Pure and Applied Geophysics

, Volume 170, Issue 3, pp 247–257 | Cite as

Simulation of Frictional Strength and Steady Relaxation Using the Rate and State Dependent Friction Model

  • Arun K. SinghEmail author
  • T. N. Singh


In this paper, frictional strength of hard solids, such as rock–rock sliding surfaces, is studied as a function of waiting time and shearing velocity. A one dimensional spring–mass sliding system is numerically simulated under the quasistatic condition using the rate and state dependent friction model. It is established that frictional strength varies linearly with the logarithm of waiting time (also known as time of stationary contact or relaxation time, etc.) as well as logarithm of shearing velocity. Analytical expression developed for frictional strength is found to be valid only in the case of high stiffness of the connecting spring. In the steady relaxation simulation, a steadily sliding mass is suddenly brought to zero velocity and relaxation of the interfacial stress and corresponding velocity at the sliding interface is studied as a function of relaxation time in the velocity strengthening regime of friction. A mathematical relation is derived between state variable and waiting time using the concept of steady relaxation. The relaxation model is also compared with the experimental data from the literature. Finally, the present study enables one to unify the slide–hold–slide friction experiments.


Relaxation Stress Shear Velocity Friction Parameter Frictional Stress Frictional Strength 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



First author is thankful to Dr. K. Ranjith for introducing the rate and state dependent friction model during his initial stage of doctoral program at IIT Bombay. We are grateful to Prof. Vinay A. Juvekar, Department of Chemical Engineering, IIT Bombay for his critical and fruitful suggestions concerning the present study. We also appreciate the efforts of Ms. Asfiya Q. C., IIT Bombay for improvement and timely correction of the manuscript.


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© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of Earth SciencesIndian Institute of Technology BombayMumbaiIndia

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