Load data under extreme conditions.  
Figure 9: (a) Point-surface coupling and (b) location of the load.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Contact Pair**} & \multirow{2}{*}{**Type**} & **Tangential Behavior** & \multirow{2}{*}{**Normal Behavior**} \\  & & **(Coefficient of Friction)** & \\ \hline Flange–Anchor plate 1 & & 0.80 & \\ Anchor plate 1–HSGL & & 0.70 & \\ Foundation–Anchor plate 2 & & 0.70 & Hard contact \\ Foundation–Soil & & 0.40 & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Contact parameters.  
To obtain the initial stress of the prestressed anchor bolt, the model is simplified. The prestressed anchor bolt adopts the T3D2 element, which does not consider the modeling details of bolt holes and bolts so as to improve the calculation efficiency and reduce the tolerable accuracy. As shown in Figure 10, the unit is divided into three sections, and the upper and lower sections are built into the flange and anchor plate. Because there is no bond between the anchor bolt and the surrounding concrete, there is no constraint between the element of the middle section and the surroundings. The model uses the cooling method [50] to apply tensile stress to the prestressed anchor bolts, without considering the influence of the tensioning sequence, and applies tensile stress to all anchor bolts at the same time. The tension control stress \(\Delta\)\(\sigma\) is calculated according to the following expression:  
\[\Delta\sigma=\mathrm{E}\alpha\Delta\mathrm{T} \tag{15}\]  
where E is the elastic modulus of the prestressed anchor bolt; \(\alpha\) is the linear expansion coefficient of prestressed anchor bolt; and \(\Delta\)T is the difference in the cooling temperature.  
The process of nonlinear analysis of the model includes six steps:  
Step 0: Set up the in situ stress balance analysis step, only retain the soil components, calculate the displacement of the soil, and ensure that the displacement of the soil under the action of self-weight is small enough. The maximum vertical displacement of the model is 4.709 \(\times 10^{-12}\)  
Step 1: Activate the foundation and other components and apply gravity and earth pressure.  
Step 2: The prestressed anchor bolt tension simulation.  
Step 3: Apply vertical force \(V\).  
Step 4: Apply horizontal force \(H\).  
Step 5: Apply horizontal torque \(T\).  
Step 6: Apply bending moment \(M\) and the calculation is terminated when the specified load is applied.