## 4 Comparison of Prediction Accuracy
### Results and Analysis
Moreover, within the range of 0\({}^{\circ}\) to \(\beta_{1}\) and \(\beta_{2}\) to 90\({}^{\circ}\), the SPW criterion underestimates the rock's strength and fails to reflect the difference in strength between rocks oriented perpendicular and parallel to the bedding plane. However, between \(\beta_{1}\) and \(\beta_{2}\), the predictive results of the SPW criterion align closely with the test values. Analyzing the characteristics of the Pariseau criterion predictive curves as shown in Figures 3b and 4b, it is noted that [PERSON]'s model comprises a single expression encompassing all stress ranges, depicting a smooth transition in strength from shear fracture, mixed failure mode to sliding along weak planes. This criterion is a continuous function of the bedding plane angle (\(\beta\)). Another aspect of [PERSON]'s model is its capability to capture strength differences between \(\beta\) = 0\({}^{\circ}\) and \(\beta\) = 90\({}^{\circ}\), unlike the JPW model, which assumes the same strength at these angles, leading to a more accurate predictive performance. A comprehensive examination of the PPW criterion's predictive behavior, as visualized in Figures 3c, 4c, 5, 6, 7, 8, 9, 10, 11, 12, 13 and 14, reveals a distinctive sinusoidal oscillation pattern in its strength-angle relationship for layered rocks, reflecting the criterion's capacity to accommodate materials with diverse anisotropy levels. The fluctuation amplitude of these characteristic curves is governed by the dimensionless parameter \(\eta\), which directly correlates with the magnitude of mechanical anisotropy exhibited by the rock strata. Strongly anisotropic formations such as Angiers Schist and Penrhyn Slate manifest heightened \(\eta\) values, producing pronounced wave-like strength variations across bedding orientations under equivalent confinement, whereas weakly anisotropic lithologies like Tournemire Shale and GreenRiver Shale sequences display subdued undulations with minimized \(\eta\) values. Furthermore, confining pressure exerts a transformative influence on curve morphology: under low confinement, the PPW criterion generates sharp, angular peaks and troughs in strength predictions, while elevated confining pressures progressively attenuate these oscillations, ultimately collapsing the waveform into a continuous, symmetrical U-shaped profile. This pressure-dependent transition from discontinuous waviness to smooth continuity is particularly evident in materials such as Austin Slate and Carbona Phyllite, where the interplay between confinement-induced stress redistribution and bedding plane weakness governs the evolution of failure mechanisms across angular domains. Figure 5: Experimental data of Vaca Muerta shale fit with [PERSON]’s model. This suggests that the PPW criterion, by introducing the dimensionless parameter \(\eta\) in the SPW criterion, brings the strength predictive results closer to the tested values within the range of \(0^{\circ}\) to \(\beta_{1}\) and \(\beta_{2}\) to \(90^{\circ}\) of bedding plane angles. Moreover, it accommodates variations in strength anisotropy under different types of rocks and different confining pressures. However, unlike the Pariseau criterion predictive results, the limitation of the PPW criterion lies in its inability to distinguish between the strength of rocks oriented perpendicular to the bedding plane and those parallel to it. Figure 8: Experimental data of GreenRiver Shale 1 fit with [PERSON]’s model. Figure 6: Experimental data of Martinsburg Slate fit with patchy plane of weakness model. Figure 7: Experimental data of Austin Slate fit by plane with patchy weakness model. Figure 11: Experimental data of Carbona Phyllite fit with [PERSON]’s model. Figure 12: Experimental data of Micaceous Phyllite fit with [PERSON]’s model. Figure 10: Experimental data of Quartz Phyllite fit with plane of patchy weakness model. Figure 4:0 Experimental data of GreenRiver Shale 2 fit with [PERSON]’s model.