Abstract
An accurate determination of Hoek–Brown constant mi is of great significance in the estimation of the failure criteria of brittle rock materials. So far, different approaches such as rigidity index method (R-index), uniaxial compressive strength-based method, and tensile strength-based method, and the combination of these two methods (combination based method) have been proposed to calculate the value of mi. This paper aims to thoroughly review the previously existing methods to calculate the value of mi and make comparison between the obtain results to propose the new material constants that provide the best fit with the experimental data. In order to fulfill this goal, a large number of data for different quasi-isotropic intact rock types from the literature were collected and statistically analyzed. Additionally, based on rock types, new material constants are introduced for igneous, sedimentary, and metamorphic rocks. The obtained results proves that for different rock groups (igneous, sedimentary, and metamorphic rocks), R-index method provides the best fit with the experimental data among the others, and it is also independent of rock type. Interestingly enough, there is significant differences in the predicted mi values using different methods, which is more probably due to the quantity and quality of data used in the statistical analysis.
Highlights
The Hoek–Brown failure criterion is widely used in rock mechanics and rock engineering practice for determining the strength of brittle intact rock and rock masses
The obtained results proves that for different rock groups, rigidity index method (R-index) method provides the best fit with the experimental data among the others, and it is independent of rock type
According to our analyses for determination of mi in respect to Eq 2 (R-index method) and Eq 5, it was observed that mi value is independent of rock type
Summary
The Hoek–Brown failure criterion is widely used in rock mechanics and rock engineering practice for determining the strength of brittle intact rock and rock masses. Hoek and Brown [33,34,35] suggested that these values should be determined by numerous triaxial tests, applying different confining pressures (r3) between zero and 0.5 rc These laboratory tests are time-consuming, expensive, and in many cases, there are not enough (or suitable) samples. Singh et al [70], Peng et al [55], and Shen and Karakus [65] demonstrated that the reliability of mi values measured from triaxial test analysis depends on the quality and quantity of test data used in the analysis They concluded that the range of r3 could have a significant influence on the calculation of mi. It is the reason why several methods were developed for determining the Hoek–Brown constant (mi) [72]
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