Nanoindentation creep of quartz, with implications for rate- and state-variable friction laws relevant to earthquake mechanics

Abstract

The frictional behavior of rocks in the laboratory is reasonably well described by rate- and state-variable friction laws, which reproduce a rich variety of natural phenomena when used in models of earthquakes. Despite the widespread adoption of the rate and state formalism in earthquake mechanics, the physical mechanisms that occur at microscopic contacting asperities on the sliding surface, which give rise to the observed rate and state effects, are still poorly understood. In an attempt to identify these underlying mechanisms, a series of nanoindentation experiments on quartz, an abundant mineral in the earth’s crust, was conducted. These experiments demonstrate the utility of using continuous stiffness measurements as a means of obtaining reliable indentation creep data on hard materials like quartz at room temperature. The projected area of indentation in quartz increases linearly with the logarithm of the time of indentation, in agreement with the increase in real area of contact with log time inferred from slide-hold-slide friction experiments on quartz rocks. However, the increase in fractional area with time in the indentation tests was larger than that inferred from friction experiments by a factor of 1.7. Differences between the rates of fractional area increase in the two tests may indicate that the increase in contact area during the hold portion of slide-hold-slide tests was modulated by slip that occurs during reloading after the hold, as was observed for other materials. The nanoindentation results suggest that the increase in frictional strength (i.e., the increase of state in the rate- and state-variable friction laws) during slide-hold-slide friction experiments was caused by creep of the highly stressed asperity contacts.