# Research on Lateral Bearing Behavior of Spliced Helical Piles with the SPH Method
## 3 Finite Element Simulation
### Helical Pile Installation  
The original pile takes 1.3 s to sink, and the extended pile takes 1.47 s to sink. The last helical blade is fully inserted into the soil at a depth of 700 mm, and the helical pile is continuously rotated into the soil by shearing the soil with the blade and transmitting torque in the form of counter-thrust. The soil suffers a large plastic deformation. The maximum shear stress reached nearly 400 Kpa, gradually transitioning from 280 Kpa near the pile to zero. The particles in the surface soil layer bulge upwards, and the particles at a depth of 14 mm below the surface layer hold a shear stress of nearly 100 Kpa. The more muscular shear stresses occur mainly in the part of the pile in contact with the surface soil layer, below the soil layer at the locations near the pile body below the surface, and most of the pile tip (Figure 2). The stress areas from 1 to 4 are observed inside the soil layer of the original pile and the stress extends to the boundary until it is zero; the pile tip part interacts strongly with the soil, and the stress is centralized. The rest of the area's pile-soil interaction is generally due to the blade shearing the soil to guide down the helical pile. The stress area near the pile body is normal. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & **Parameters** & **Type** & **Parameters** \\ \hline Mat & RIGID & Mat & SOIL\_AND\_FOAM \\ RO & 7800 Kg/m\({}^{3}\) & RO & 1850 Kg/m\({}^{3}\) \\ E & 210 GPa & G & 24 MPa \\ PR & 0.3 & Bulk & 16.7 MPa \\ N & 0 & AO & 53.3 GPa \\ M & 0 & PC & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Pile and soil material. Figure 2: Finite element simulation of pile–soil installation process: (**a**) Original pile; (**b**) Extended pile. When t = 0.69 s, a wave peak occurs, and the torque is 270.67 N-m (Figure 3). The red area around the pile accumulates, and the soil is severely compressed and stressed. After the wave peak, the consolidated soil is destroyed due to blade shearing, the red area gradually fades, and the torque reaches the maximum value of 669.72 N-m when the stress is reduced. The maximum torque of the original pile was 700.38 N-m at 1.2 s, and the maximum torque of the lengthened pile was 699 N-m at 1.24 s. The results show that the maximum torque required for the lengthened pile and the original pile during the sinking process is the same, and there is no effect on the torque after the lengthening of the structure. When additional modifications are required to the keyword file for subsequent dynamic analyses [25], the analysis can be split into two sessions of research. The dynamic file is generated by invoking the *INTERFACE_SPRINGBACK_LSDYNA option [26], and the output corresponds to the dynain file, which corresponds to the position at the end moment of the sunken pile in the first session, as well as to the model cell stress and strain data. The state at the end of the first session of the sunken piles is used as the initial condition for the second session of the lateral loading for stress initialization. When additional models need to be added for import, *INCLUDE and *TRANSFORM can be used to make the appropriate adjustments to the model and keywords [27]. The end state of the spliced pile is retained after the complete sinking of the pile (Figure 2). The state at this point is given a horizontal load of 150 mm below the top of the pile along the x-direction, and the horizontal force is applied to the top of the pile in a gradual linear manner (Figure 2). The direct effect of the external forces acting on the model is expressed as kinetic and internal energy. At a deficient speed, the kinetic energy can be negligible compared to the internal energy. Therefore, when using this method for stress initialization, the preloading time should be relatively long to minimize the inertial force and the kinetic energy, and to avoid interfering with the subsequent dynamic analysis [28].