Obtaining Robust Estimates of Rock Strength for Rock Engineering Design

"It is common in rock engineering practice to characterize the triaxial strength of intact rock by using only data samples of small size. Practical guidelines such as ASTM support such sample sizes. In this paper, we investigate the reliability of the Hoek-Brown strength criterion estimated from such samples. For this purpose, we use an unusually large published set of triaxial strength data to randomly select a large number of data samples of small size to simulate the situation that frequently encounters in practice. The samples are generated with different arrangements with regards to the confining pressure. We fit the Hoek-Brown criterion to each of these samples, obtain estimates of strength parameters and compare them to those obtained from the complete data set. Our analysis suggests that estimates based on small samples are not reliable and can lead to both over- and under-estimation of strength.Additionally, we use these small samples to investigate the statistical methods for obtaining design values of strength as suggested by limit state design standards such as Eurocode 7. We show that, if used in conjunction with small samples, these methods do not guarantee a safe estimate of strength and in many cases lead to highly over-conservative estimates.We present a potential solution to this problem by augmenting the small data sets with Bayesian informative priors to give much more reliable estimates of strength. We conclude with suggestions for the development of informative prior distributions."