Abstract
We investigate the propagation of a slip front in a visco-elastic body on a rigid substrate. The body is one-dimensional, and the loading stress is applied at one end. By employing a local friction law that has a quadratic form of the slip velocity and gives vanishing friction stress at vanishing velocity or above a certain velocity, we show analytically that macroscopic steady slippage and creep motion can be understood in a single framework. The critical values of the end-loading stress causing macroscopic steady slippage and the slip-front propagation velocity appear are obtained. These values are completely determined by the gradient of the slip velocity-friction curve at the vanishing friction stress. These results are extended to more general friction laws, and found to be consistent with numerical calculations. Furthermore, we discuss some seismological implications based on the analytical and numerical results.
Highlights
When we apply a small loading stress in a tangential direction to a solid object on a solid substrate and increase the force slowly, the block slips as a whole only when the force exceeds a critical value, i.e., the macroscopic static friction force
We find a critical value of the applied stress, above which the slip-front propagation (SFP) has a finite propagation velocity; below the critical value, the SFP decays
We examined a 1D visco-elastic model under endloading stress to investigate the macroscopic slip initiation
Summary
When we apply a small loading stress in a tangential direction to a solid object on a solid substrate and increase the force slowly, the block slips as a whole only when the force exceeds a critical value, i.e., the macroscopic static friction force Though this behavior has long been recognized, the condition determining whether or not macroscopic steady slippage occurs has not been clarified in a single framework. We find a critical value of the applied stress, above which the SFP has a finite propagation velocity; below the critical value, the SFP decays This means that the transition between macroscopic steady slippage and creep motion appears in the model with the local friction law employed here. Implications of this work for precursors and slow earthquakes based on slippage with a driving stress less than the critical value are presented
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