Examination of the rate-state friction equations under large perturbations from steady sliding: A theoretical and experimental study.

Abstract

The laboratory derived rate-state friction (RSF) relationships are the most widely used

constitutive equations for fault friction in numerical models of fault mechanics. But even

after more than three decades of these being first proposed, we are far from certain about the identity of the ‘proper’ set of these equations which describe all laboratory friction data. In

fact, the two most popular choices of the ‘state’ evolution component of RSF represent two

end-member physical pictures of how frictional strength evolves – with time even without

slip (Aging law) or only with slip (Slip law). Yet both these view points have traditionally

been inferred to be independently supported by different classes of friction experiments

which (sometimes) access similar portions of the RSF parameter space. We present a set of

comprehensive studies which establish, both theoretically and with inversion of laboratory

data, that in fact all the widely used experimental protocols provide evidence that friction

dominantly evolves with slip even when the interface is sliding at the lowest slip rates

accessed by these experiments.

We examined these state evolution laws under a diverse range of sliding conditions –

up to 3.5 orders of velocity steps on both initially bare rock and gouge, up to 3X10^4 s

long holds on initially bare rock performed using machine stiffnesses differing by 1.5 orders

of magnitude and 5% normal stress steps on initially bare rock carried out at an order of

magnitude different sliding rates. For all of these experimental regimes, the widely used

Aging law generally performed worse than the Slip law, even in those parts of the parameter

space where conventional RSF wisdom would have predicted it to find strong support.

Additionally, across all these experiments, more recent prescriptions of state evolution

were generally found to fit the data only as well as the Slip law even with the freedom of

extra parameters. We argue that these findings contradict the traditional view that the state

variable is a proxy for the ‘quantity’ of true contact area alone, it is likely that some measure

of the ‘quality’ of contacts contributes significantly to state evolution as well.