# Driven Pile Effects on Nearby Cylindrical and Semi-Tapered Pile in Sandy Clay
## 3 Numerical Model and Verification  
The analysis method used in this paper involved two steps: (1) driving a single pile into the soil without any other structures and comparing the results with the field measurement presented by [PERSON] (1981) [51]; (2) driving the pile adjacent to the nearby existing pile and carrying out parametric studies on the pile shape and pile spacing effects, pile bending moment, axial force, and lateral movement. The Abaqus/explicit [38] was adopted to drive the pile from the initial depth to the final position. A three-dimensional model was chosen to complete the simulation phase, and the results were compared with the case study by [PERSON] (1981). The driven pile induced soil movement, which developed a bending moment and axial forces on the existing nearby piles. Damage or cracking (concrete pile) could occur caused by these developed forces. The response of the adjacent piles during the vibration procedures could be studied by means of parametric values such as pile shape and pile spacing to observe the influence of these parameters on the generated axial forces, bending moment, and lateral movement. Commonly, the pile is driven until it reaches a harder stratum. Figure 1 shows the fundamental problem and describes some of the same parameters of the geometric as the one provided by [51]. Figures 2 and 3 show the geometry of the soil and pile models. A uniform soil layer was taken (sandy clay), the diameter of the concrete pile was 0.5 m, the length was evaluated as 10 m, and 60\({}^{\circ}\) was taken as the conical tip angle. A total of 25,120 nodes and 25,120 elements were used to build the model. Figure 1: Driven pile near the already-installed pile. The material properties adopted are listed in Table 1. Their characteristics were the same as the model proposed by [15; 51; 52]. Hence, the reliability of the method was evaluated by comparing the results with the field measurement presented by [PERSON] (1981). An elastic model was used to capture the pile behavior, and the Drucker-Prager model was used to define the elastoplastic behavior of the soil with the friction angle (\(\phi\)) set to 25\({}^{\circ}\), the flow stress ratio (K) set to one, and the dilation angle (\(\psi\)) set to 1\({}^{\circ}\). Due to the computer size limitation during the dynamic simulation, only one part of the model was mapped in a computational domain. Generally, the part of the ground that was expected to have a significant effect was mapped. The remaining area was taken into account in the definition of the boundary conditions, which intended to limit the wave reflection. These boundary conditions were intended to capture the wave reflection during a dynamic simulation of pile driving. The reflection of the outward-propagating wave could be caused by the fixed boundary conditions, by adding energy inside the model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & **Elastic File** & & \\ \hline Diameter & Length & Density & Young’s modulus & Poisson’s ratio \\
0.5 m & 10 m & 2500 kg/m\({}^{3}\) & 40,000 MPa & 0.25 \\  & & **Sandy Clay** & & \\ Friction angle & Cohesion & Density & Young’s modulus & Poisson’s ratio \\
25 degrees & 15 kPa & 2000 kg/m3 & 80 MPa & 0.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Soil and pile material properties. Figure 3: Three-dimensional model equivalent. Figure 2: Two-dimensional section of the model. An infinite element at the side and bottom part of the finite element mesh to prevent wave reflection was used in [17; 20]. The boundary element was proposed by [47] to capture the soil behavior. Other papers used artificial boundaries to absorb the wave deriving from the driven pile [15; 16; 48; 52]. A regular augmentation of the damping was adopted for absorbing the wave and its limited the errors before model verification [53]. An artificial boundary can be summarized in the following steps:  
1. Divide the side and bottom part of the finite element mesh into subzones
2.