## 3 Results
### Mechanic Behavior of Fracture While Water Pressurization  
The fracture is expected to slide during water pressurization while the normal stress on the surface remains constant so that the servo-control system can modify the confining pressure and the axial stress simultaneously. The shear stress (\(\tau\)) and normal stress (\(\sigma_{n}\)) of the fracture are determined by the axial stress (\(\sigma_{1}\)) and confining pressure (\(\sigma_{3}\)):  
\[\sigma_{n}=\frac{1}{2}[(\sigma_{1}+\sigma_{3})+(\sigma_{1}-\sigma_{3})\cos 2\theta] \tag{1}\]  
\[\tau=\frac{1}{2}(\sigma_{1}-\sigma_{3})\sin 2\theta \tag{2}\]  
where \(\theta\) is the normal angle of the fracture surface, equaling \(60^{\circ}\) in this experiment. Shear displacement (\(D\)) can be calculated according to axial displacement instead of direct measurement. The initial pore pressure inside the fracture is \(p\). Therefore, the friction coefficient (\(\mu\)) is the ratio between shear strength (\(\tau_{c}\)) and the effective normal stress (\(\sigma_{n}-p\)). \(\tau_{\tau}\) is defined as the ratio between the shear stress and shear strength of the fracture while under water pressurization [12]. Since the fracture slip can release elastic energy and induce seismicity, we introduced the moment \(M_{0}\) to describe the energy released while sliding. \(M_{0}\) is the product of the  
Figure 5: The contour of the roughness of the smooth fracture surface. (**a**) before shearing; (**b**) after shearing; (**c**) shear surface. fracture area (\(A\)), shear displacement (\(D\)) and shear modulus (\(G\)), determined by the Young's modulus and Poisson ratio. \[M_{0}=GAD \tag{3}\]  
\[M_{W}=\frac{2}{3}\log M_{0}-6.07 \tag{4}\]  
Figure 6 shows that the fracture is pressurized at 20.8 MPa under normal stress and 13.6 MPa under shear stress. The friction coefficient is 0.87, and the ratio \(r_{\tau}\) is 98%. The outlet pressure rises at a nonlinear incremental rate, depending on the water pressure diffusion along the fracture. There are 23 seismic events during the process. The fault failure is expected when the water pressure exceeds 5.2 MPa, due to \(r_{\tau}\). This happens when the outlet pressure reaches this level, meaning that the distribution of the pore pressure on the whole fault surface is over 5.2 MPa. In the first cycle, the inlet pressure is maintained at 6.0 MPa, and the outlet pressure continuously increases. The fracture permeability before the fracture slip is 7.23 mD, which is measured based on the constant inlet pressure and increasing outlet pressure. At 282 s, when the outlet pressure reaches 5.30 MPa, the fracture slip occurs, accompanied by a shear stress drop and shear displacement jump. The outlet pressure drops immediately after the slip event because of the shear dilation of the fracture [13]. However, after two stick slips, the outlet pressure still increases due to the imbalance between the inlet and outlet pressures. At the end of the first cycle, the outlet pressure is approximately equal to the inlet pressure. This fault is transitioning from stick-slip to stable sliding. In the second cycle, the occurrence of the slip events is also accompanied by a slight drop in the outlet pressure followed by a remarkable increase until the outlet pore pressure reaches 5.5 MPa, instead of the maximum pressure (6.8 MPa), in the second pressurization stage. However, there is no slip event in the third cycle and this could be regarded as a  
Figure 6: The cyclic pressurization instability of a saw-cut fracture. (**a**) The shear stress and shear displacement with shearing time; (**b**) The inlet pressure and outlet pressure with shearing time. stable state in the second stage. After nine slip events, the fracture permeability becomes 12.06 mD, indicating permeability enhancement during the fracture slip. In the third stage, the fault begins to slip at the time the outlet pressure exceeds the maximum water pressure in the second stage. Twelve slips occur subsequently with the rise in inlet pressure and outlet pressure.