Statistical description of rock mass properties is essential for two reasons: 1 -Analyses in rock engineering require statistical descriptions to take the distributive character of properties into account and 2-Field sampling requires statistical descriptions to develop sampling plans and to draw inferences from data. For both purposes, it is essential to know appropriate distributions of rock mass properties. Based on the evaluation of a large number of joint data and taking previous work into account, it was determined that the best fitting distribution for joint "length" is lognormal and for joint spacing exponential. Based on these conclusions, a model was developed for inferring joint set parameters and for estimating the intensity of jointing (joint surface area per volume) from outcrop data. Intensity of jointing is an indicator of persistence.
Accuracy in predicting rock mass behavior depends on adequate characterization of in situ rock properties. The performance of natural and cut slopes, of underground openings and of foundations on rock depends on geometric characteristics of discontinuities (attitude, spacing and persistence), on the resistance characteristics of the discontinuities and the intact rock, and on the effect of water. Difficulties arise because parameters describing these characteristics are not unique, but distributed. This distributive character affects both analyses in which rock mass parameters are used and sampling plans by which parameters are obtained. Analysis should incorporate uncertainty associated with parameter distribution. Traditionally, this has been done using factors of safety. Factors of- Safety do not relate parameter distributions with the probability of failure or excessive deformation. Such predictions can only be made using probabilistic approaches. Field sampling is in part a statistical problem. Thus statistical techniques should be used both to develop sampling plans and to draw inferences from collected data. As probabilistic analysis in rock engineering becomes more common, statistical sampling will become absolutely necessary. Statistical analyses depend on assumptions, of which an important one is the distributional form of the properties sampled. Most uses of statistics in sampling and analysis are based on standard assumptions, the most common of which is Normality. To the extent these assumptions reflect reality, inferences are accurate. However, the assumptions themselves are seldom tested. This paper concentrates on determining appropriate distributions of joint spacing and joint surface or "length" (surface or length are related to persistence), Extensive joint data from two rock excavation sites were analyzed and various analytical forms tested. In Section 2 the literature on distributional properties of jointing is summarized, and in Section 3 the present data is reviewed in light of that previous work. In Section 4, a model of joint geometry is presented and used to draw inferences from field data. In Section 5 these inferences are related to estimates of persistence.
Since 1970 attempts have been made to determine appropriate distributional forms of joint length and spacing. These are summarized in Table 1. Priest and Hudson (lg76) have shown that combinations of evenly spaced, clustered and randomly spaced discontinuities will yield an exponential distribution of spacing. However, large predominances of evenly spaced joints lead to normal distributions.