Probabilistic characterization of Brazilian tensile strength of rock from both direct and indirect measurements

Abstract

The determination of Brazilian tensile strength (BTS) is an essential step in the analysis and design of mining structures at a particular site. The estimated design parameters are affected by the inherent variability of BTS, measurement errors arising from laboratory testing, and transformation uncertainty associated with the empirical model linking BTS to other rock properties when it is indirectly estimated. These uncertainties are usually lumped together as the total variability of BTS. However, it is the inherent variability resulting from natural geological factors, not the total variability, that directly affects the actual response of rock structures. Hence, there is a need for proper characterization of the inherent variability of BTS while the measurement errors and transformation uncertainty are explicitly incorporated. This paper develops a Bayesian approach which uses sequential updating, that is multi-input oriented for probabilistic characterization of the inherent variability of BTS of rock. The proposed approach systematically combines previous engineering experience and site information from both direct BTS data and data from indirect tests like point load test to inversely infer the inherent variability of BTS. The proposed approach quantitatively accounts for the effects of measurement errors and transformation uncertainty on the characterization of the inherent variability of BTS. The proposed approach is illustrated and validated using real-life data and simulated data. The result shows that the proposed approach provides a proper characterization of the inherent variability of BTS based on available information from multiple sources. Sensitivity studies are also performed to explore the effects of measurement errors on the performance of the proposed approach.