5:15 PM - 7:15 PM
[SSS10-P01] Spontaneous crack tip propagation outside the nucleation zone taking account of the rate-and-state friction law and the interaction between heat and fluid
Keywords:heat, fluid, rate-and-state friction law, crack tip propagation, nucleation zone
The propagation velocity of fault tips and nucleation mechanism of cracks have attracted interests of researchers. For example, Suzuki and Yamashita (2009, JGR) simulated the propagation of crack tips by incorporating the effects of the interaction among heat, fluid, and pore generation. This model successfully explains both the fast and slow earthquakes. However, note that Suzuki and Yamashita (2009) used a simple friction coefficient consisting of a constant static friction coefficient and a kinetic friction coefficient. Recent studies have suggested that a rate-and-state dependent friction law is a more appropriate friction law. The rate-and-state-dependent friction law characterizes the effect of the slip velocity on the friction coefficient and the effect of the state variables with the parameters A and B, respectively. It should be noted that the larger A-B induces the stronger velocity strengthening. Moreover, they did not treat tremors.
In the current study, the rate-and-state-dependent friction law and the interaction between the heat and fluid are incorporated in a single framework. Spontaneous crack propagation in a two-dimensional anti-plane shear crack is considered. We consider the slip zone whose thickness is wh, where the heat and fluid effects work. In addition, we consider a nucleation zone, within which the crack tip is assumed to grow at a constant propagation speed. After the crack tip reaches the edge of the nucleation zone, spontaneous propagation begins. In this model, we investigated whether a crack propagates spontaneously or nor by changing the parameters of the rate-and-state-dependent friction law and wh. The results of the numerical calculations suggest that when the value of wh is fixed, propagation outside the nucleation zone occurs when the A-B value is in small and large regions, and does not occur in the intermediate region. Furthermore, it was found that the time when the propagation occurs differs between the small and large A-B groups. In the small A-B group, the propagation begins relatively soon after the crack tip reaches the edge of the nucleation zone, and the larger A-B, the later the propagation occurred. However, in the large A-B group, the propagation exhibits a delay in initiation after the crack tip reaches the edge of the nucleation zone. Additionally, the larger A-B, the earlier the propagation occurred.
We investigate the reason for the difference in the behavior between small and large A-B groups. For the small A-B group, the system behavior is easy to understand. Since the velocity strengthening is weaker for the smaller A-B value, the slip velocity inside the nucleation zone is smaller for larger A-B, and the stress concentration is also smaller for larger A-B. Consequently, the later propagation emerges for the larger A-B value, which is intuitively reasonable. However, the system behaves contrary to intuition for large A-B group. For this group, we first emphasize that the slip velocity inside the nucleation zone is smaller for larger A-B value before the reflected waves arrive on the point. After the reflected waves pass, the slip velocity can become larger for the larger A-B value because the deceleration effect due to the rate-and-state friction law is weaker for the larger A-B. We then note that the heat and fluid effects work inside the nucleation zone during the slip, and the effect can completely release the stress on the crack plane eventually. This effect can emerge earlier for larger A-B, since the slip velocity after the reflected waves pass the point is larger. This induces the earlier stress concentration and earlier propagation outside the nucleation zone.
The result obtained here implies that we should consider both the rate-and-state friction law and the interaction between heat and fluid to investigate the dynamic earthquake source process. This may provide important insights also for the mechanisms of slow earthquakes such as tremors.
In the current study, the rate-and-state-dependent friction law and the interaction between the heat and fluid are incorporated in a single framework. Spontaneous crack propagation in a two-dimensional anti-plane shear crack is considered. We consider the slip zone whose thickness is wh, where the heat and fluid effects work. In addition, we consider a nucleation zone, within which the crack tip is assumed to grow at a constant propagation speed. After the crack tip reaches the edge of the nucleation zone, spontaneous propagation begins. In this model, we investigated whether a crack propagates spontaneously or nor by changing the parameters of the rate-and-state-dependent friction law and wh. The results of the numerical calculations suggest that when the value of wh is fixed, propagation outside the nucleation zone occurs when the A-B value is in small and large regions, and does not occur in the intermediate region. Furthermore, it was found that the time when the propagation occurs differs between the small and large A-B groups. In the small A-B group, the propagation begins relatively soon after the crack tip reaches the edge of the nucleation zone, and the larger A-B, the later the propagation occurred. However, in the large A-B group, the propagation exhibits a delay in initiation after the crack tip reaches the edge of the nucleation zone. Additionally, the larger A-B, the earlier the propagation occurred.
We investigate the reason for the difference in the behavior between small and large A-B groups. For the small A-B group, the system behavior is easy to understand. Since the velocity strengthening is weaker for the smaller A-B value, the slip velocity inside the nucleation zone is smaller for larger A-B, and the stress concentration is also smaller for larger A-B. Consequently, the later propagation emerges for the larger A-B value, which is intuitively reasonable. However, the system behaves contrary to intuition for large A-B group. For this group, we first emphasize that the slip velocity inside the nucleation zone is smaller for larger A-B value before the reflected waves arrive on the point. After the reflected waves pass, the slip velocity can become larger for the larger A-B value because the deceleration effect due to the rate-and-state friction law is weaker for the larger A-B. We then note that the heat and fluid effects work inside the nucleation zone during the slip, and the effect can completely release the stress on the crack plane eventually. This effect can emerge earlier for larger A-B, since the slip velocity after the reflected waves pass the point is larger. This induces the earlier stress concentration and earlier propagation outside the nucleation zone.
The result obtained here implies that we should consider both the rate-and-state friction law and the interaction between heat and fluid to investigate the dynamic earthquake source process. This may provide important insights also for the mechanisms of slow earthquakes such as tremors.