A theoretical analysis of sliding of rough surfaces

Abstract

[1] I used a model proposed by Greenwood and Williamson [1966], who analyzed closure between a rough surface and a smooth surface under normal stress, to analyze the growth of slip under increasing shear stress, normal stress remaining constant. The two bodies are elastic half-spaces, one rough and one smooth, and Coulomb friction resists slip at sliding contacts. The elastic and dissipative components of the constitutive relation in shear depend upon statistical parameters which describe the topography of the rough surface. I made a parametric study of the effect of topography on the constitutive relations in shear by comparing a model in which the progress of slip at a contact is continuous with one in which the contact goes discontinuously from ''stuck'' to sliding. The effect of topography was also studied by assuming that the probability density distribution of the heights of asperities is Gaussian or, alternatively, a negative exponential. These variations in topography produced only minor differences in the constitutive behavior. This insensitivity of the constitutive behavior to differences in the statistical description of the topography arises in part because, only relatively, a small range of asperity heights is active in typical experiments. Work done against friction introduces a dissipative component into the constitutive behavior which I evaluated analytically; I show that the components have a simple graphical construction on plots of shear stress versus displacement developed from experimental observations. Sliding in the reverse sense which occurs when the applied shear stress is relaxed is analyzed, resulting in expressions which describe the shape of hysteresis loops formed when shear stress is cycled. Introducing measurements made on surfaces of specimens of granite and quartzite into the theoretical relations, I found reasonable agreement with experimental data.INDEX TERMS: 7260 Seismology: Theory and modeling; KEYWORDS: friction, rough surfaces, sliding Citation: Walsh, J. B., A theoretical analysis of sliding of rough surfaces,

A new model for analyzing the effect of fractures on triaxial deformation

“…Mindlin and Deresiewicz [9] show for a single asperity that cyclic loading is almost elastic at small amplitudes, and further that the compliance of the contact to cyclic loading does not depend on the shear stress acting on the joint. Walsh [7] found that these observations held as well for rough surfaces.…”

“…To make the calculations easier, we have chosen to approximate the distribution g(h/λ) of asperity heights h by a negative exponential e -h/λ (see (4)), where λ is found by fitting the exponential to the appropriate part of the distribution function. We make the further simplification that all asperities have the same tip radius R. The justification for using these approximations and the procedure for estimating λ are discussed by Walsh [7].…”

“…The deformation of the surface to this stress system---both the normal and shear components of joint deformation (∆w, ∆u)---depends on the topography of the surfaces in contact. The topography of the microfractures that comprise porosity isn't known, of course, but fortunately the simple model proposed by Greenwood and Williamson [6] has been found to provide a good simulation for a variety of fault surfaces [7]. We assume that it is adequate for the analysis here.…”

Sliding of a rough surface under oblique loading

“…The model we use was proposed by Greenwood and Williamson [1966] to analyze the closure between rough surfaces under normal stress. Walsh [2003] used Greenwood and Williamson's model in a study of sliding between rough surfaces under constant normal stress. In the analysis here, we analyze deformation of rough surfaces, again using Greenwood and Williamson's model, when both applied normal stress and shear stress are increased simultaneously.…”

“…[7] Walsh [2003] derived the theoretical constitutive relationship for slip under applied shear stress, the normal stress remaining constant, using Greenwood and Williamson's [1966] model as the basis of his study. He found that the final form of the constitutive relationship was relatively insensitive to choice taken for the probability density function g(h/l) for asperity heights or for the radii of asperity tips; that is, uncertainties in experimental sliding data masked the differences between various theoretical constitutive relationships.…”