No abstract

A theory of contact between two elastic rough surfaces is presented that predicts, from knowledge of the surface topography, both the normal and shear deformation. The theory was modified from one developed by others in order to properly account for initial overlap of the two surfaces and to allow for calculation of shear stiffnesses under no‐slip conditions. Since the theory is critically dependent on the surface topography, a new method is introduced for the derivation of the real topographic parameters. The result of theoretical calculation shows that the normal closure nonlinearly increases with normal stress and is larger for rougher surfaces and that the shear stiffness also nonlinearly increases with normal stress and is greater for smoother surfaces than rougher ones. The verification of the theory will be made by comparing it with experimental data in a companion paper.

A constitutive model is developed which predicts the mechanical properties of two rough surfaces in contact under shear load during the early stages of the development of frictional sliding. The model includes the development of slip at the contacts, a phenomenon which begins immediately upon shear loading. Upon initial application of the normal load, the model predicts that the joint consists of a finite number of contacts which are subject to a wide variety of local normal loads. As the shear load is increased, sliding of the contacts develops progressively, with the contacts under low local normal load sliding first. This gradual development of sliding is the cause of the experimentally observed nonlinear force‐displacement relation for deformation of the joint in shear. Two asperity scale strength laws are examined, one based on the adhesion theory of friction and the other based on observations of frictional strength for brittle elastic solids. The model is tested with experiments on lapped surfaces of Westerly Granite with a variety of surface roughnesses and under a range of normal loads from 10 to 35 MPa. Geometric parameters used in the model are constrained by direct measurement of surface profiles. For both strength laws, the model quantitatively predicts the shear compliance and development of slip for the first few microns of shear displacement, successfully describing the effect of surface roughness and normal load. This model helps explain the initial yield in the friction curve which corresponds to the gradual transition from the elastic deformation and partial slip of asperity contacts to a condition of fully sliding contacts. When a large population of contacts are fully sliding, the model under‐estimates the frictional strength, indicating that displacement strengthening mechanisms are important to the ultimate frictional strength of rocks.

Fracture energy was estimated on the basis of experimental results with respect to both the amount and the particle size distribution of the gouges which were developed during frictional slidings. The result shows that the fracture energy occupies only 0.01-0.1 % in the total energy released by the testing machine: the heat energy due to friction and the elastic wave energy are the main two forms in the distribution process. Nevertheless the gouge and the roughness of the sliding surface play an important role in the distribution process of energy. The energy budget during sliding depends upon the existence of gouge. In addition, gouge and surface roughness reflect the history of sliding or the sliding behaviour. It is useful to study the variation of gouge and surface roughness in experiments for investigating the earthquake source mechanism.

Frictional behavior of Westerly granite sheared in a rotary apparatus was observed up to 20 MPa normal stress. Before and after each experiment, surface roughness was measured with a profilometer. Macroscopic frictional properties were observed to evolve toward steady state through two distinct stages denoted initial slip and slip hardening. Total slip was less than 200 •tm, but some experiments were extended to several centimeters. The instant a shear load was applied, a finite shear stiffness was observed which decreased nonlinearly with displacement. Initial stiffness was roughness dependent; the smoother samples supported equal or higher shear stresses than rough samples at any given displacement. In the shear stress-displacement data, a distinct yield point was observed which was roughness and normal load dependent. Samples with rougher surfaces and/or higher normal loads required longer displacements to reach a yield point. The yield point marked the start of the slip-hardening stage during which the shear strength of the surfaces continued to increase at a rate that was roughness and normal load dependent. Rougher surfaces exhibited higher rates of slip hardening than smooth, and over much greater slip distances. During slip hardening, normal closure continued, but at a diminished rate with increasing displacement. The closure rate and slip hardening were correllated: rougher surfaces exhibited higher rates of slip related closure which produced increased asperity interlock and, consequently, increased friction. Beyond 100 to 300 gm displacement, slip hardening and closure nearly ceased, beginning a third stage in which friction is nearly steady state. At steady state, friction of the rough surfaces (0.60 to 0.65) was greater than that of the smooth (0.50 to 0.55).The sliding of two surfaces past one another produces frictional forces between microscopically contacting asperities. Friction in metals is known to originate from several different micromechanical mechanisms operating at the asperity scale. Bowden and Tabor [1950, 1964] experimentally determined an asperity scale shear strength for metals that could only account for a fraction of the total friction observed. To narrow the difference between observation and theory, various strengthening mechanisms have been proposed for metallic friction [Green, 1955; Challen and Oxley, 1979]. Similarly, in rock the strength term for elastically contacting asperities contributes only marginally to steady state friction [Byerlee, 1967a; Buckley and Miyoshi, 1984, 1990]. Consequently, additional slip-hardening mechanisms have been proposed which are both roughness and displacement dependent [Scholz and Engelder, 1976; Engelder and Schoh, 1976]. Since rock is an elastic material, these mechanisms should operate differently than in metal. An important objective of this study was elucidation of those slip-hardening mechanisms as they evolve with displacement. In his classical work, Byerlee [1967a] examined the dependence of steady state rock friction on surface rou...