pure and applied geophysics

, Volume 142, Issue 3–4, pp 795–808 | Cite as

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

  • Hiroyuki Nagahama
  • Norihiro Nakamura
Frictional Slip, Failure, and Deformation Mechanics: Laboratory Studies


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
$$\frac{t}{d} = C_\sigma \sigma ^{m\sigma } ,\frac{t}{d} = C_\tau \tau ^{m\tau }$$
wheret 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, andCσ,Cτ,mσ andmτ are constants. These results indicate that the exponent coefficientsmσ andmτ and the coefficientsCσ andCτ 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.

Key words

Pi theorem wear rate stress frictional sliding fault zones 


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Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • Hiroyuki Nagahama
    • 1
  • Norihiro Nakamura
    • 2
  1. 1.Institute of Geosciences, School of ScienceShizuoka UniversityShizuokaJapan
  2. 2.Department of Geoenvironmental Science, Faculty of ScienceTohoku UniversitySendaiJapan

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