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AGU: Journal of Geophysical Research, Solid Earth

 

Keywords

  • Rate and state friction
  • linear viscoelasticity
  • slide-hold-slide tests

Index Terms

  • Tectonophysics: Rheology and friction of fault zones
  • Structural Geology: Rheology and friction of fault zones
  • Physical Properties of Rocks: Fracture and flow
  • Physical Properties of Rocks
  • Tectonophysics
Abstract
Cited By (0)
 

Abstract

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, B09408, 12 PP., 2008
doi:10.1029/2007JB005160

Modeling the mechanics of rate and state friction with linear viscoelasticity

Joseph B. Walsh

Box 22, Adamsville, Rhode Island, USA

David L. Goldsby

Department of Geological Sciences, Brown University, Providence, Rhode Island, USA

In slide-hold-slide friction experiments, rock surfaces loaded by normal stress σ slide against one another at velocity V until steady-state conditions prevail; the applied shear stress τ required for steady-state sliding is , where f is the friction coefficient. Sliding is then stopped abruptly for a specified hold time t H , and then resumed at velocity V. Shear stress τ and the separation Δw between the rough surfaces are measured throughout the test. During the hold period, both applied shear stress and separation are found to decay with time from their steady-state values. We show that the constitutive behavior in shear during the hold period is in effect a relaxation test, and likewise, the closure measurements describe a creep test. Analyzing the data in detail, we find that they can be modeled as the response of a standard linear solid, with a characteristic time T 1 for creep of 1900 s and a characteristic time T 2 for relaxation of 1400 s. The shear stress required to initiate sliding at the end of the hold period is found to peak Δ above the steady-state stress , then decay over a distance D c to the steady-state value. In our experiments, measurements of separation and shear load were made for hold periods as long as 106 s, i.e., one hundred times longer than in similar previous studies. We find that our measured values of Δf increase gradually with increasing hold times—in agreement with previous measurements up to about 104 s—but then approach a limiting value asymptotically. In our analysis we show that Δf is equal to (1 + f 2δ H /, where Δδ H is the total decrease in separation during the hold period and λ is a length parameter that describes the roughness of the surfaces. The parameter D c is found to be given by Δδ H f. Using measurements from our experiments, we find that both relationships are valid to a reasonable degree, considering the uncertainties in the data and the simplicity of the analysis.

Received 6 May 2007; accepted 28 April 2008; published 16 September 2008.

Citation: Walsh, J. B., and D. L. Goldsby (2008), Modeling the mechanics of rate and state friction with linear viscoelasticity, J. Geophys. Res., 113, B09408, doi:10.1029/2007JB005160.

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