A computer program was developed to estimate the fractal dimension (D), based on the box-counting technique. It was verified by estimating D of the triadic Koch curve for which the theoretical D is known. The influence of a number of input parameters of the box counting method on the estimated D was evaluated using the same Koch curve. Employed size range of the applied box networks was found to be the parameter which has the strongest influence on estimated D. The computer program was then applied to different block sizes sampled from three generated two dimensional joint patterns to estimate the box fractal dimension. Results indicated that the box fractal dimension can capture the combined influence of joint size distribution and joint density on the statistical homogeneity of rock masses. For the same block sizes sampled from the three generated joint networks, the first invariant of fracture tensor (I1F) was calculated. Results indicated the capability of I1F to capture the combined effect of joint size and joint density on the statistical homogeneity of rock masses.
The presence of discontinuities strongly affects the mechanical and hydraulic behaviour of discontinuous rock masses. At present, discontinuum approaches are used in estimating both mechanical (Kulatilake et al. 1993a) and hydraulic (Panda and Kulatilake 1995) properties of jointed rock masses. To apply these discontinuum techniques, it is necessary to describe the joint network pattern in the considered rock mass. Because the joint geometry pattern can vary from one statistically homogeneous region to another, each statistically homogeneous region should be represented by a separate joint geometry model. Therefore, the first step in the procedure of joint geometry modelling in a rock mass should be the identification of statistically homogeneous regions (Kulatilake et al., 1993b). For complete statistical homogeneity of two selected regions in a rock mass, the joint sets in the two regions should have similar distributions for density, orientation, spacing, size, shape, roughness, and joint constitutive properties. However, at present, mainly the number of joint sets, their orientation distributions, and visual inspection of the structural conditions of the site are considered in determining statistically homogeneous regions (Miller 1983; Mahatab and Yegulalp 1984; Kulatilake et al. 1990). Recently, Kulatilake et al. (1996) evaluated the statistical homogeneity in the Shiplock area of the Three Gorges dam site, performing (a) a detailed quantitative evaluation of the number of joint sets and their orientation distributions, (b) a semi- quantitative evaluation of discontinuity spatial distribution and intensity, and (c) a qualitative visual geological evaluation of the site. It is important to develop simple techniques which can be applied rapidly to obtain measures of statistical homogeneity of rock masses. This paper investigates the possibility of using the box fractal dimension and the first invariant of fracture tensor of fracture networks as indices of the combined effect of joint density and joint size distribution, and in turn, as additional parameters to investigate the statistical homogeneity of rock masses.
