It has long been known that significantly different estimates of the Hoek-Brown mi constant occur if curve fitting regressions are made including or ignoring tensile strength data. These differences in curve fit regression estimates can become even more pronounced if inappropriate corrections are made to adjust indirect (Brazilian) tensile test (BTS) results to equivalence with direct tensile strength (DTS) values. Equations for properly correcting BTS results to calculate theoretically equivalent DTS and Hoek-Brown (H-B) pseudo tensile strength values are presented, along with a suggested iterative approach for utilizing derived H-B strength estimates for better refining a representative failure envelope. The concept of this envelope being valid only in the compressional range and being transitional to a hybrid sigmoidal tensile envelope at lower stress ranges is discussed. Suggestions are then provided on how to prescriptively address the problems created by incorrectly utilizing tensile strength test data in defining the compressional envelope. Methods and guidelines for resolving these problems are presented.
There has been much debate in the literature and throughout the rock mechanics community regarding whether or not direct or indirect tensile strength data should be incorporated in the regression methodology for correct derivation of the Hoek-Brown (H-B) constant mi for a specific data set. In the latest update paper on the H-B Criteria, Hoek and Brown, 2018 recommend only including compressional data as basis for establishing the regression constant, while others (e.g., Richards and Read, 2011 et seq) suggest that tensile strength data should be incorporated as part of the curve fitting procedure in order to properly condition the curve fit in the low stress range.
The principal dilemma of the problem is that the tensile intercept of the Hoek-Brown envelope does not generally match with actual uniaxial tensile strengths for most rock types, especially for those with low mi values, as is clear from Figure 1. Hence Hoek and Martin, 2014 and Hoek and Brown, 2018 recommend adopting a tensile cut off, rather than including tensile data in the overall regression fit.