Transient and Steady-State Friction in Non-Isobaric Conditions

The frictional properties of faults control the initiation and propagation of earthquakes and the associated hazards. Although the ambient temperature and instantaneous slip velocity controls on friction in isobaric conditions are increasingly well understood, the role of normal stress on steady-state and transient frictional behaviors remains elusive. The friction coefficient of rocks exhibits a strong dependence on normal stress at typical crustal depths. Furthermore, rapid changes in normal stress cause a direct effect on friction followed by an evolutionary response. Here, we derive a constitutive friction law that consistently explains the yield strength of rocks from atmospheric pressure to gigapascals while capturing the transient behavior following perturbations in normal stress. The model explains the frictional strength of a variety of sedimentary, metamorphic, and igneous rocks and the slip-dependent response upon normal stress steps of Westerly granite bare contact and synthetic gouges made of quartz and a mixture of quartz and smectite. The nonlinear normal stress dependence of the frictional resistance may originate from the distribution of asperities that control the real area of contact. The direct and transient effects may be important for induced seismicity by hydraulic fracturing or for naturally occurring normal stress perturbations within fault zones in the brittle crust. A long-term research goal in earthquake science is the development of friction laws describing how rocks break under stress and heal over quiescent periods to enable the seismic cycle. The constitutive behavior of rocks remains elusive because of the wide range of hydrothermal, barometric, and lithological conditions found in the brittle crust. A long-standing enigma in rock mechanics is the nonlinear effect of normal stress on frictional strength across the confining pressures relevant to seismogenic faults. Equally puzzling are the sudden and delayed variations of friction upon rapid changes in normal stress. In this study, we explain the connection between these seemingly unrelated observations. The transient evolution of friction under perturbations of normal stress is due to the competition between normal-stress-dependent healing of the frictional interface, which strengthens the fault, and the direct effect of normal stress, which reduces the frictional strength. If the two effects do not compensate exactly, a dependence of steady-state friction with normal stress ensues. We propose a constitutive model that explains quantitatively the frictional resistance of various rocks types and the mechanical data of bare contact and gouge friction during sliding at different normal stress for Westerly granite, pure quartz, and a mixture of quartz and smectite. The study helps build increasingly realistic representations of fault mechanics during seismic cycles. For a wide range of lithology, fault strength and fault friction are nonlinear functions of normal stress Normal stress change causes direct and evolutionary effects on the effective friction coefficient, possibly of different amplitudes The direct and transient effects upon normal stress change are controlled by the area of contact and slip-dependent healing