Although a seemingly simple problem, there is still a large degree of conjecture as to how to estimate the strength of a rock defect. At the laboratory scale (approximately 100 mm) there are numerous models available most notably the Barton criterion andwhat is generally defined as the Patton criterion. These models, developed on the basis of curve fitting to laboratory results, perform reasonably well at this small scale. Issues arise where these criteria or the results from the laboratory testing are used to predict the strength of critical defects encountered in the field. Current models in use require an estimate of a basic friction angle, small roughness component and a field roughness or dilation angle that represents the friction the defect ‘sees’ in the field. In this paper, the authors have performed numerical analyses on rock defects of varying scales using PFC 2D. The results are presented with a comparison with the Bandis scale effect equations.


Most shear strength criteria were developed predominately from laboratory samples. Larger specimens require field tests which are costly and yet, even the largest test may not be able to simulate the behaviour of defects of hundreds of square metres. The most practical method is then to carry out small-scale tests, and extrapolate from these the properties of full-scale defects. The issue of how to achieve this remains a continual topic of research and discussion. The authors are currently assessing the effect of defect length or area on strength using published data, back-analysis and numerical methods. Cundall (2000) used the micromechanical model PFC 2D (Particle Flow Code in two Dimensions) to simulate the behaviour of rock defects in a direct shear test. In this paper, the work by Cundall is extended to investigate the effects of scale on the shear strength of rock defects. This study extends this work by modelling a similar defect at different scales. The results are compared with those obtained by Bandis et al. (1981).


Patton (1966) showed a bi-linear equation, Equation 1, could be used to estimate the shear strength of defects. The issue with this equation is that the dilation angle, i, is stress and scale dependent. There is, at present, no definitive way of measuring the dilation angle, i, for field scale defects. The approach by McMahon (1985) or similar, where asperities are measured for a certain wavelength (or interlimb angle) of the defect and used to predict i, is probably the best current approach. Stacey and Page (1986) suggest an additional increase in friction angle of up to 14° could be made to a field scale defect based on the 100mm scale roughness contribution.


Cundall (2000) described a process by which a 100mm rock defect could be modelled and tested in shear using the Distinct Element Method as incorporated in the model PFC 2D. The results from Cundall's numerical experiments corresponded well to the Barton-Bandis model for 100mm long rock joints.

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