## 4 Sensitivity Analyses: Results and Discussion
### Influence of the Far Field Stresses and Pore Fluid Pressure on Mud Weight Prediction  
The results reported in Section 4.2 evidenced some influence of the far field stresses and pore fluid pressure on the mud weight calculated with WPM and HBm. We investigated this influence with comparative analyses. Figure 10 shows a quantitative comparison of SG shown in Figure 9 and Table 3. The figure shows that almost all mud weights with \(R>1\) are well approximated with second-order polynomial functions (solid and dotted lines). Figure 10a (case \(R=1\)) shows that SG calculated with WPM is slightly higher than the SG calculated with HBm, when the far field stresses are 20-20 MPa with \(p_{f}=11\) MPa and 33-33 MPa with \(p_{f}=15\) MPa. On the other hand, SG coincide when the far field stresses are 33-33 MPa with \(p_{f}=11\) MPa. The reason for the mismatch and coincidence of the two approaches can be attributed to the different sensitivity to the far field stresses and pore fluid pressure. In all cases with \(R>1\), the SG calculated with the two criteria are alternatively higher/lower as a function of the inclination \(\delta\) and the far field stress anisotropy \(R\) (Figure 9b-d). The trend for mud weight with \(\delta\) is practically parallel in each approach. WPM predicts higher SG in the range \(\delta=0^{\circ}\)-\(45^{\circ}\) and lower SG in the range \(\delta=45^{\circ}\)-\(90^{\circ}\) at high \(R\). Figure 10b-d indicate that the difference between WPM and HBm predictions does not change with the magnitude of the pore fluid pressure. In fact, the change in trend (higher/lower SG) almost always occurs at the same \(\delta\), regardless of the variation of the pore fluid pressure. Figure 9: Comparison of SG calculated with WPM (**a**,**c**,**e**,**g**) and HBm (**b**,**d**,**f**,**h**) at different inclinations of the weak planes \(\delta\), far field stresses \(R=\sigma_{MAX}/\sigma_{min}\) and pore fluid pressures \(p_{f}\). SG related to the plateau strength is called the rock matrix. The instantaneous dimensionless constant was fixed at the average value \(m_{\beta w}=5.16\). The increase in pore fluid pressure (see Table 3) is \(\Delta p_{f}=+36\%\) (case \(R=1.5\)) and \(\Delta p_{f}=+37\%\) (cases \(R=1.1\) and \(R=1.25\)). This increase is practically equal. Figure 10e shows the percentage change in SG with the change in pore fluid pressure \(\Delta p_{f}\). The figure indicates that the percentage increase in SG is higher at \(R=1.1\) for both criteria. This result indicates that SG is more sensitive to an increase in pore fluid pressure at low anisotropy of the far field stresses. The maximum SG always occurs at \(\delta=0^{\circ}\) (HBm) and at \(\delta=90^{\circ}\) (WPM). The  
Figure 10: (**a**) Quantitative comparison between SG calculated with WPM and HBm. (**a**) \(R=1\) and \(p_{f}=11\)–\(15\) MPa. (**b**) \(R=1.1\) and \(p_{f}=8\)–\(11\) MPa. (**c**) \(R=1.25\) and \(p_{f}=8\)–\(11\) MPa. (**d**) \(R=1.5\) and \(p_{f}=11\)–\(15\) MPa. (**e**) Variation percentage of SG calculated with WPM and HBm with variation of the pore fluid pressure from \(p_{f}=11\) MPa to \(p_{f}=15\) MPa, resulting in a percentage increase in \(\Delta p_{f}=+36\%\). (**f**) Percentage change in SG calculated with HBm and WPM. difference between the percentage change in SG calculated with the two criteria becomes relevant when \(R>1.1\) and \(\delta>50^{\circ}\). The trends of the percentage change obtained with Hbm are almost parallel for all cases (\(R=1.1\), \(R=1.25\) and \(R=1.5\)). On the other hand, the trends of the percentage change obtained with WPM vary with \(R\), with a remarkable rise from \(\delta=30^{\circ}\) to \(90^{\circ}\), when \(R=1.5\). Figure 10f shows the comparison between the WPM and Hbm predictions of SG, in terms of percentage change, when \(R=1.1\) and \(R=1.5\). The figure shows that the most significant decrease in SG of Hbm (\(-9\%\)), occurs when \(R=1.1\) at \(\delta=0^{\circ}\).