A note on contact stress and closure in models of rock joints and faults

We have re-examined asperity deformation predicted by joint closure models based on Greenwood and Williamson [1966] which use a statistical representation of loaded, rough surfaces. Although such models assume small elastic strains within contacting asperities (Hertzian contact) and well predict the observed dependence of closure on normal stress, large elastic normal strains measured in experiments violate the model assumptions. This inconsistency between observations and models can be resolved. The model dependence of closure on macroscopic normal stress results primarily from the statistics of the surface topography, and the functional dependence of closure on normal stress can be independent of assumed contact-scale elastic interactions. Thus, a joint model of the Greenwood and Williamson kind, modified to allow a portion of the elastic deformation to occur outside of the asperity contact region, predicts macroscopic behavior consistent with Hertzian models. Contact stresses derived from previously published models of this kind may be in error.