2:15 PM - 2:30 PM
[SCG44-09] Study on the dynamical system of development of faults
Keywords:Strain concentration zone, Physical model, Tribology, Viscoelastic-plastic body
Multiple shear planes could develop in a bedrock although a single shear plane has been often assumed in laboratory experiments to study slip behaviors and in dynamical models to account for the size distribution of earthquakes. The condition of fault development and the interaction processes among multiple faults are unsolved interesting issues. We proposed a spring-block model for a bedrock including multiple slip planes as shown in Fig.1 to study the development of fault structures theoretically and carried out numerical simulations. We apply a velocity-dependent friction law to each slip surface of adjacent elements in this model. For the frictional law that the frictional force increases rapidly with increasing velocity and then decreases, as shown in Fig. 2, this simple model describes development of a single fault or multiple faults, and we can clarify their development conditions by analyzing it as a dynamical system. In this study, we introduced two dimensionless parameters representing the shear velocity of the system, V, and the elastic modulus of each element, p, and focused on the spatiotemporal distribution of slip and the average of frictional forces.
Numerical results revealed four phases that exhibit qualitatively different spatiotemporal behaviors in slip. We defined entropy as a measure of the uniformity of the spatial distribution of slip to make the phase diagram in the V-p plot, shown in Fig.3. In the cases that both V and p are small, only uniform creep deformation occurs with no rapid slip anywhere. This phase corresponds to uniform steady states, and such solutions are linearly stable only in the velocity range where the slope of the friction law is positive.
As V or p increases, the uniform steady states become unstable, and three phases appear in slip pattern. A typical pattern of rapid slips in each phase is shown in Fig. 4. In the region (a) in Fig. 3a), short-time rapid slips occur in every slip planes. As shown in Fig. 4a), complex patterns appear such that positions of rapid slips change temporally and always exit somewhere in the system. In the small island-like region (b) in Fig. 3, rapid slips always occur everywhere, as shown in Fig. 4b). By contrast, in the region (c) in Fig.3, a plane that slides continuously and rapidly develops locally, as shown in Fig. 4c). It is inferred to corresponds to the creation of a strain concentration zone.
The average resistant force of an entire bedrock to applied shear deformation depends on how slip occurs in the system, and does not match the microscopic friction forces between rocks, which corresponds to the frictional law applied in each slip plane in our model. Numerical results in Fig.5 indicates that macroscopic friction forces are much smaller than the microscopic friction forces in cases that rapid slips occur.
Experiments on rock frictions indicate friction laws with memory effects, in which frictional forces between rocks increase with the holding time and decrease with the velocity in the form of log(v). Therefore, we are attempting to apply such a friction law to our model. In this presentation, we will also report the effect of the memory effects in the friction law to fault development and the interaction of multiple faults.
Numerical results revealed four phases that exhibit qualitatively different spatiotemporal behaviors in slip. We defined entropy as a measure of the uniformity of the spatial distribution of slip to make the phase diagram in the V-p plot, shown in Fig.3. In the cases that both V and p are small, only uniform creep deformation occurs with no rapid slip anywhere. This phase corresponds to uniform steady states, and such solutions are linearly stable only in the velocity range where the slope of the friction law is positive.
As V or p increases, the uniform steady states become unstable, and three phases appear in slip pattern. A typical pattern of rapid slips in each phase is shown in Fig. 4. In the region (a) in Fig. 3a), short-time rapid slips occur in every slip planes. As shown in Fig. 4a), complex patterns appear such that positions of rapid slips change temporally and always exit somewhere in the system. In the small island-like region (b) in Fig. 3, rapid slips always occur everywhere, as shown in Fig. 4b). By contrast, in the region (c) in Fig.3, a plane that slides continuously and rapidly develops locally, as shown in Fig. 4c). It is inferred to corresponds to the creation of a strain concentration zone.
The average resistant force of an entire bedrock to applied shear deformation depends on how slip occurs in the system, and does not match the microscopic friction forces between rocks, which corresponds to the frictional law applied in each slip plane in our model. Numerical results in Fig.5 indicates that macroscopic friction forces are much smaller than the microscopic friction forces in cases that rapid slips occur.
Experiments on rock frictions indicate friction laws with memory effects, in which frictional forces between rocks increase with the holding time and decrease with the velocity in the form of log(v). Therefore, we are attempting to apply such a friction law to our model. In this presentation, we will also report the effect of the memory effects in the friction law to fault development and the interaction of multiple faults.