## 3 Results and Discussions
### Incident P Wave
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{\(\boldsymbol{E_{2}=30\) GPa, \(\boldsymbol{\
u_{2}=0.25\), \(\boldsymbol{\rho_{2}=2.4\) g/cm\({}^{3}\)}}} \\ \cline{2-7}  & \(\boldsymbol{\theta_{1}(^{\circ})}\) & \multicolumn{2}{c}{**Zero**} & \multicolumn{2}{c}{**Peak**} & \multicolumn{2}{c}{\(\boldsymbol{f}\) **for Peak**} & \multicolumn{2}{c}{**Roll-off**} & \multicolumn{2}{c}{**1\%**} & \multicolumn{2}{c}{\(\boldsymbol{f}\) **for 1\%**} \\  & & **Frequency Gain** & \multicolumn{2}{c}{**Value**} & \multicolumn{2}{c}{**Value**} & \multicolumn{2}{c}{**dB/dec**} & \multicolumn{2}{c}{**Bandwidth**} & \multicolumn{2}{c}{**Bandwidth**} \\ \hline  & 0 & 2.78 (3.00) & 3.05 (3.26) & 5543 (5121) & 7.33 (7.98) & 2.81 (3.03) & 1214 (1199) \\  & 15 & 2.78 (3.00) & 3.06 (3.27) & 5598 (5173) & 6.95 (7.54) & 2.81 (3.03) & 1207 (1194) \\  & 30 & 2.78 (3.00) & 3.08 (3.28) & 5709 (5278) & 6.23 (6.71) & 2.81 (3.03) & 1194 (1185) \\ \(FV_{2}\) & 45 & 2.78 (3.00) & 3.09 (3.29) & 5765 (5331) & 5.89 (6.32) & 2.81 (3.03) & 1188 (1180) \\  & 60 & 2.78 (3.00) & 3.08 (3.28) & 5709 (5278) & 6.23 (6.71) & 2.81 (3.03) & 1194 (1185) \\  & 75 & 2.78 (3.00) & 3.06 (3.27) & 5598 (5173) & 6.95 (7.54) & 2.81 (3.03) & 1207 (1194) \\  & 90 & 2.78 (3.00) & 3.05 (3.26) & 5543 (5121) & 7.33 (7.98) & 2.81 (3.03) & 1214 (1199) \\ \hline  & 0 & 2.90 (3.00) & 3.33 (3.33) & 3885 (3533) & 8.33 (8.42) & 2.95 (3.04) & 926 (905) \\  & 15 & 2.51 (2.60) & 2.89 (2.88) & 3885 (3533) & 8.35 (8.43) & 2.53 (2.63) & 926 (905) \\  & 30 & 1.45 (1.50) & 1.67 (1.66) & 3885 (3533) & 8.40 (8.45) & 1.46 (1.53) & 926 (905) \\ \(FS\) & 45 & 0 (0) & 0 (0) & 0 (0) & 0 (0) & 0 (0) & 0 (0) \\  & 60 & 1.45 (1.50) & 1.67 (1.66) & 3885 (3533) & 8.30 (8.45) & 1.46 (1.52) & 926 (905) \\  & 75 & 2.51 (2.60) & 2.88 (2.88) & 3885 (3533) & 8.32 (8.43) & 2.54 (2.63) & 926 (905) \\  & 90 & 2.90 (3.00) & 3.33 (3.33) & 3885 (3533) & 8.33 (8.42) & 2.93 (3.04) & 926 (905) \\ \hline  & 0 & 2.78 (3.00) & 3.07 (3.27) & 5654 (5226) & 6.59 (7.12) & 2.81 (3.03) & 1200 (1189) \\  & 15 & 2.78 (3.00) & 3.07 (3.27) & 5654 (5226) & 6.59 (7.12) & 2.81 (3.03) & 1200 (1189) \\  & 30 & 2.78 (3.00) & 3.07 (3.27) & 5654 (5226) & 6.59 (7.12) & 2.81 (3.03) & 1200 (1189) \\ \(FV_{4}\) & 45 & 2.78 (3.00) & 3.07 (3.27) & 5654 (5226) & 6.59 (7.12) & 2.81 (3.03) & 1200 (1189) \\  & 60 & 2.78 (3.00) & 3.07 (3.27) & 5654 (5226) & 6.59 (7.12) & 2.81 (3.03) & 1200 (1189) \\  & 75 & 2.78 (3.00) & 3.07 Figure 3: Influence of Young’s modulus of the expansive grout on the theoretical amplitude spectrum of gauge combination \(FV_{2}\) for the incident P wave. Figure 2: Theoretical amplitude spectrum of gauge combination \(FV_{2}\) for the incident P wave. Figure 4: Influence of Poisson’s ratio of the expansive grout on the theoretical amplitude spectrum of gauge combination \(FV_{2}\) for the incident P wave. Figure 5: Influence of the expansive grout density on theoretical amplitude spectrum of gauge combination \(FV_{2}\) for the incident P wave. In order to study the influence of the mechanical parameters of the expansive grout on gauge combinations, the effect of the Young's modulus, the Poisson's ratio and the density of the expansive grout on the characteristic values of theoretical frequency responses are listed in Tables 2-4, respectively. It can be seen in Table 2 that as the Young's modulus of the expansive grout increases, the zero-frequency gain, peak value and corresponding frequency of \(FV_{2}\), \(FV_{4}\), and \(TV\), reflecting the areal strain, decrease slightly. Similarly, the zero-frequency gain and peak values of \(FS\) and \(TS\) decrease slightly, but the corresponding frequency of the peak value of \(TS\) increases. From Table 3, we can see that the Poisson's ratio in the expansive grout makes the zero-frequency gain, peak value and corresponding frequency of \(FV_{2}\), \(FV_{4}\) and \(TV\) increase, but makes the zero-frequency gain, peak value and corresponding frequency of \(FS\) decrease slightly, as the Poisson's ratio in the expansive grout increases.