## 4 Results  
### Test Analysis of Transmitted Wave in the Pile  
Figure 8a is the original data diagram of the results of the transmission wave test in the No. 1 pile. After data extraction and redrawing, the processing diagram can be obtained, as shown in Figure 8b, which is consistent with Figure 4. Figure 8 shows that the pile bottom elevation of No. 1 pile is \(-\)88 m, which is basically consistent with the design elevation, thus verifying the correctness of the method. The second turning point of the curve is \(-\)90 m, so the depth of the pile base reinforcement is 2 m. In addition, the wave speed of the pile body is about 3570 m/s, the wave speed of the reinforcement body is about 394 m/s, and the wave speed of the bearing layer is about 285 m/s. From Equations (1) and (2), it can be known that the elastic modulus of the reinforcement is about 1.9 times more than that of the bearing layer.  
\[V_{pp}=\sqrt{\frac{E}{\rho}} \tag{1}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Hammer Quality** & **Drop Distance** & **Probe Diameter** & **Probe Cone Angle** & **Probe Rod** & **Target Penetration** \\
**(kg)** & **(cm)** & **(mm)** & **(°)** & **Diameter (mm)** & **Depth (cm)** \\ \hline
10 & 76 & 74 & 60 & 42 & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Heavy-duty dynamic penetration parameters.  
Figure 7: Dynamic penetration test.  
\[V_{sp}=\sqrt{\frac{(1-v)E}{(1+v)(1-2v)\rho}} \tag{2}\]  
where \(E\) and \(v\) are the elastic modulus and [PERSON]'s ratio, respectively, \(\rho\) is the mass density, \(V_{pp}\) and \(V_{sp}\) are the \(p\)-wave velocity of the pile and soil, respectively.  
Figure 9a is the original data diagram of the results of the transmission wave test in the No. 2 pile. After data extraction and redrawing, the processing diagram can be obtained, as shown in Figure 9b, which is consistent with Figure 4. Figure 9 shows that the pile bottom elevation of No. 2 pile is \(-\)88 m, which is basically consistent with the design elevation, thus verifying the correctness of the method. The second turning point of the curve is \(-\)89 m, so the depth of the pile bottom reinforcement is 1 m. In addition, the wave speed of the pile body is about 3453 m/s, the wave speed of the reinforcement body is about 405 m/s, and the wave speed of the bearing layer is about 257 m/s. From Equations (1) and (2), it  
Figure 8: Test result of transmission wave in the No. 1 pile: (**a**) original data; (**b**) processed Data.  
can be known that the elastic modulus of the reinforcement is about 2.48 times more than that of the bearing layer.  
If the shape of the reinforcement body is assumed to be a cylinder passing through the bottom of the pile, the volume formula of the three-dimensional reinforcement body is shown in Equation (3):  
\[V=\pi R^{2}H \tag{3}\]  
If the diameter of the pile bottom is 1.5 m as the diameter of the reinforcement cylinder, it can be seen from the above test that the reinforcement depths of the No. 1 pile and No. 2 pile are 2 m and 1 m, respectively. From Equation (3), \(V1=3.534\) m\({}^{3}\), \(V2=1.767\) m\({}^{3}\), the ratio of the two volumes is 2, which is consistent with the ratio of the grouting amount of 500/250, so it can be shown that the assumption about the shape of the cylinder is reasonable.