# Experimental Study on High-Energy Gas Fracturing Artificial Coal
## 4 Test Results and Analysis
### Strain Waves Test Results and Analysis  
The radial strains were tested at four measurement points at 125 mm, 225 mm, 350 mm, and 500 mm from the borehole. To facilitate analysis, the distinctive parts of the waveform were exported from the DHDAS dynamic signal analysis software. Some of the test results are shown in Figure 5. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Statistical Items** & **Location of Measurement Points** & **Test Results** \\ \hline Peak pressure/MPa & Borehole middle & 118.1 \\  & Borehole bottom & 85.3 \\ \hline Pressure increase time/ms & Borehole middle & 18.4 \\  & Borehole bottom & 18.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Statistical results of borehole wall pressure test. Figure 5: Strain wave in coal under the action of high-energy gas. From Figure 5, it can be seen that each point generally forms two-part strain waves. From its first complete strain wave, it can be seen that the points are first subjected to compressive stress and then to tensile stress. In terms of the time of action, the duration of the strain wave compressive phase is shorter than the tensile phase in the role of high-energy gas, and the overall strain wave duration is much longer than that of explosive blasting. The action time of the strain wave compressive phase produced by the high-energy gas is about 2.3\(-\)5.6 ms, and the tensile phase is about 3.1\(-\)8.7 ms, while the action time of the strain wave compressive phase produced by the explosive blasting is about 40\(-\)50 \(\upmu\)s, and the tensile phase is more than 100 \(\upmu\)s [30]. Three simulated coal samples were selected for high-energy gas fracturing tests in this paper, three specimens with a total of 12 stress wave measurement points, of which nine valid waveforms were obtained. Three of the waveforms were invalid due to destructed strain sensors, the burial of strain bricks, etc. To reduce the influence of the strain transducer on the test results, the average of the valid data from three sets of tests was taken as the study. The results of the peak strain statistics are given in Table 6.  
The results of the peak strain statistics are given in Table 7. The peak strain at each measurement point is multiplied by the dynamic Young's modulus of the coal to obtain their dynamic stress peaks. The calculation formula of dynamic Young's modulus of coal rock mass is as follows:  
\[E_{d}=\frac{c_{p}^{2}(1+\mu_{d})(1-2\mu_{d})}{(1-\mu_{d})} \tag{4}\]  
In Formula (4), \(E_{d}\) is the dynamic [PERSON]'s modulus; \(c_{p}\) is the longitudinal wave velocity of coal; \(\mu_{d}\) is the dynamic [PERSON]'s ratio of coal. In the case of high-energy gas loading at high speed, \(\mu_{d}=0.8u\), \(u\) is the static [PERSON]'s ratio. The calculation yields that \(\mu_{d}=0.144\), \(E_{d}=6.34\) GPa. To analyze the law of stress wave propagation and attenuation in coal under the action of high-energy gas, the scatter plot of the peak radial stress wave with distance at each measurement point was plotted, and then the scatter plot was fitted nonlinearly (the fitting formula, is \(y=\mathrm{a}\vec{r}^{\alpha}\vec{r}\), is the proportional distance, it equal to the ratio of the distance from the measurement point to the borehole and the radius of the borehole). The fitting results are shown in Figure 6. From the fitting results, it can be seen that the stress wave attenuation index \(\alpha\) in the coal under the action of high-energy gas is 1.67, which is consistent with \(\alpha=2-\mu/(1-\mu)\) (\(\mu\) is [PERSON]'s ratio of coal, 0.14\(-\)0.3). However, the stress wave attenuation index in the coal under the action of explosive blasting is basically consistent with \(\alpha=3-\mu/(1-\mu)\)[31], which means that the stress wave attenuation is slower in the coal under the action of high-energy gas.