Analytical Treatments of Static Friction Force and Propagation Velocity of Slip Front with Viscosity and Friction Nonlinearly depending on the Slip Velocity
Abstract
We consider a block on a rigid and fixed substrate and apply the shear force to the block in order to understand systematically the emergence of the macroscopic static friction force and the selection mechanism of the slip front velocity. The block is assumed to be one-dimensional system along x direction and a semi-infinite homogeneous medium. The shear force is applied along x direction by pushing left side of the block. We consider here slip front propagation (SFP) into an intact area and require the boundary condition for the strain p: p(-∞)=p∞ and p(∞)=0, where p∞ (<0) is constant; that is, we load the block at x → -∞ to initiate the slip and the slip of block at x → ∞ is fixed to be zero. We employ the friction law having a quadratic form of the slip velocity; the friction force is given by -av2+2abv, where v is the slip velocity and a and bare constants. Additionally, we consider two cases; cases with and without the viscosity of the block. We first treat the case in the absence of the viscosity. We can obtain the relationship between p∞ and the slip front velocity c for this case; |p∞|=2b/c. It is also important to note that c must be smaller than the elastic wave velocity for the block, ve, for the existence of the steady state. These statements indicate that p∞ has the critical value; if |p∞|<2b/ve, the steady propagation cannot be observed, while if |p∞|>2b/ve, the steady propagation of slip appears. This behavior implies spontaneous emergence of the macroscopic static friction force even though the local friction has vanishing static friction force. Macroscopic static friction force is given by 2bE1/ve, where E1 is the Young modulus. If we introduce the viscosity of the block, the SFP velocity c' is found to be , and the static friction force is given by 2 bE1/c'. These results may play an important role for understanding seismological phenomena such as foreshocks.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2016
- Bibcode:
- 2016AGUFM.S21B2707S
- Keywords:
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- 7209 Earthquake dynamics;
- SEISMOLOGYDE: 7215 Earthquake source observations;
- SEISMOLOGYDE: 8118 Dynamics and mechanics of faulting;
- TECTONOPHYSICSDE: 8163 Rheology and friction of fault zones;
- TECTONOPHYSICS