## 3 Analysis of Test Data
### Dynamic Performance Analysis
#### 3.2.2 Dynamic Tensile Strength Analysis  
The tensile strength of the specimen is consistent with the peak stress, and the instability failure occurs when the sandstone specimen reaches the tensile strength. After testing and data processing, the peak of the dynamic stress-strain curve is the dynamic tensile strength.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Annular Sandstone Specimens**} & \multicolumn{3}{c}{**Intact Sandstone Specimens**} \\ \cline{3-8}
**Temperature** & **Specimen** & **Peak Stress** & **Average** & **Peak Strain** & **Specimen** & **Peak Stress** & **Average** & **Peak Strain** \\ (\({}^{\circ}\)**C)** & **Number** & **(MPa)** & **Strain Rate** & **(\(\times 10^{-3}\))** & **Number** & **(MPa)** & **Strain Rate** & **(\(\times 10^{-3}\))** \\ \hline
25 & GB33-01 & 17.06 & 84.50 & 2.86 & GB33-17 & 25.26 & 81.30 & 3.62 \\ GB33-02 & 15.29 & 84.40 & 2.81 & GB33-18 & 26.19 & 81.70 & 3.54 \\ \hline
35 & GB33-03 & 17.21 & 83.50 & 2.64 & GB33-19 & 26.91 & 80.80 & 3.43 \\ GB33-04 & 16.69 & 83.30 & 2.73 & GB33-20 & 26.25 & 80.70 & 3.49 \\ \hline
45 & GB33-05 & 16.48 & 83.60 & 2.50 & GB33-21 & 27.31 & 80.70 & 3.03 \\ GB33-06 & 17.54 & 83.10 & 2.40 & GB33-22 & 26.60 & 79.90 & 3.38 \\ \hline
55 & GB33-07 & 15.10 & 83.40 & 2.60 & GB33-23 & 26.62 & 80.30 & 3.58 \\ GB33-08 & 17.52 & 83.80 & 2.88 & GB33-24 & 26.32 & 80.90 & 3.56 \\ \hline
65 & GB33-09 & 16.73 & 84.60 & 3.24 & GB33-25 & 26.41 & 79.70 & 4.02 \\ GB33-10 & 14.51 & 84.00 & 2.81 & GB33-26 & 26.10 & 83.20 & 4.09 \\ \hline
75 & GB33-11 & 15.48 & 84.60 & 3.89 & GB33-27 & 25.73 & 82.00 & 4.52 \\ GB33-12 & 15.08 & 85.30 & 3.97 & GB33-28 & 25.96 & 81.30 & 4.54 \\ \hline
85 & GB33-13 & 15.00 & 85.90 & 4.93 & GB33-29 & 25.01 & 83.20 & 5.21 \\ GB33-14 & 13.26 & 86.20 & 4.68 & GB33-30 & 25.33 & 83.10 & 5.25 \\ \hline
95 & GB33-15 & 13.80 & 85.60 & 5.46 & GB33-31 & 21.97 & 85.20 & 5.61 \\ GB33-16 & 12.95 & 88.00 & 5.02 & GB33-32 & 25.36 & 83.30 & 5.64 \\ \hline \hline \end{tabular}
\end{table}
Table 2: SHPB test data.  
Figure 8: Stress-strain curves: (**a**) stress–strain curves of annular sandstone specimens; (**b**) stress–strain curves of intact sandstone specimens.  
Dynamic tensile strength is shown in Figure 9.  
\[\left.\begin{aligned} P_{1}(t)&=15.045-0.085t+0.001 \times 10^{-5}t^{2}\Big{(}\mathrm{R}^{2}=0.9598\Big{)}\\ P_{2}(t)&=23.133-0.145t+0.001\times 10^{-5}t^{2}\Big{(} \mathrm{R}^{2}=0.9682\Big{)}\end{aligned}\right\} \tag{5}\]  
where \(P_{1}(t)\) is the annular sandstone specimen's dynamic tensile strength; \(P_{2}(t)\) is the intact sandstone specimen's dynamic tensile strength.  
According to the analysis, the peak tensile strength of the two sandstone specimens changed at 45 \({}^{\circ}\)C. Through quadratic function fitting, the correlation coefficients reached 0.9598 and 0.9682, respectively, showing strong correlation. In the process of testing, water entered the internal void. Considering the influence of water bonding force and the Stefan effect [36], the strength of the specimens was enhanced to a certain extent. After 45 \({}^{\circ}\)C, the effects of temperature and water on the damage to the specimen are greater than its enhancement. Partial spalling occurred on the surface of the specimens, internal cracks increased, and the specimens were more prone to instability failure. Therefore, the peak strength of both specimens gradually decreased. Because the annular sandstone specimen had lower integrity, its peak tensile strength was lower than that of the annular sandstone specimen.