A model describing the mechanical and hydraulic behavior of rock fractures subjected to shear loading is introduced. The model is based on statistical and geostatistical descriptions of fracture surface topography, an elastic deformation mechanism, and equivalent aperture concepts. The performance of the representation is demonstrated by modelling the behavior of a hypothetical fracture specimen.
A hydromechanical model of a rock fracture describes both the mechanical and hydraulic behavior of the fracture. The description of mechanical behavior includes stress-displacement relations while the description of hydraulic behavior includes the rates of fluid flow and solute transport. Hydromechanical models find application in the prediction of fracture behavior and, if adequate, allow fracture behavior under differing test conditions to be assessed. A comprehensive review of the various hydromechanical models which have been introduced in the literature is presented by Barton and Bakhtar (1987). Considerable success has been realized in attempts to describe the behavior of fractures subjected to normal compression based on fundamental fracture characteristics and in the derivation of empirical relationships for the behavior of fractures subjected to shear loading. Limited progress has been achieved in developing models which describe the behavior of fractures subjected to shear loading based on surface characteristics. The contrast between the irregular nature of fracture surfaces and the simple geometries for which analytical statements may be derived appears to be the primary obstacle to progress. The model combines a description of fracture surface topography with an elastic deformation mechanism and equivalent aperture concepts. The assembled model describes the behavior of fractures subjected to generalized normal and shear loading. This presentation addresses fracture behavior during shear loading under conditions of constant normal stress.
The topography of fracture surfaces is widely regarded as a factor which influences both the mechanical and fluid transport properties of fractures. This is exemplified by the use of qualitative descriptions of surface roughness in empirical relations for joint and rock mass properties [Barton and Choubey (1977), Barton et al. (1974), Bieniawski (1974)]. While qualitative descriptions of surface topography are an appropriate basis for empirical correlations, quantitative descriptions are required as the basis for analytical models of fracture behavior. Numerous models and methods of analysis have been applied to the description of rock fracture surface topography. The self-affine fractal model, described by Voss (1985) and applied to fracture surface topography by Brown and Scholz (1985), reflects many of the characteristics of fracture surfaces and, when coupled to a statistical model, provides an operational representation of fracture surfaces. The formulation of the hydromechanical model presented in this paper relies upon statistical and geostatistical descriptions of surface topography. To illustrate the description of surface topography using these methods, data from an experimental study of fracture surface topography is presented [Piggott (1990)]. Figure 1 shows a cumulative probability function of surface elevation as defined by a two- dimensional profile (AECLXY) measured on the surface of a fracture specimen obtained from the Underground Research Laboratory of Atomic Energy of Canada Limited.