## 4 Discussions  
Generally speaking, the main difference between underwater blasting and land blasting is the medium of solid contact surface, involving water and air. According to the continuity condition of interface and [PERSON]'s third law [19], the reflection and transmission of stress wave produced by a solid medium blast would occur at the interface of two kinds of medium:  
\[\sigma_{r}=\sigma_{i}(\rho_{2}C_{P2}-\rho_{1}C_{P1})/(\rho_{2}C_{P2}+\rho_{1}C_{ P1})=F\sigma_{i} \tag{2}\]  
where \(\rho_{1}\) and \(\rho_{2}\) are densities of different media (kg/m\({}^{3}\)), \(C_{P1}\) and \(C_{P2}\) are \(p\)-wave propagation velocities of different media (m/s), \(\sigma_{r}\), \(\sigma_{i}\) are stress of reflected wave and incident wave in solid medium, and \(F\) is the reflection coefficient. When blasting on land, the acoustic impedance of air (\(\rho_{2}C_{P2}\)) can be approximated to 0; that is,  
\[\sigma_{r1}=F\sigma_{i1} \tag{3}\]  
When blasting underwater, \(\rho_{2}C_{P2}\)\(<\)\(\rho_{1}C_{P1}\), \(F\)\(<\)0, the reflected wave stress is  
\[\sigma_{r2}=F\sigma_{P2} \tag{4}\]  
Figure 8: Regression results of _PPV_ and scaled distance in (x) longitudinal, (y) tangential and (z) vertical directions. (**a**) Masonry, (**b**) plain concrete, and (**c**) roller compacted concrete. The underwater solid medium is subjected to pre-stress, its tensile strength increases, and the dynamic tensile strength coefficient \(K\) is  
\[K=\left([\sigma]+0.01h\right)/[\sigma] \tag{5}\]  
where \([\sigma]\) is dynamic tensile strength (MPa) and \(h\) is the depth of water (m). Therefore, to achieve the same blast effect for the same solid medium both on land and underwater, the following conditions should be satisfied:  
\[\sigma_{r1}=K\sigma_{r2}, \tag{6}\]  
\[\sigma_{i1}=-F\sigma_{i2}/K \tag{7}\]  
Because the pressure of shock wave in solid medium tends to attenuate during its propagation,  
\[\sigma_{i}=P_{0}/R^{\alpha} \tag{8}\]  
\[R^{\alpha}=\left(R/R_{e}\right)^{\alpha} \tag{9}\]  
where \(P_{0}\) is the initial shock wave pressure produced by explosion (MPa), \(R^{\alpha}\) is the proportional distance, \(R_{e}\) is the cartridge radius (m), \(\alpha\) is the pressure attenuation coefficient of solid medium, and \(\alpha=1\sim 3\). Substituting Equation (8) into Equation (9) finds,  
\[R_{2}^{\alpha}=-FR_{1}^{\alpha}/K \tag{10}\]  
\[\sigma_{r1}=F\sigma_{i1} \tag{3}\]0  
\[\sigma_{r1}=F\sigma_{i1} \tag{3}\]1  
when \(R_{1}=R_{2}\). Substituting Equation (11) and (12) into Equation (10) finds,  
\[\sigma_{r1}=F\sigma_{i1} \tag{3}\]2  
where \(Q_{1}\) and \(Q_{2}\) are explosive unit consumption in land and underwater blasting (kg/m\({}^{3}\)), and \(\beta\) is the volume conversion constant. According to the characteristics of concrete structures in different regions, the parameters of underwater blasting can be accurately calculated as shown in \[\sigma_{r1}=F\sigma_{i1} \tag{3}\]3 Water pressure affects fracture radius when emulsion explosive explodes in concrete under water: the deeper the water is, the smaller the fracture radius is. Therefore, compared with land blasting, in order for the underwater blasting on same solid medium to have satisfactory effectiveness there should be an increase of 1.69 times and 1.91 times the explosives in region V and VI, respectively. The EUC would be better if increased from 0.53 kg/m\({}^{3}\) and 0.61 kg/m\({}^{3}\) to 0.89 kg/m\({}^{3}\) and 1.16 kg/m\({}^{3}\) in regions V and VI, as shown in \[\sigma_{r1}=F\sigma_{i1} \tag{3}\]4 \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Regions** & \(h\) **(m)** & **[\(\sigma\)] (MPa)** & \(\alpha\) & \(\rho_{1}\) (kg/m\({}^{3}\))** & \(C_{P1}\) (kg/m\({}^{3}\)) & \(C_{P2}\) (kg/m\({}^{3}\))** & **Q2/Q1** \\ \hline V & 6 & 1.05 & 3 & 2400 & 2700 & 1000 & 1500 & 1.69 \\ VI & 6 & 1.65 & 2 & 2560 & 3000 & 1000 & 1500 & 1.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Relevant parameters of underwater blasting.