Steadystate: A MATLAB-based routine for determining steady-state friction conditions in the framework of rate-and-state friction analysis

Abstract

Reliable determination of rate-and-state friction (RSF) parameters depends on achieving steady-state (SS) friction conditions before and after experimental velocity-stepping friction tests. This operation, through nonlinear least squares fitting, is commonly preceded by the removal of any overall slip weakening/hardening after friction velocity steps (VSs) through a sufficiently large window of slip displacement at SS ( = linear detrend). However, to date, the identification of SS and thus the correct linear detrend is dependent on the user, which potentially results in differing RSF outputs from the same data set. Here, we demonstrate that large errors in the determination of the fitted RSF parameters can result if SS conditions are not reached before and after VSs. Such errors can be particularly relevant for materials characterized by long evolution of frictional resistance with slip, such as clay-rich gouge layers, in which identifying SS after VSs is not always obvious. To this end, we propose a methodology to accurately and consistently identify where SS is achieved after VSs. This methodology is coded into a new MATLAB-based routine, steadystate. We show the key features of the methodology, as well as how to use steadystate and read its output. We also illustrate the broad applicability of the approach to friction data with different noise levels and sampling frequencies referenced to slip velocity, by reviewing observations from synthetic data sets and specific examples of experiments from different laboratories involving various sheared materials.