ISSN:
1420-9136
Keywords:
Rock friction
;
constitutive behaviour
;
earthquakes
;
stability analysis
Source:
Springer Online Journal Archives 1860-2000
Topics:
Geosciences
,
Physics
Notes:
Abstract The nature of sliding on natural faults and laboratory rock friction samples depends on the interaction between the material along the slip surface and the elastically distorted material that loads the surface. Similar systems involving a single friction block and a spring show stable or unstable sliding for a given spring stiffness, depending on the details of the friction constitutive law. State variable constitutive laws describing laboratory rock friction have been used previously byGu et al. (1984) in an analysis of the behavior and stability of spring and block models, with an emphasis on constitutive laws having only one state variable. Since two state variables are often necessary to describe adequately laboratory rock frictional resistance, we have conducted a numerical study of the behavior of systems with this type of friction constitutive law. The behavior and stability of such systems depends on the values of the five constitutive parameters and the spring stiffness, but the most important single quantity is the ratio of the spring stiffness to a critical stiffness. The behavior of such systems can be usefully represented in a three dimensional phase space plot. If the steady state friction shows a negative dependence on slip velocity, then for spring stiffnesses nearly equal to or greater than the critical stiffness a stability surface separates points in phase space that remain stable from those that will become unstable. Two dimensional projections from phase space, while not complete descriptions of system behavior, are useful in many situations and are similar to the simpler phase plane plots used for one state variable systems. Good agreement is found between the predictions of our analysis and laboratory observations of stability. Such predictions, based upon two dimensional projections of behavior, can be done simply enough to be made in real time during experiments for comparison with actual behavior. Generally, if the steady state friction shows a positive dependence on slip velocity, the system will exhibit only stable sliding, but an interesting exception to this can occur if the two state variables evolve with opposite signs in such a way that the more rapidly evolving one acting alone would produce a negative velocity dependence. In such situations the sliding always eventually slows down and becomes stable, but it is possible for the velocities to become so high before this happens that for practical purposes in the laboratory the behavior would be called stick slip, and on a fault it would be called an earthquake.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00877210
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