## 4 Discussion  
### Effects of Pressurization Rate on Fault Slip Initiation  
Under conditions of different factors and different levels, the injection pressure at the onset of slip was noticeably different, and it was higher than what the fault reactivation criterion predicted. To analyze the potential causes, the overpressure ratio (_px_) was computed in this research:  
\[px=\frac{p}{\sigma_{n}-\frac{\tau}{\mu}} \tag{7}\]  
where _px_ is the ratio of the injection pressure \(p\) (MPa) at the initiation of slip to the theoretical fluid pressure when slip occurs, and \(\sigma_{n}\) (MPa) and \(\tau\) (MPa) are the normal stress and shear stress on the fault, respectively. The friction coefficient \(\mu=0.64\) was fitted with the shear strength obtained by the displacement-driven shear test under different confining pressures (Figure 7a).  
Taking the pressurization rate as an example, since there are three sets of repeating groups at each level, the overpressure ratio of each group is calculated by Formula (7) (Table 3). Excluding data with relative deviations exceeding \(\pm\)5%, the average overpressure ratio under various levels was calculated, as shown in Figure 7b. The closer the value of the overpressure ratio is to 1, the closer the measured value is to the theoretical prediction. As the pressurization rate increased, the results demonstrated that the measured injection pressure deviated more from the expected fluid pressure, which caused the fluid overpressure ratio to gradually increase from 1.19 to 3.7 (Figure 7b). Furthermore, the overpressure ratio exhibited a similar trend with respect to the impact of the confining pressure. The overpressure ratio rises from 1.78 to 3.24 when the confining pressure increases from 10 MPa to 30 MPa. The overpressure ratio rises from 2.19 to 2.75, while the initial stress state rises from 80% to 90%. However, the values for faults with different initial stress states were 2.22, 2.54, and 2.57, which showed little difference.  
The experimental results showed that the injection pressure required for fault reactivation at a high pressurization rate was greater than that at a low pressurization rate and  
Figure 7: (**a**) The frictional coefficient obtained by fitting shear the strength. (**b**) The overpressure ratio for different factors and levels.  
greater than that predicted by theory, possibly showing that the fluid pressure distribution on the fault was not uniform. [PERSON] [37] reproduced the distribution of fluid pressure on the fault through numerical simulation. The results show that the closer it was to the borehole, the greater the fluid pressure, as shown in Figure 8. In addition, a high injection rate increased the degree of non-uniformity of the fluid pressure distribution, as the pressurized area at a high injection rate was significantly smaller than at a low injection rate before slip initiation. Therefore, under a high injection rate, the pressurized area expands continuously before slip starts, but the pressurized area is still much smaller than the fracture area. Because only a small part of the fault is in the pressurized area, higher local pressure is needed to propagate the slip front. As a result, when the pressurization was high, fault slip initiation required a higher injection pressure. However, when the injection rate was low, the pressurized area extended to almost the entire fault when the fault slip started.