Analysis of normal stress stepping experiments indicates that friction evolution depends on contact area quality rather than quantity

We conduced a series of friction experiments in which sudden normal stress step increases were imposed, while fault-normal displacements were monitored and the slip velocity was maintained nearly constant using a stiff servo-control system. The initial normal stress was 15 MPa and the ratios of step size to initial stress were 0.09, 0.14, 0.19, 0.27, 0.37, 0.46, 0.70, and 0.93. Upon step increases in normal stress, step increases in fault-normal closure also occurred followed by no further changes in fault-normal displacement, suggesting that no additional changes in contact area occurred as a function of slip after the normal stress change. The slip velocity can be calculated from the known stiffness of the servoed loading and the constant loading velocity. In response to the normal stress step, the slip velocity suddenly decreased by less than an order of magnitude and gradually returned to the original velocity. In contrast, the frictional shear resistance did not undergo a step change, but rather, consistent with the constraints of elasticity, gradually increased to a new steady-state value at the new normal stress, the change occurring over the same displacement scale as the velocity increased.

We show that the only way to understand quantitatively the observed behavior is to assume that the bonding strength per real-area-of-contact (i.e. contact quality) is less for the new contact area that instantaneously formed upon the normal stress step than for the preexisting area. Were this not the case, models show that the velocity reduction at the normal stress step would have been orders of magnitude larger than observed. That the velocity decreases less than an order of magnitude can only be explained by the new contact area having lower contact quality. The evolution in the strength as the velocity climbs back to the imposed value reflects an increase in the contact quality with slip, at constant contact area. Finally, we provide a simple constitutive law for the evolution of frictional strength in response to normal stress changes which explicitly accounts for such quality contrasts between old and new contacts.