Application of the Pi theorem to the wear rate of gouge formation in frictional sliding of rocks

A simple law of wear rate is examined for the process of gouge generation during the frictional sliding of simulated faults in rocks, by use of the Pi theorem method (dimensional analysis) and existing experimental data. The relationship between wear rate (t/d) and the applied stress can be expressed by the power-law relations {Mathematical expression} where t is the thickness of the gouge generated on the frictional surfaces, d is the fault displacement, σ and τ are normal stress and shear stress, respectively, and C_σ, C_τ, m_σ and m_τ are constants. These results indicate that the exponent coefficients m_σ and m_τ and the coefficients C_σ and C_τ depend on the material hardness of the frictional surfaces. By using the wear rates of natural faults, these power-law relationships may prove to be an acceptable palaeopiezometer of natural faults and the lithosphere.