## 4 ABAQUS Finite Element Simulation
### Model Establishment  
In this paper, a three-dimensional model of a composite foundation for bag grouting pile is established, and the essential components include the bag grouting pile, bedding layer, and soil layer. Considering the boundary effect caused by the construction of the bag grouting pile, the model height was taken as twice the pile length, i.e., 24 m, and the width was taken as 10 m. Nine piles were arranged in a square configuration, and graded loading was applied to the pile in the middle with a maximum loading of 360 kN. The pile spacing was 1.3 m, the pile length was 12 m, the pile diameter was 0.4 m, and the thickness of the bedding layer was 0.6 m.  
In the composite foundation model of the bag grouting pile, the simulation was carried out by employing three eight-node solid units, while the principal model of both the pile body and bedding layer was represented using a linear elastic model. As the project involved foundation reinforcement treatment in a soft soil area, the influence of principal stresses on the calculation results was relatively insignificant. The parameters were easily determined and can reflect the actual deformation under load. Therefore, the Mohr-Coulomb model could be chosen in combination with the calculation procedure [6,8,9,16]. The parameters of this model were determined according to the static touching and geological drilling data of this project, combined with the commonly accepted range of soil and pile parameters found in the literature [6,17,18]. After undergoing multiple trial calculations, the specific parameter values were finalized and are presented in Tables 3 and 4. The interaction between the contact surfaces consists of two parts: normal action and tangential action [15], and two pairs of contact surfaces were set in this model. The normal action between the bag grouting pile and the soil around the pile is \"hard contact\", and the tangential action of the friction formula is \"penalty\". The friction coefficient between the geotextile bag and the soil is 0.5-0.6 according to the literature [18], and it was set as 0.6 in this paper. The normal action is \"hard contact\", and the tangential action is frictionless. Considering the effect of grouting pressure, the expansion coefficient of the pile body was set and the grouting pressure was simulated using the heating method. We set displacement constraints in the X and Y directions (U1 = 0, U2 = 0) and fixed constraints at the bottom of the model (U1 = U2 = U3 = 0). During the grid partitioning, special attention was given to locally refining the soil elements around the pile to analyze the characteristics of the pile-soil contact. During the model's establishment, careful consideration was given to the factors that contribute to soil deformation, such as the self-weight stress of the soil and other influencing factors. Consequently, ground stress equilibrium was required before graded loading. After the equilibrium, nine analysis steps were set, and the contact action of the pile-soil interface was defined in the \"interaction\" module. Finally, the graded loading was conducted. The model schematic diagram is shown in Figures 14 and 15, and the settlement cloud of the model at maximum loading is shown in Figure 16.  
Figure 16: Model settlement cloud map at maximum loading.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **Mass Density/kN/m3** & **Young’s Modulus/MPa**[17] & **Poisson’s Ratio** & **Expansion Coefficient** \\ \hline Bedding layer & 21 & 4.5 & 0.25 & - \\ Pile & 23 & 20,000 & 0.20 & \(10^{-5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Pile body and cushion parameter value table.  
Figure 14: Calculation model of composite foundation with bag grouting pile.  
Figure 15: Pile meshing.