## 4 Comparison of Prediction Accuracy
### Results and Analysis  
Employing a methodological framework based on the least-squares principle, this study applied the three distinct anisotropic strength criteria outlined in Section 2 to perform quantitative evaluation of strength parameters across 12 lithological varieties. Through rigorous optimization processes focused on RMSE minimization, the computational procedure successfully identified optimal parameter configurations for each criterion, thereby establishing robust correlations between theoretical predictions and experimental rock strength data. The resultant calibration parameters, representing the most accurate predictive solutions for the SPW, PPW, and Pariseau criteria, are documented in Tables 1-3, corresponding to each respective criterion. This parametric optimization not only validates the mathematical applicability of these criteria but also provides critical reference values for future geo-mechanical modeling involving anisotropic rock formations. \begin{table}
\begin{tabular}{c c c c c c} \hline
**No.** & **Rock Type** & \(\mathbf{\varphi_{o}}l^{c}\) & \(\mathbf{\mathrm{S_{o}}/\text{MPa}}\) & \(\mathbf{\phi_{\text{bp}}}l^{c}\) & \(\mathbf{\mathrm{S_{bp}}/\text{MPa}}\) \\ \hline
1 & Bossier shale & 29.1 & 30.6 & 16.7 & 17.4 \\ \hline
2 & Vaca Muerta shale & 26.9 & 34.1 & 26.1 & 18.2 \\ \hline
3 & Angiers Schist & 41.3 & 35.7 & 8.2 & 11.1 \\ \hline
4 & Martinsburg Slate & 30.2 & 49.3 & 16.6 & 14.1 \\ \hline
5 & Austin Slate & 22.2 & 81 & 13.6 & 45.1 \\ \hline
6 & GreenRiver Shale 1 & 27.5 & 69.1 & 30.5 & 41.9 \\ \hline
7 & GreenRiver Shale 2 & 19.7 & 42 & 18.6 & 27.8 \\ \hline \end{tabular}
\end{table} 
Table 1: Fitting parameters of single plane of weakness model. Using the fitting results from Table 1 to Table 3, the experimental data of Bossier shale and Anigiers Schist, along with the predicted results of SPW, PPW, and Pariseau criteria, are simultaneously plotted in Figures 3 and 4. \begin{table}
\begin{tabular}{c c c c c c} \hline
**No.** & **Rock Type** & \(\mathbf{\varphi_{o}}\)\({}^{C}\) & **S\({}_{o}\)/MPa** & \(\mathbf{\phi_{\text{bp}}}\)\({}^{C}\) & **S\({}_{\text{bp}}\)/MPa** \\ \hline
8 & Quartz Phyllite & 32.4 & 23.9 & 25.9 & 15.4 \\ \hline
9 & Carbona Phyllite & 33.3 & 21 & 29.1 & 11.8 \\ \hline
10 & Micaceous Phyllite & 38.7 & 20.4 & 10.7 & 17.1 \\ \hline
11 & Penrhyn Slate & 35.1 & 48.33 & 14.7 & 34.27 \\ \hline
12 & Tourmemire Shale & 27 & 9.9 & 2 & 30.5 \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._ \begin{table}
\begin{tabular}{c c c c c c} \hline
**No.** & **Rock Type** & \(\mathbf{\varphi_{o}}\)\({}^{C}\) & **S\({}_{o}\)/MPa** & \(\mathbf{\phi_{\text{bp}}}\)\({}^{C}\) & **S\({}_{\text{bp}}\)/MPa** & \(\mathbf{\eta}\) \\ \hline
1 & Bossier shale & 30.6 & 30 & 34.8 & 10.8 & 0.42 \\ \hline
2 & Vaca Muerta shale & 26.8 & 34.6 & 28 & 20 & 0.1 \\ \hline
3 & Anigiers Schist & 40.8 & 36.4 & 8 & 12 & 0.14 \\ \hline
4 & Martinsburg Slate & 31.2 & 48.4 & 19.2 & 14 & 0.3 \\ \hline
5 & Austin Slate & 22 & 92.2 & 30 & 23 & 0.5 \\ \hline
6 & GreenRiver Shale 1 & 28 & 69 & 33.2 & 40 & 0.07 \\ \hline
7 & GreenRiver Shale 2 & 20 & 44.2 & 21.2 & 30 & 0.16 \\ \hline
8 & Quartz Phyllite & 33.2 & 24.6 & 29.2 & 17 & 0.2 \\ \hline
9 & Carbona Phyllite & 33.2 & 23.6 & 36 & 13 & 0.28 \\ \hline
10 & Micaceous Phyllite & 36.8 & 24.2 & 26.8 & 13 & 0.71 \\ \hline
11 & Penrhyn Slate & 36 & 50 & 33.2 & 29 & 0.57 \\ \hline
12 & Tourmemire Shale & 24 & 14 & 32.6 & 7 & 0.32 \\ \hline \end{tabular}
\end{table} 
Table 2: Fitting parameters of patchy plane of weakness model.