## 4 Numerical Results and Discussion  
Initially, a wave propagation comparison study was conducted between the web and flange of a 7.5 m U-pile and a plate having the same length and cross-sectional area as the web of the pile. This was completed in order to understand the added complexity of the U profile on wave propagation. In the case of wave propagation on the web of the \begin{table}
\begin{tabular}{c c} \hline \hline
**Defects Identifier** & **Defect Description** \\ \hline Defect A & 50 mm diameter hole \\ Defect B & 100 mm diameter hole \\ Defect C & 150 mm diameter hole \\ Defect D & 200 mm diameter hole \\ Defect E & 100 mm slot \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Defect scenarios considered. Figure 9: Defect scenarios using 50 mm, 100 mm, 150 mm, 200 mm diameter defects and a slot defect were considered. U-pile and the plate, a 12 \(\times\) 2 configuration shear transducer array, represented by 24 point sources, was placed at 1 m from one end of the web of the pile to excite the 10-cycle signal at 70 kHz central frequency. In the case of wave propagation in the flange of the U-pile, a 7 \(\times\) 2 configuration shear transducer array, represented by 14 point sources, was placed at 1 m from one end of the flange of the pile to excite the 10-cycle signal at 70 kHz central frequency. Apodisation of the amplitude of excitation signal was applied across each row of transduction points as shown in Figures 10 and 11. Figure 12a demonstrates how the shear waves propagated on the web of the U-pile. It is evident that as the shear wave propagated, a part of the signal energy travelled into the flanges of the U-pile and interacted with the edges, due to which the signal spread over time. Figure 12b,c illustrates the excitation signal on the web when it reached the distances of 5.65 m and 7.12 m, respectively. It can be noted that the excitation signal at 5.65 m had higher Y and \(Z\) displacements due to the higher reflections from the edges at that distance. Figure 11: Apodisation of the amplitude of the excitation signal applied across each row of 7 \(\times\) 2 array transduction points. Figure 10: Apodisation of the amplitude of the excitation signal applied across each row of 12 \(\times\) 2 array transduction points. Figure 13 exhibits the shear wave propagation in the plate travelling in a similar manner as in the web of the U-pile. Figure 14 shows a wave propagation comparison between the plate and the web of the U-pile. Simulated data collection was carried out at 0.5 m ahead of the transduction points in both the plate and the U-pile in order to clearly capture the excitation signal and back wall reflection for comparison purposes. Results were normalized to the excitation signal on the web of the U-pile. The back wall reflection signal from the U-pile web was 11.5% higher than that from the plate. This is because a part of the signal energy reflected from the edges of the plate, leading to destructive interference, whereas in the case of the web of the U-pile, the signal energy travelled through the flanges, avoiding interference. Figure 12: (**a**) Shear wave propagation in the web of the U-pile, (**b**,**c**) the excitation signal when it reached the distance of 5.65 m and 7.12 m, respectively. Figure 15a illustrates how the shear wave propagated in the flange of the U-pile. It can be perceived that as the wave propagated, a part of the signal reflected from the edge of the flange and travelled into the web of the structure, causing the signal to lose energy in the flange. Figure 15b,c illustrates the excitation signal in the flange when it reached the distances of 5.65 m and 7.12 m, respectively. Results were normalized to the excitation signal on the web of the U-pile as shown in Figure 12. The results demonstrate that the excitation signal in the flange at 5.65 m and 7.12 m was respectively 35% and 46% less than the excitation signal in the web at the same distance.