# Experimental and Numerical Studies on Ground Shock Generated by Large Equivalent Surface Explosions
## 3 Experimental Results and Analysis
Likewise, the maximum negative accelerations in the X and Y directions were 1.52 and 2.67 times that in the Z direction. At 42 m, the maximum positive accelerations in the X and Y directions were 5.04 and 3.04 times that in the Z direction, while the maximum negative accelerations in the X and Y directions were 1.22 and 0.86 times that in the Z direction. It is apparent that the intensity of the explosion-induced ground shock decreased with the increasing distance from the blast site, and that the accelerations in the X and Y direction were both higher than that in the Z direction. The numerical dominance of the ground-shock-induced accelerations in the X and Y values implies that the structural effects of ground shocks are concentrated in the X and Y direction, while the effects in the Z direction are considerably weaker. Figure 7 is the velocity-time curve of the 21 m point. It may be observed that the real particle vibration velocity exceeded the range of the velocity sensor, which caused clipping in the measured velocity-time curve. Figure 6: Acceleration data measured at 42 m in the one-ton TNT ground explosion test. Figure 7: Velocity\(-\)time curve at the 21 m point. There are many factors that affect the parameters of explosion-induced ground shocks. The _Design And Analysis Of Hardened Structures To Conventional Weapon Effects_[3] used by the U.S. military provides empirical equations that relate the charge weight to the propagation of the ground shock in soil. The equations for calculating the maximum ground shock acceleration and velocity are:  
\[\alpha_{0}W^{1/3}=f\times 0\times c\times(\frac{R}{W^{1/3}})^{-(n+1)} \tag{1}\]  
\[v_{0}=f\times 160\times(\frac{R}{W^{1/3}})^{-n} \tag{2}\]  
where \(\alpha_{0}\) is the maximum acceleration (g); \(v_{0}\) is the maximum velocity (ft/s); \(W\) is the C4 weight (lbs); \(f\) is the ground-shock coupling factor, which is always 0.14 for contact explosions or explosions in air, regardless of the type of ground [3]; \(c\) is the velocity of the seismic wave (ft/s); \(R\) is the distance of the measurement point from the epicenter of the explosion (ft); and \(n\) is the attenuation coefficient. So, Equation (1) can be used for calculating the attenuation parameters, substituting the maximum acceleration measurements obtained from the 1 t TNT explosion at 21 and 42 m into Equation (1), the values of parameters \(c\) and \(n\) were obtained as follows: \(c\) = 457 m/s (1500 ft/s) and \(n\) = 2.55. Parameters \(c\) and \(n\) vary from one type of soil to another, as shown in Table 2.  
Based on the velocities and attenuation coefficients shown in Table 2, the calculated \(c\) and \(n\) values resemble those for compacted sandy soil with a high relative density which matches the ground conditions at the experimental site. By substituting the calculated \(c\) and \(n\) values obtained for the 1 t TNT explosion test into Equation (2), it was determined that the maximum particle vibration velocity at the 21 m point \(v_{0-21}\) was equal to 0.116 m/s. The attenuation of the ground-shock-induced particle velocities can be described using an exponential function. The ground-shock stress wave widens as it propagates, while simultaneously, the maximum particle vibration velocity decays rapidly in relation to the increasing distance from the blast site. The ground-shock wave's arrival time \(t_{a}\) denotes the time taken by the wave to reach some point from the epicenter of the explosion, and it may be expressed as [3]:  
\[t_{a}=\frac{R}{c} \tag{3}\]  
where \(R\) is the distance from the epicenter of the explosion measured in m.  
The waveform of the ground shock will rise to its maximum in a very short time after arrival. The rise time \(t_{r}\) is given by:  
Figure 3:0