Many of the proposed techniques for calculating the reliability of rock slopes utilize Monte Carlo simulation. Monte Carlo approaches are attractive because they provide means of solving probabilistic problems with deterministic algorithms. One disadvantage shared by all simulation-based stability analyses is that they assume all the random variables are independently distributed. The paper focuses on the independence assumption and examines the effect of correlation on the probability of failure. In particular it considers the influence of possible (albeit hypothetical) correlation between joint attitudes (?) and joint friction angles (f). The study indicates that neglecting correlation can introduce significant errors into the reliability computations. With a modest positive correlation between ? and f the error can lead to a 100% overestimate of the probability of failure.
Reliability analyses provide an alternate approach to assessing the reliability of rock slopes. In reliability analyses the integrity of a slope is expressed as its probability of failure (Pf) rather than the traditional factor of safety (FS). One of the primary advantages of a probabilistic approach is that it explicitly considers the uncertainty associated with engineering parameters in that it characterizes parameters in terms of probability density functions rather than deterministic values. At the present time there are a number of techniques available for examining the reliability of rock slopes. The techniques are remarkably varied with respect to sophistication and requisite computational effort. They range from graphical methods (McMahon, 1975) based on pole diagrams and steronets to stochastic models (Call and Nicholas, 1978; Veneziano, 1978) that treat jointing in rock masses as a analytically describable random process. The approaches which currently provide the most versatile means for estimating Pf rely on Monte Carlo simulation (Major et al., 1978; Glynn, 1978). In these approaches a deterministic algorithm that computes FS is mated with a routine that randomly selects sets of input parameters through Monte Carlo techniques. Monte Carlo simulation is an attractive tool in reliability analyses because it can be applied to virtually any problem that can be modelled deterministically. As rock slope analyses become increasingly sophisticated with the addition of toppling and rotational failure modes the new analytical (albeit deterministic) models can be incorporated directly into Monte Carlo simulations. The weakness of Monte Carlo methods lies not so much in the FS algorithm, but rather in the selection of input parameters during simulation. Each random variable must have a rigorously defined probability density function (pdf). The paper discusses one of the problems encountered in selecting pdf's: are some (or perhaps many) of the random variables correlated and should their pdf's be defined as multivariate distributions?
Consider the following scenario. Two random variables ? (joint attitude) and f (joint friction angle) have a joint probability density function f?f (?, f). An individual interested in performing a reliability analysis would presumably be interested in identifying this function and could approximate it by fitting a curve over a statistically representative sample of "n" pair of (?, f) data points.
