# A New Look at the Stress State Across the Bohai Strait, China
## 5 Discussion
### Implications for Fault Reactivation  
The Earth's crust contains faults, fractures, and geological discontinuities on various scales and orientations. It is widely accepted that the strength of the crust is controlled by the strength of these discontinuities and is maintained at a critical failure state [1; 3; 7]. By summarizing the measured stress data from deep boreholes worldwide, [PERSON] and [PERSON] [82] noted that the stress state in the upper crust, i.e., several kilometers, can be described using the Coulomb friction criterion. Generally, the Coulomb friction criterion is as follows:  
\[\tau\ =\ \mu S_{n}\ +\ C, \tag{8}\]  
Figure 10: Sketch map illustrating the relationship between the stress state across the Bohai Strait and the tectonic framework. Figure 9: The graph shows the variation in maximum horizontal shear stress across the Bohai Strait as a function of distance from the Zhangjiakou–Bohai Fault. where \(\tau\) is the shear stress, \(S_{\rm n}\) is the effective normal stress, \(\mu\) is the coefficient of friction, and \(C\) is cohesion. The normal stress and shear stress acting on a fault plane can be expressed using the following formulas:  
\[\tau=\frac{1}{2}(S_{1}-S_{3})\sin 2\theta \tag{9}\]  
\[S_{\rm n}=\frac{1}{2}(S_{1}+S_{3})+\frac{1}{2}(S_{1}-S_{3})\cos 2\theta \tag{10}\]  
where \(\theta\) is the angle between the fault normal. \(S_{1}\)-\(S_{3}\) are the maximum, intermediate, and minimum principal stresses, respectively, and can be determined from the measured stresses by considering the stress regime. Assuming \(C\) = 0, the Coulomb friction criterion can be expressed by the following equations:  
\[\frac{S_{1}-P_{0}}{S_{3}-P_{0}}=(\sqrt{\mu^{2}+1}+\mu)^{2}, \tag{11}\]  
\[\theta=\frac{1}{2}(\frac{\pi}{2}+\tan^{-1}\mu) \tag{12}\]  
where \(P_{0}\) is the pore pressure, which is usually equivalent to hydrostatic pressure [82; 83]. Based on experiments on various intact rocks, [PERSON] [84] noted that \(\mu\) mainly ranges from 0.6 to 1.0, which is commonly referred to as [PERSON]'s law. Both theories and extensive deep borehole measurement data demonstrate that [PERSON]'s law and the Coulomb friction criterion are suitable for analyzing the shallow crustal stress state [1; 3; 82]. Therefore, this study adopts the commonly accepted range of 0.6 to 1.0. If the value of the left side of Equation (11) is equal to or greater than the limit on the right side, that is, determined using a \(\mu\) of 0.6, the optimally oriented fault will reactivate and slip. On the contrary, when the value of the left side is lower than this limit, the fault is in a temporary stability state. We estimated the stress state of the four boreholes and plotted the results in Figure 11. The results indicate that the stress state in the four boreholes has not reached the critical failure threshold yet (i.e., the line marked \(\mu\) = 0.6 in Figure 11). This implies that faults in the Bohai Strait region, regardless of whether they are optimally or non-optimally oriented, are temporarily in a stable state and have a low chance of slipping. It was also found that the apparent values of \(\mu\) for the PD and GZ boreholes are much lower than those of the XL and CD boreholes. The CD and XL boreholes are closer to the threshold that induces fault slipping, revealing a consistent feature with the stress level and seismic activities in the Bohai Strait region. Thus, the stress state in the Bohai Strait is temporarily far from the critical failure limit, and the faults show low reactivation potential. It should be noted here that the estimation of the potential reactivation of faults in this study does not consider the possible influence of pore pressure variation, thermal effects, or fault heterogeneity, which are crucial factors and may lead to reassessment of the slipping tendency. Without sufficient and reliable data that match the scale of this study at present, research including these factors may be performed in the future. Moreover, the above estimation is upon based on certain values of in-situ stress.