Friction constitutive law with rate and state dependences
- 178 Downloads
A general formula for the Dieterich-Ruina friction constitutive law with rate and state (n-state variables,n=1, 2,...) dependences has been obtained and discussed under the assumption that the slip acceleration a varies ion a linearly with the slip displacement δ, namelya = a0 + α(δ-δ0). Wherea0, δ0 are initial constants, α is the acceleration rate and constant.a0 and α may be arbitrary constants (positive, negative or zero).
The extreme value of frictional resistance and the existence condition of the extreme value, which are very important and govern to some degree the motion process of a frictionally slipping mechanical system, have been analyzed. A critical value λc which is the measure of the velocity weakening and velocity strengthening of the mechanical system, and its properties and the relationship to the extreme problem have been studied. Again, according to the critical value λc, the concepts of light or strong velocity weakening (or strengthening) are introduced.
A possibly new phenomenon that frictional resistance may vary in some kind of decayed oscillation is found. Finally, the condition for the smallest frictional resistance for a slipping mechanical system with nonuniform acceleration has been obtained.
Key wordsFiction constitutive law accelerating slip
Unable to display preview. Download preview PDF.
- Dieterich, J. H. (1972),Time-dependent friction in rock. J. of Geophys. Res.77, 3690–3697.Google Scholar
- Dieterich, J. H.,Constitutive properties of faults with simulated gouge. InMechanical Behavior of Crystal Rocks (the Handin Volume) (eds. Carter, N. L., Friedman, M., Logan, J. M., and Stearns, D. W.) Geophys. Monograph Ser.,24, (Am. Geophys. Union, 1981) pp. 103–120.Google Scholar
- Dieterich, J. H. (1978),Time-dependent friction and the mechanics of stick-slip. Pure and Appl. Geophys.116, 790–806.Google Scholar
- Dieterich, J. H. (1979a),Modeling of rock friction: 1.Experimental results and constitutive equations. J. Geophys. Res.84, (B5), 2161–2168.Google Scholar
- Dieterich, J. H. (1979b),Modeling of rock friction: 2.Simulation of preseismic slip. J. Geophys. Res.84(B5), 2169–2175.Google Scholar
- Dieterich, J. H.,Experimental and model study of fault constitutive properties. InSolid Earth Geophysics and Geotechnology, (ed. Nemet-Nasser, S.) Appl. Mech. Div. 42 (Am. Soc. of Mech. Eng., New York 1980, pp. 21–30.Google Scholar
- Gu, J., Rice, J. R., Ruina, A. L., andTse, S. T. (1984),Slip motion and stability of a single degree of freedom elastic system with rate and state dependent friction. J. Mech. Phys. Solids32, 167–196.Google Scholar
- Gu, J. (1984/85),Frictional resistance to accelerating slip. Pure and Appl. Geophys.122, 662–679.Google Scholar
- Rabinowitz, E. (1958),The intrinsic variation affecting the stick-slip process, Proc. Phys. Soc.71, (4), 668–675.Google Scholar
- Rabinowitz, E. (1959),Friction and Wear, Proc. of the Symp. on Friction and Wear, (ed. R. Davies) Elsevier Publishing Cor., 149–164.Google Scholar
- Rice, J. R. andGu, J. (1983),Earthquake aftereffects and triggered seismic. Pure and Appl. Geophys.121, 187–219.Google Scholar
- Ruina, A. L.,Friction laws and instabilities: a quasistatic analysis of some dry frictional behavior. Ph. D. Thesis, (Brown University, Providence, RI, Nov. 1980).Google Scholar
- Ruina, A. L. (1983),Slip instability and state variable friction laws, J. Geophys. Res. (in press).Google Scholar
- Sampson, J. B., Morgan, F., Reed, D. W., andMuskat, M. (1943),Studies in lubrication, XII. Friction behavior during the slip portion of the stick-slip process. J. Appl. Phys.14, 689–700.Google Scholar
- Tullis, T.E. andWeeks, J. D. (1984),Constitutive behaviour and stability of frictional sliding of granite.Google Scholar