# Energy Generation and Attenuation of Blast-Induced Seismic Waves under In Situ Stress Conditions
## 4 A Case Study
### Seismic Energy Attenuation Analysis and Discussion  
According to the in situ stress measurements in the CJPL, [PERSON] et al. [56] numerically analyzed the stress redistribution surrounding the traffic tunnel. The numerical results show that at these monitoring points where the velocity sensors are placed, the vertical in situ stress varies from 45.0 to 51.3 MPa with a small difference. However, the horizontal in situ stress for the monitoring points at different depths is quite different. For Nos. 1-4 monitoring points at a depth of 3 m, the average horizontal stress ranges from 17.2 to 20.6 MPa. While for Nos. 5-8 monitoring points at a depth of 10 m, the average horizontal stress reaches 28.6-32.4 MPa. The horizontal in situ stress at Nos. 5-8 monitoring points is significantly higher than that at 1-4 monitoring points. Therefore, comparing the horizontal vibrations between Nos. 1-4 points and Nos. 5-8 points can reflect the influence of in situ stress levels on the blasting seismic energy attenuation. The seismic waves produced in the cutting hole blasting are used for analysis in this study because in this delay, the strongest vibration is induced. Due to the small number of monitoring points, the measured waves from eight blasting tests are collected for analysis. In practical blasts, it is a great challenge to determine the seismic wavefront shape, the stress and velocity on the entire wavefront, and the rock mass properties on the wave propagation path. Therefore, the rigorous theoretical Equations (3) and (17) are rarely used to calculate the seismic energy and the seismic energy density for practical blasts. Instead, twice the kinetic energy per unit mass is usually used to characterize the vibration energy or seismic energy at a point. After obtaining the horizontal radial and horizontal tangential velocity histories at a point, the seismic energy of the horizontal vibration is given by:  
\[E_{\mathrm{s}}=\int_{0}^{T}\left({v_{1}}^{2}+{v_{2}}^{2}\right)dt \tag{18}\]  
where \(T\) is the period of the velocity history. According to the measured velocity histories, the seismic energy versus distance on a logarithmic plot is shown in Figure 13. In this figure, the circular symbol represents the monitoring points at a depth of 3 m, and the triangular symbol denotes the monitoring  
Figure 12: Arrangements of monitoring for blast-induced seismic waves (unit: m). points at a depth of 10 m. Their best fit straight lines are plotted by the solid blue line and red dashed line, respectively. Based on the regression analysis results, the seismic energy attenuation for the monitoring points at a depth of 3 m is:  
\[E_{\rm S}=0.130Q_{\rm e}W_{\rm e}e^{-0.082r}(R^{2}=0.9578) \tag{19}\]  
and for the monitoring points at a depth of 10 m, the seismic energy attenuation follows:  
\[E_{\rm S}=0.117Q_{\rm e}W_{\rm e}e^{-0.061r}(R^{2}=0.9047) \tag{20}\]  
The squared correlation coefficients exceed 0.90. For the field monitoring vibration signals, their seismic energy attenuation with distance also follows the exponential function law well. For the seismic wave propagation paths with depths of 3 m and 10 m, the attenuation indexes of seismic energy are 0.082 and 0.061, respectively, with a relative difference of 26%. The seismic energy decays more slowly along Nos. 5-8 monitoring points at a greater depth of 10 m. This is because, at a greater depth from the traffic tunnel wall, the rock mass is subjected to higher horizontal in situ stress. Hence the seismic \(Q\) at this location is higher, and then the seismic energy of the horizontal vibration decays at a slower rate. This conclusion is consistent with the theoretical and numerical results obtained above. According to the analysis of the field monitoring data, it is demonstrated that in situ stress does have an important effect on the energy attenuation of blast-induced seismic waves.