Project Abstract
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This project explored the multi-scale dynamic behavior of multi-degree of freedom systems with strong rate weakening friction, a feature that has been proposed to explain the paucity of frictional melts observed in exhumed faults. In particular, we investigate the chaotic behavior of slip pulses that propagate in a spring block slider model with velocity weakening friction by numerically solving a computationally intensive set of n coupled non-linear equations, where n is the number of blocks. We observe that the system evolves into a spatially heterogeneous pre-stress after the occurrence of a sufficient number of events. We observe that, although the spatio-temporal evolution of the amplitude of a slip pulse in a single event is surprisingly complex, the geometric description of the pulses is simple and self-similar with respect to the size of the pulse. This observation allows us to write an energy balance equation that describes the evolution of the pulse as it propagates through the known prestress. The equation predicts the evolution of individual ruptures and reduces the computational time dramatically. The long time solution of the equation reveals its multi-scale nature and its potential to match many of the long time statistics of the original system, but with a much shorter computational time. |
