Self-sustained Oscillations in the Transition Zone From a Spring - block Model with Lubricated Surfaces

Abstract:

The mechanism of SSE’s is still not clear but investigations suggest that fluids play an important role and that failures are lubricated regardless of the composition of the rocks and the frictional mechanism involved. Experimental data show that the physical and mechanical parameters that control changes in SSE’s are rates of convergence, frictional parameters and effective normal stress among others. A path to study of SSE’s is through spring-block model for ordinary earthquakes, concentrated around the critical value of nucleation (transition region). Many of these models display oscillatory complex behavior associated with this zone and is presented as changing when there is a variation in any parameter related with it. This behavior corresponds to self-oscillations (it oscillates in presence or absence of external forces that perturb the system but eventually converge to a standard limit cycle) and can be explained by the Hopf bifurcation mechanism. The self-oscillations occur in the conditionally stable region related with SSE’s.The self-oscillations are explained in the context of fault’s system. The movement’s modeling in a single failure is affected by external forces that can be due to vibrations or stress transfered from neighboring faults, that make the system is going from a limit cycle to another, leaving differents paths of recurrence. In this investigation it analyzed the Madariaga's spring-block model coupled with Dieterich-Ruina friction law and complemented by the Stribeck's effect which shows the transition from dry interfaces or lubricated at the border to separated by a layer of lubricant as a shear melting combining the macroscopic and microscopic mechanism between the contacting surfaces. It introduced an external periodic perturbation, in order to show that system exhibits self-sustained oscillations near the Hopf bifurcation (critical value of nucleation). This analysis was focussed on the parameter related with the oscillation frequency of the block. It proposed a limit for this region with mathematical and numerical relations in terms of frictional and seismic parameters in the unstable region. It was shown analitically and computationally that within this limit self-oscillations are observed and out of this the system is unstable displaying more transitions.