## 4 Finite Element Method (FEM) Simulation and Analysis of Impact Echo Test  
In connection with theoretical and numerical studies on piles, various researchers [31; 32] have shown that three-dimensional (3D) modeling results are very similar in general terms to those predicted by the usual one-dimensional (1D) solutions. In this study, impact echo test simulations of intact and defective piles were performed using the finite element program ABAQUS [33]. Numerical studies were performed on various cases of intact and defective piles, as shown in Figure 8. Each case was assumed to be a bored pile, and was 0.50 m in diameter (\(D\)), bearing on a stiff soil layer at 15 m length (\(L\)). Figure 8a is the case for an intact pile having a uniform diameter with no geometric and material defects, while Figure 8b,c are example cases of defective piles with material defect, such as having the poor concrete quality or weak material in a certain zone. Figure 8d-f are example cases of the pile with geometric defects, while Figure 8h-j are example cases of the pile with multiple defects. Figure 8b is an example case of a pile with uniform diameter but had a low-quality concrete material through its length, while Figure 8c is an example case with a material defect at a segment along the shaft length. Figure 8d is an example of a pile with a neck defect that was modeled by a decrease in the cross-sectional area at the position shown. In Figure 8d,h,j, necking at the sections were modeled with a gradual reduction in diameter to a minimum 10% decrease of pile diameter (\(D_{\text{n}}=0.9D\)) in the middle of the respective positions shown. Figure 8e is an example of a pile with bulge imperfection that was modeled by an increase in the cross-sectional area at the position shown. In Figure 8e,i,j, bulging at the sections were modeled with a gradual increase in diameter to a maximum of 20% increase of  
Figure 7: Pile defect identification scheme: (**a**) Flowchart for pile defect diagnosis; (**b**) Detailed flowchart for diagnosis based on reference reflection time and the number of peaks. pile diameter (\(D_{\rm b}=1.2D\)) in the middle of the respective positions shown. The pile and bearing soil layer were modeled in ABAQUS using three-dimensional 8-node linear brick elements of type C3D8R. The C3D8R element in ABAQUS is a general-purpose linear brick (continuum) element with reduced integration. Using the material properties \(\rho\) and \(E\), the wave speed (\(c\)) of the material was calculated using Equation (3). At this speed (\(c\)), the wave passed to the bottom of the pile and traveled back to the top of the pile in total time (\(t\)) as given by Equation (6). To be able to see the wave propagate along the length of the pile through time, the mesh is adequately refined to capture the wave travel accurately. It is adequate to have the impact load take place over the span of 10 elements [33], and this means that the impact of duration times on the wave speed must equal the length of 10 elements. In this study, an element mesh size of 0.02 m was considered, which was consistent with the duration of impact as produced with the maximum force generated with typical handheld hammers and range of wave velocity of normal weight concrete used for piles. To keep the mesh uniform, the same size of the element (0.02 m) was considered for meshing in both the longitudinal and the transverse directions. Model boundaries of 5 times the width of the pile were considered in the horizontal direction and from the bottom of the pile in order to minimize boundary effects. The bottom boundary condition was constrained against displacement in all three directions, the vertical sides were constrained in the horizontal direction, and the top surface boundary was free. The analysis was based on an explicit method (ABAQUS/Explicit) that was especially well-suited for efficiently solving high-speed and short duration dynamic events, such as an impact load, which required many small increments to obtain a high-resolution solution.