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Mixed state variable friction laws: Some implications for experiments and a stability analysis
Author(s) -
Horowitz Franklin G.
Publication year - 1988
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/gl015i011p01243
Subject(s) - monotonic function , state variable , variable (mathematics) , slip (aerodynamics) , instability , mechanics , range (aeronautics) , state dependent , law , geology , physics , classical mechanics , mathematics , materials science , thermodynamics , mathematical analysis , mathematical economics , political science , composite material
Friction laws that depend on both the rate and past history (or state) of a sliding surface have been previously used to describe the sliding friction of rocks and to model some earthquake features. It has been proposed that these laws require an overall velocity weakening for stick‐slip instability to begin. This proposal is based on the assumption that the stress evolution after step changes in slip rate is monotonic. Recent experiments show, however, an irregularly present ‘mixed state variable’ effect in which it appears that a short range state variable is velocity weakening, and a long range state variable velocity strengthening. The stress evolution is clearly not monotonic after imposed step changes in velocity in these cases. It is shown here that instabilities can occur in the presence of overall velocity strengthening. Indeed, mixed state variable laws can explain some paradoxical laboratory observations in a natural way: Slow experiments may be too short to see the effects of the long state variable. Fast experiments may be too fast to resolve the effects of the short state variable. Thus similar experiments can show both velocity strengthening and velocity weakening depending on the total slip length increment measured.