The Importance of Cross-Correlation in Probabilistic Analyses of Rock Slopes Using Generalized Hoek-Brown Criterion

The generalized Hoek-Brown failure criterion is widely used in rock mechanics to predict the failure of rock masses. It was introduced to the industry in its entirety in 2002. With the help of this criterion, the difficult to obtain rock mass material constants m(b), s, and alpha (herein termed the "derived parameters") can be estimated with the use of the more easily obtained field parameters, GSI, m(i), and D (herein termed the "primary parameters"). As a result, the primary parameters and the generalized Hoek-Brown criterion have gained wide acceptance in the industry. At the same time, probabilistic analysis has become more popular in recent years. This paper considers the probabilistic analysis of a rock slope. Two cases are considered: (1) the random variables are assigned to the primary parameters; and (2) the random variables are assigned to the equivalent derived parameters. It was found that converting from primary to derived parameters resulted in a very significant difference in results if the correlation of the derived parameters is not considered. The importance of considering cross-correlation coefficients when performing a probabilistic analysis with derived parameters is highlighted.