ABSTRACT: This paper surveys the published literature in stochastic joint geometry modeling. The review covers materials published through middle of 1987. It is mainly intended as a point of access to the literature. The paper also provides strengths and weaknesses of the available techniques to model the joint geometry parameters. The areas where future research efforts should be focused are summarized in the 'CONCLUSIONS.
Accurate representation of joint geometry is important in studying the hydraulic and/or mechanical behavior of jointed rock masses. The suggested discontinuum models to study the mechanical response (Cundall and Hart, 1985; Lorig et al., 1986; Goodman and Shi, 1985; Kulatilake, 1985b) and the suggested discrete fracture flow models to study the hydraulic response (Long et al., 1985; Elsworth, 1986; Dershowitz and Einstein, 1987) need possible joint geometry patterns as one of the inputs. The aim of this paper is to provide the state-of-the-art in modeling the joint geometry. To model joint geometry in three dimensional (3D) space, one needs to know the joint intensity in 3D, the location of these joints, their orientation, shape and dimensions. All of these joint parameters are statistical in nature. Sample values of joint parameters provided by the field data represent one or two dimensional properties. These sample values usually contain errors due to sampling biases. Therefore, it is necessary to make appropriate corrections for these sampling biases before making inferences about joint parameter distributions. In addition to these, one needs to use principles of stochastic geometry (Underwood, 1970; Santalo, 1976; Kendall and Moran, 1963) when inferring the hidden three dimensional structures of the joints from one or two dimensional parameter values. The state-of-the art is covered under the following topics: (a) Delineation of statistically homogeneous structural regions, (b) Modeling of joint geometry parameters and (c) Joint geometry conceptual models.
2 DELINEATION OF STATISTICALLY HOMOGENEOUS STRUCTURAL REGIONS
An important aspect in joint geometry modeling is the evaluation of statistical homogeneity between chosen structural regions. For complete statistical homogeneity, the joint sets should have similar distributions of orientation, spacing, size, shape, roughness, gouge and joint constitutive properties. At present, only joint orientation distribution is used in determining statistically homogeneous regions. Such regions are often determined by visually comparing samples of structure orientations, each of which consists of a polar, equal-area plot with at least 150 poles to joints. owever, when joint orientations do not show definite pole clusters, visual comparisons often are not sufficient to evaluate statistical homogeneity between chosen structural regions. In such situations, the methods suggested by Miller (1983) and Mahtab and Yegulalp (1984) are useful in obtaining statistically homogeneous regions. Miller uses a contingency table analysis based on the frequencies of joint poles that occur in corresponding patches on the polar, equal-area plots being compared. An undesirable feature of this method is the non-uniqueness in the selection of network of patches in equal-area plots. Different patch networks may produce varying results. Mahtab and Yegulalp's method (1984) is based on a comparison between clusters coming from different samples.