The Energetic Assessment of Frictional Instability Based on Rowe’s Theory

Abstract:

Frictional instability that controls the occurrence of unstable slips has been related to (1) rate and state dependent friction law (Dieterich, 1979; Ruina, 1983) and (2) shear localization in a gouge layer (e.g., Byerlee et al., 1978; Logan et al., 1979). Ikari et al. (2011) indicated that the transitions of frictional parameters obtained from the rate and state dependent friction law involve shear localization. However, the underlining theoretical background for their link has been unknown. Therefore, in this study, we investigate their relation theoretically and experimentally based on Rowe’s theory on constant minimum energy ratio (Rowe, 1962) describing particle deformations quantitatively by energetic analysis. In theoretical analysis using analytical dynamics and irreversible thermodynamics, the energetic criterion about frictional instability is obtained; unstable slip occurs at energy ratios below 1. In friction experiments using a gas medium apparatus, simulated fault gouge deforms obeying the Rowe’s theory. Additionally, the energy ratios change gradually with shear and show below 1 before the occurrence of unstable slip. Moreover, energy ratios are derived from volume changes. Transition of energy ratios from increase to decrease, which has been confirmed at the end of compaction, indicates the onset of volume increase toward the occurrence of unstable slip. The volume increases likely correspond to the formation of R1-shears with open mode character, which occurs prior to the unstable slip. Shear localization leads to a change in internal friction angle which is a statistical parameter to constitute a energy ratio. In short, changes in internal friction angle play an important role in evolving from being frictionally stable to unstable. From these results, the physical and energetic background for their link between the frictional parameter and shear localization becomes clear.