1. INTRODUCTION ABSTRACT: The design of mining or civil works in discontinuous rock requires quantification of the joint orientations. Five schemes for partitioning the joint orientations from a site into homogeneous domains are first reviewed and then applied to the data from two mines. The structural data in both cases were collected from stations distributed along the mine drifts. A comparison of the results shows that the choice of a general procedure for testing similarity is difficult. Sequential use of several schemes may be useful.
A description of the structural features of rock mass is required for design and development of excavations in rock; this is particularly true for the case of underground mines-the source of the examples discussed in this paper. The description includes a definition of the suitable geometric parameters of joints and a subdivision of the site into homogeneous structural domains. One of the important and well-used geometric properties of joints is the orientation. Joint orientations form the basis for definition of joint sets (or clusters of joints around preferred orientations) and comparative tests for similarity of joint populations (Grossman, 1983; Miller, 1983; Mahtab & Yegulalp, 1984). In what follows we first examine the bases of five similarity criteria, or schemes, that have been proposed in the literature for differentiation between two joint samples. We then apply these schemes for combining joint orientations (from two example mines) into homogeneous domains.
2.1 Delineation of Clusters 2. PROCEDURES FOR DEFINING HOMOGENEOUS DOMAINS Four of the selected schemes involve delineation of clusters in the orientation data prior to defining homogeneous domains. The following discussion is, therefore, directed first to the delineation of clusters and second to the criteria for determining similarity between clusters or the entire sample from different observation stations or zones.
In the method of Mahtab and Yegulalp (1984), scheme 1, and its relaxed version by Berry et al. (1990), scheme 2, the orientation clusters are defined through the use of program PATCH of (Mahtab et al., 1972). In this approach the poles of the observed joints are projected on the upper hemisphere which is divided into 100, equal-area, quadrilateral cells or patches. A cluster is defined as a collection of adjacent patches such that the density of points in each patch exceeds a random cut-off defined by Poisson distribution. The distribution of points in a cluster is compared with the hemi- spherical-normal distribution of Arnold (1941), together with computation of the distribution parameters: mean orientation; the cone of confidence, within which the population mean will occur with a given probability; and a concentration factor. The selection of the Poisson cut-off level (5% in our case), the probability level for the cone of confidence (90% and 95% in our case), and the significance threshold for the size of a cluster (usually 5% or 10%) will, as pointed out by Kulatilake (1990), affect the resulting clusters. However, as in several other statistical techniques for analyzing structural data, user-selected cut-off (tempered with experience) are a practical requirement.