## 3 Application
### Analysis of Test Results  
According to the pre-inversion results of several pile-side profiles, when the number of iterations reached 10, the inversion results basically reached stability. Hence, when the inversion of detection results was carried out, the number of iterations was unified to 10. In addition, the receiving-angle was set at 45\({}^{\circ}\), the sampling density was 1 m, and the detection profile model grid was meshed into a 0.5 m \(\times\) 0.5 m square grid. Figure 5 shows the inversion results of the three pile side profiles, C3-C6, C6-C1, and C6-C5, before grouting. The X-coordinates in the figure are the spacing between the transmitting and receiving holes, and the Y-coordinates are the depths from the ground downwards, all in m (the same below). Comparing the three profiles, combined with the geotechnical investigation data near the pier, the following common stratigraphic interfaces can be seen: (1) the interface between mudd and muddy silty clay around 14 m depth; (2) the interface between muddy silty clay and silt near 20 m depth; (3) the interface between silt and cohesive soil around 27 m depth; (4) the interface between cohesive soil and silty clay near 33 m depth; (5) the interface between silty clay and silt near 51 m. The propagation velocity of elastic wave in the layer above 14 m was below 900 m/s, which is due to the fact that the layer above 14 m was mostly mud or muddy soil. In addition, the layer was basically in a flow-plastic state and was relatively soft; the propagation velocity of elastic wave in the layer from 20 to 27 m was about 1000 m/s, and the layer was relatively soft silt. The propagation velocity of elastic wave in the layer from 27 to 33 m was about 1100 m/s, and the layer was soft-plastic-cohesive soil. The propagation velocity of elastic wave in the layer from 33 to 51 m was about 1200 m/s, and the layer was plastic silty clay. The propagation velocity of elastic wave in the layer below 51 m was more than 1300 m/s, and the layer was medium dense silt and plastic silty clay. Overall, the velocity cloud map reflects the distribution of elastic wave propagation velocity of elastic wave in each layer in the depth direction and the inversion nephogram, which had a high degree of coincidence with the geotechnical investigation data. Figure 6 shows the inversion clouds of the pile profile before grouting. In the C1-C3 profile, the stratified layer was basically invisible, but the interface of mud and muddy silty clay at the depth 14 m and the interface of cohesive soil and silty clay near 33 m could still be discerned. According to the velocity spectrum, the propagation velocity of the layer gradually decreased from 1500 m/s to about 1150 m/s as the distance from the pile became closer and closer in the range above 14 m in depth; in the range of depth 14-33 m, the propagation velocity of layer gradually decreased from 1600 m/s to about 1250 m/s, while in the depth of 33-50 m, the propagation velocity of the elastic wave in the layer gradually decreased from 1850 m/s to about 1450 m/s. It can be seen that in the area far from the pile, the propagation velocity of elastic wave in the layer at the same depth was basically the same as the pile side profile in Figure 5, but the closer to the pile, the smaller the propagation velocity of elastic wave in the layer was. \begin{table}
\begin{tabular}{c c c c c} \hline
**Pile Number** & **Launch** & **Receive** & **Distance (m)** & **Profile** \\ \hline \multirow{4}{*}{7-3} & C1 & C3 & 8.75 & C1-C3 \\  & C6 & C1 & 9.80 & C6-C1 \\  & C3 & C6 & 4.15 & C3-C6 \\ \hline \multirow{2}{*}{7-2} & C3 & C5 & 5.65 & C3-C5 \\  & C6 & C5 & 6.90 & C6-C5 \\ \hline \end{tabular}
\end{table} 
Table 2: Transmitting–receiving hole number and section number. Figure 5: Side profile of pile (before grouting). Figure 6: Cross-pile section (before grouting). In the C3-C5 profile, the stratified layer was basically visible, and the soil stratigraphic interfaces near the depths of 14 m and 33 m were clearly discernible.