# Study on Explosive Fracturing Mechanism of Qianjiang Shale Oil
## 3 Results and Discussion
### Material Model
#### 3.2.1 Rock [32]
\begin{array}{l}\frac{1+sinp}{1-sinp}=6\\ \frac{2 cosp}{1-sinp}=236.455\end{array} \right. \tag{13}\]  
From Equation (9), we derive \(A=0.251\). Subsequently, Equation (8) can be transformed into \(\sigma^{*}=0.251+BP^{*N}\). The standardized equivalent stress \(\sigma^{*}\) and the standardized hydrostatic pressure \(P^{*}\) can be determined using the following respective formulas:  
\[\sigma^{*}=\frac{\sigma_{1}-\sigma_{3}}{f_{c}} \tag{14}\]  
\[P^{*}=\frac{\sigma_{1}+2\sigma_{3}}{3f_{c}} \tag{15}\]  
By substituting the static compressed data presented in Table 2 into Equations (14) and (15), seven sets of data listed in Table 3 can be derived. Through fitting these seven data sets with the equation \(\sigma^{*}=0.251+BP^{*N}\), the parameters \(B=2.11\) and \(N=0.894\) are obtained, as illustrated in Figure 3. \begin{table}
\begin{tabular}{c c} \hline \(\sigma_{2}\)=\(\sigma_{3}\)/MPa & \(\sigma_{1}\)/MPa \\ \hline
0 & 192.5 \\
5 & 250.268 \\
10 & 298.542 \\
20 & 379.8 \\
30 & 449.114 \\
50 & 567.741 \\
100 & 806.439 \\ \hline \end{tabular}
\end{table} 
Table 2: Static compressive strength of reservoir rock under different confining pressures. Figure 2: Mohr–Coulomb criterion fitting. The maximum normalized intensity \(S_{max}\) signifies the critical threshold beyond which \(\sigma^{*}\) ceases to increase with further increments in \(P^{*}\). When taking the value, it is imperative that the condition \(\sigma^{*}\leq S_{max}\) is satisfied. Based on the maximum value of the second invariant of the partial stress tensor for reservoir rock under hydrostatic pressure [36], this study adopted \(S_{max}=6.3\). When the loading rate is within the range of \(10^{-5}\)/s to \(10^{-1}\)/s, the rock chamber test is classified as a static test. Both the triaxial compression process and the confining pressure increase process are characterized as static processes [37]. Therefore, the influence of strain rate on the test results is negligible, leading to the assumption that the strain rate coefficient \(C=0\). The damage parameter \(D_{1}\) can be determined using Equation (16), where \(T^{*}=\frac{T}{f_{e}}\), resulting in \(D_{1}=0.0473\). The parameters \(D_{2}\) and \(EF_{min}\) exert minimal influence on the simulation outcomes; therefore, following the literature [38], the values adopted are \(D_{2}=1\) and \(EF_{min}=0.01\). \[D_{1}=\frac{0.01}{\left(\frac{1}{6}+T^{*}\right)} \tag{16}\] \begin{table}
\begin{tabular}{c c} \hline \(\mathbf{P^{*}}\) & \(\mathbf{\sigma^{*}}\) \\ \hline
0.409 & 1.228 \\
0.478 & 1.358 \\
0.548 & 1.488 \\
0.687 & 1.748 \\
0.825 & 2.008 \\
1.102 & 2.527 \\
1.795 & 3.826 \\ \hline \end{tabular}
\end{table} 
Table 3: Equivalent stress and hydrostatic pressure of reservoir rock under different confining pressures. Figure 3: Failure surface fitting. When the rock attains its elastic limit, the crushing pressure \(P_{crush}\) and the crushing volume strain \(\mu_{crush}\) can be determined using Equations (17) and (18). \[P_{crush}=\frac{f_{c}}{3} \tag{17}\]  
\[\mu_{crush}=\frac{p_{crush}}{K} \tag{18}\]  
Obtain \(P_{crush}\) = 64.167 MPa, \(\mu_{crush}\) = 0.00758. \(\mu_{lock}\) represents the volumetric strain at the compaction limit state, which can be determined using the following equations:  
\[\rho_{g}=\frac{\rho_{0}}{(1-q)} \tag{19}\]  
\[\mu_{lock}=\frac{\rho_{g}}{\rho_{0}-1} \tag{20}\]  
In these equations, \(\rho_{g}\) represents the real-time density of the material under pressure; \(q\) denotes the initial porosity of the rock, with \(q\) = 15.9%. By applying Equations (19) and (20), we obtain \(\mu_{lock}\) = 0.189. For conventional rock materials, in the absence of [PERSON] experimental data, an empirical formula can be derived as follows:  
\[P=\frac{C_{0}^{2}\rho_{0}\mu(\mu+1)}{[(1-S)\mu+1]}^{2} \tag{21}\]  
In the formula, \(\rho_{0}\) represents the initial density of the rock, with a value of 2370 kg/m\({}^{3}\). \(C_{0}\) and \(S\) are empirical parameters.