## 2 Experimental Study
### Experimental Results
#### 2.2.1 Strength Characteristics  
The stress-strain curves of gas-bearing coal under the two sets of paths are shown in Figures 3 and 4. During the process of reaching the hydrostatic stress state, the samples were compacted to some extent due to the loading of the axial stress and radial stress. As a result, the compaction phase of the stress-strain curve under each path was not obvious. The stress-strain curve mainly included the elastic deformation, plastic deformation, yield failure, and residual stress phase. Under different initial conditions and stress paths, the strength characteristics of the samples were significantly different. The experimental results are listed in Tables 1 and 2. In Table 1, \(\sigma_{3}\) is the initial radial stress, P is the gas pressure, V is the loading rate, \(\sigma_{1}\)' is the axial peak strength under triaxial compression, \(\sigma_{\rm r}\) is the residual strength, \(\sigma\) is the difference between the peak strength and residual strength, \(\rm n\) is the reduction ratio of the peak stress, and \(\rm t\) is the time required for failure under the loading paths. In Table 2, \(\sigma_{1}\)\" represents the axial stress at the start of unloading the radial stress, V' represents the unloading rate, \(\sigma_{3}\)' represents the radial stress at the time of sample failure, \(\sigma\)' represents the unloaded radial stress at failure, N represents the unloading ratio (the ratio of unloaded radial stress to initial radial stress), and \(\rm t\)' represents the time required for failure under the unloading paths. Figure 3: Stress–strain curves under different loading paths: (**a**) CTC (\(\sigma_{3}\) = 4 MPa); (**b**) CTC (P = 2 MPa); (**c**) ATC (\(\sigma_{3}\) = 4 MPa); (**d**) ATC (P = 2 MPa). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Paths** & **No.** & \(\sigma_{3}\)/MPa & **P/MPa** & \(\sigma_{1}\)**\({}^{\prime\prime}\)/MPa** & **V/N-s-1** & \(\sigma_{3}\)**\({}^{\prime}\)/MPa** & \(\sigma^{\prime}\)/MPa** & **N/\%** & **t/s** \\ \hline  & 3-1 & 4 & 1 & 20.4 & 20 & 1.34 & 2.66 & 66.50 & 904 \\  & 3-2 & 4 & 1.5 & 17.5 & 20 & 1.85 & 2.15 & 53.75 & 740 \\ UCP & 3-3 & 4 & 2 & 14.9 & 20 & 2.97 & 1.03 & 25.75 & 528 \\  & 3-4 & 7 & 2 & 23.1 & 20 & 4.42 & 2.58 & 36.86 & 884 \\  & 3-5 & 10 & 2 & 28.4 & 20 & 5.65 & 4.35 & 43.50 & 1148 \\  & 4-1 & 4 & 1 & 20.4 & 20/80 & 1.51 & 2.49 & 62.25 & 734 \\  & 4-2 & 4 & 1.5 & 17.5 & 20/80 & 1.91 & 2.09 & 52.25 & 610 \\ AUCP & 4-3 & 4 & 2 & 14.9 & 20/80 & 3.02 & 0.98 & 24.50 & 481 \\  & 4-4 & 7 & 2 & 23.1 & 20/80 & 4.63 & 2.37 & 33.86 & 741 \\  & 4-5 & 10 & 2 & 28.4 & 20/80 & 5.99 & 4.01 & 40.10 & 893 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental results under different unloading paths. Figure 4: Stress–strain curves under different unloading paths: (**a**) UCP (\(\sigma_{3}\) = 4 MPa); (**b**) UCP (P = 2 MPa); (**c**) AUCP (\(\sigma_{3}\) = 4 MPa); (**d**) AUCP (P = 2 MPa). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Paths** & **No. ** & \(\sigma_{3}\)/MPa & **P/MPa** & **V/N-s-1** & \(\sigma_{1}\)/MPa** & \(\sigma_{1}\)**/MPa** & \(\sigma_{1}\)**/MPa** & \(\sigma_{1}\)**/MPa** & **\(\sigma_{1}\)**/MPa** & **n/\%** & **t/s** \\ \hline  & 1-1 & 4 & 1 & 50 & 32.19 & 23.10 & 9.09 &It can be concluded from the results in Figure 3 and Table 1 that under the two loading paths, the strengths of the samples were significantly different under different initial conditions. Under the two loading paths, the two loading paths, the peak strength of the sample decreased as the gas pressure increased, while increasing significantly as the confining pressure increased. [PERSON] (2018) and [PERSON] (2018) also pointed out that under the same confining pressure, an increase in the gas pressure decreased the peak strength of coal, and the effect of the gas pressure on the peak strength was weakened as the confining pressure increased.