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.
Highlights
The Hoek–brown failure criterion (Hoek and Brown 1980) is widely used in rock engineering for the determination of rock mass properties such as rock mass strength and deformation modulus (e.g., Peng et al 2014)
This paper develops a Bayesian approach for probabilistic characterization of Hoek–Brown constant mi through Bayesian integration of information from Hoek’s guideline chart, regression model and site-specific uniaxial compression strength (UCS) data
A Bayesian approach is developed for probabilistic characterization of Hoek–Brown constant mi, which systematically synthesizes and integrates information from regression model, site-specific UCS data and ranges of mi reported in Hoek’s guideline chart, to give better predictions of mi values
Summary
The Hoek–brown failure criterion (Hoek and Brown 1980) is widely used in rock engineering for the determination of rock mass properties such as rock mass strength and deformation modulus (e.g., Peng et al 2014). Another approach is guideline chart developed for obtaining mi values in the absence of laboratory triaxial test data (Hoek and Brown 1997; Hoek 2007) Another approach is R index, which estimates mi value as a ratio of UCS to tensile strength (e.g., Cai 2010; Read and Richards 2011). When triaxial test results are not available at a project site, rock engineers and engineering practitioners frequently adopt the guideline chart proposed by Hoek (2007) or regression models available in the literature for predicting values of mi. Several sets of simulated data are used to explore the evolution of mi as the number of site-specific data increases
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