Frictional resistance to accelerating slip |
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| Authors: | J C Gu |
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| Institution: | 1. Institute of Geophysics, State Seismological Bureau, Beijing, China
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| Abstract: | General analytical expressions for the friction stress and state variable, based on a rate and state-dependent constitutive friction law proposed by Dieterich and Ruina, have been obtained as an explicit function of slip rateV or slip timet or slip displacement δ under the assumption that slip accelerationa is constant or piecewise constant. Properties of the solutions have been discussed, and reviewed, for uniformly accelerating (or decelerating) slip, the following. - Frictional stress increases (or decreases) with increasing time, or slip rate, or slippage at the beginning of motion, until a maximum (or a minimum) value (when it exists) has been reached, then decreases (or increases), and finally approaches a special frictional state, namely a steady state, for which stress depends on instantaneous slip rate.
- The maximal value of frictional stress is dependent on accelerationa; the larger thea, the larger the magnitude of the maximum.
The energy expense ε needed to overcome the frictional stress has been estimated. And therefore the optimal value of acceleration for saving energy for a slipping mechanical system has been obtained. The energy release rateG for an abrupt rupture process of a crack or fault has been estimated. |
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