ABSTRACT:

Proprietary probabilistic software generally requires discontinuity orientation to be defined according to two distributions, one for dip-direction and one for dip-angle. Determining these distributions is time consuming and the statistical characteristics of the discontinuities generated by the software may be significantly different from these characteristics in-situ. In this paper a number of suggestions are made for improving the results if two distributions are to be used. These suggestions include the necessity to incorporate random discontinuities into the model and the necessity to apply truncation to distributions having infinitely long "tails". It also recommends that the beta distribution not be used for modelling dipdirection. Dip-direction data must be divided into quadrants and a distribution determined for the data in each quadrant. The paper also presents a solution for generating discontinuities from one distribution using a Fisher distribution that produces significantly more reliable data with less effort than the two-distribution method. The method presented is easily written into a spreadsheet and can therefore be incorporated into probabilistic-based models.

INTRODUCTION

The occurrence of instabilities at random locations within an excavation is due in part to variability in the orientation of the discontinuities within each set. The engineer who chooses to ignore this variability also chooses to accept a greater risk of instabilities occurring. Examples of ignoring variability would be to base the stability of an excavation solely on the relative locations of great circles, representing the mean orientation of the discontinuity sets and the free face, on a lower hemisphere projection or to use deterministic rather than probabilistic analytical models. The necessity to quantify risk has been understood by geotechnical engineers for many years. Considering risk, requires quantification of the probability for an event to occur. Monte-Carlo type models have been used for decades to estimate these probabilities.

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