Modeling earthquake fault slip requires reliable constitutive relations describing friction. A commonly accepted empirical framework, known as “Rate- and State-dependent Friction” (RSF), suggests that frictional strength depends on the fault slip rate and (history dependent) ‘state’ variable. 

Although none of the empirical RSF laws proposed thus far, including RSF “Aging” and “Slip” versions, adequately describes the full range of laboratory friction data, the Slip law is clearly superior, and does an excellent job of modeling both velocity steps and slide-holds rock laboratory loading protocols.  Despite this, and unlike the Aging law, there is no clearly-established physical basis for the Slip law.

In this seminar, I will first provide an overview of the RSF laboratory observations and the empirical (standard) RSF modeling framework. I will discuss the shortcomings of the standard model and that at the moment, unfortunately, no physics-based constitutive relation exists for rock friction. 

It is noteworthy that natural fault zones typically contain a localized shear zone, also known as the granular gouge layer, and that laboratory experiments on even initially bare rock surfaces develop a gouge layer through mechanical wear. 

Based on this observation, I have developed a granular physics-based simulation to investigate the origins of RSF in rocks. In my model, I have intentionally left out time-dependent plasticity at the grain contact-scale, that is traditionally thought to be the primary origin of RSF in the standard model. 

I will show results from the granular simulations that reproduce and explain robust features of real rock and gouge friction data. Namely, the granular model captures: (i) the functional form of the transition to new values of the dynamic friction following a change in shearing velocity; (ii) logarithmic-with-time healing of the frictional interface and its dependence on prior shear rate, during the load-point hold. 

These laboratory observations currently have no other first-principles or physics-based explanations. The success of the granular model seems to be arising from the logarithmic-with-time (slow) compaction and slow relaxation dynamics in the model that is a hallmark of granular materials and disordered solids.

I will next discuss how I am working to further unify the search for constitutive relations for friction and deformation of rocks with the recent exciting developments within the broader community of soft condensed matter physicists for a state variable and an Equation of State for granular systems. Such a state variable and equation of state are essential for confidently applying laboratory-derived friction laws to fault slip in the Earth.  

In addition to earthquake fault zones, the RSF behavior is ubiquitously observed in friction of disordered Earth materials and interfaces, including ice-on-rock, sediments on Earth’s surface and damaged rocks in the shallow crust. 

Therefore, the implications and applications of my work are broad. I will discuss some of my near future research plans related to Earth’s near-surface processes, in addition to earthquake source physics.