Probabilistic Characterization of Hoek\u2013Brown Constant mi of Rock Using Hoek\u2019s Guideline Chart, Regression Model and Uniaxial Compression Test

Abstract

The Hoek–Brown constant mi is a key input parameter in the Hoek–Brown failure criterion developed for estimating rock mass properties. The Hoek–Brown constant mi values are traditionally estimated from results of triaxial compression tests, but these tests are time-consuming and expensive. In the absence of laboratory test data, guideline chart and empirical regression models have been proposed in the literature to estimate mi values, and they give a general trend of mi. Instead of only using either the guideline chart or regression models, information from both sources can be systematically integrated to improve estimates of mi. In this study, a Bayesian approach is developed for probabilistic characterization of mi, using information from guideline chart, regression model and site-specific uniaxial compression strength (UCS) test values. The probabilistic characterization of mi provides a large number of mi samples for conventional statistical analysis of mi, including its full probability distribution. The proposed approach is illustrated and validated using real UCS and triaxial compression test data from a granite site at Forsmark, Sweden. To evaluate the reliability of the proposed method, mi values estimated from the proposed method are compared with those predicted from a separate analysis which uses triaxial compression tests data. In addition, a sensitivity study is performed to explore the effect of site-specific input on the evolution of mi. The approach provides reasonable statistics and probability distribution of mi at a specific site, and the mi samples can be directly used in rock engineering design and analysis, especially in Hoek–Brown failure criterion to predict rock failure.