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A Visco-Elastic Damage Rheology and Rate- and State-Dependent Friction

Vladimir Lyakhovsky, Yehuda Ben-Zion, & Amotz Agnon

Published April 26, 2005, SCEC Contribution #854

We analyse the relations between a viscoelastic damage rheology model and rate- and state-dependent (RS) friction. Both frameworks describe brittle deformation, although the former models localization zones in a deforming volume while the latter is associated with sliding on existing surfaces. The viscoelastic damage model accounts for evolving elastic properties and inelastic strain. The evolving elastic properties are related quantitatively to a damage state variable representing the local density of microcracks. Positive and negative changes of the damage variable lead, respectively, to degradation and recovery of the material in response to loading. A model configuration having an existing narrow zone with localized damage produces for appropriate loading and temperature–pressure conditions an overall cyclic stick–slip motion compatible with a frictional response. Each deformation cycle (limit cycle) can be divided into healing and weakening periods associated with decreasing and increasing damage, respectively. The direct effect of the RS friction and the magnitude of the frictional parameter a are related to material strengthening with increasing rate of loading. The strength and residence time of asperities (model elements) in the weakening stage depend on the rates of damage evolution and accumulation of irreversible strain. The evolutionary effect of the RS friction and overall change in the friction parameters (a−b) are controlled by the duration of the healing period and asperity (element) strengthening during this stage. For a model with spatially variable properties, the damage rheology reproduces the logarithmic dependency of the steady-state friction coefficient on the sliding velocity and the normal stress. The transition from a velocity strengthening regime to a velocity weakening one can be obtained by varying the rate of inelastic strain accumulation and keeping the other damage rheology parameters fixed. The developments unify previous damage rheology results on deformation localization leading to formation of new fault zones with detailed experimental results on frictional sliding. The results provide a route for extending the formulation of RS friction into a non-linear continuum mechanics framework.

Key Words
cracked media, damage, earthquakes, fractures, friction, rheology

Lyakhovsky, V., Ben-Zion, Y., & Agnon, A. (2005). A Visco-Elastic Damage Rheology and Rate- and State-Dependent Friction. Geophysical Journal International, 161(1), 179-190. doi: 10.1111/j.1365-246X.2005.02583.x.