Estimation of the Hoek–Brown Constant mi from Analyzing the Uniaxial Compressive Test

Abstract

The Hoek–Brown failure criterion is a cornerstone of rock mechanics and is widely applied in the design of underground excavations, slopes, and foundations. However, determining its intact rock constant (mi) conventionally requires multiple triaxial compression tests under varying confining pressures, which are costly, time-consuming, and often infeasible when core quality or sample availability is limited. Building upon recent advances in empirical, probabilistic, and elastic-based approaches, this study develops and validates a practical method for estimating mi from standard uniaxial compressive strength (UCS) tests through analysis of the stress-dependent Poisson's ratio. The proposed framework establishes a mechanical linkage between m_i and the lateral deformation behavior of intact rock, reflecting the influence of microcrack closure and brittleness. Extensive UCS data for granite, limestone, marl, sandstone, and rock salt were analyzed to evaluate the method's reliability. The estimated m_i values show excellent agreement with triaxial test results for brittle lithologies and acceptable accuracy for more ductile rocks. Monte Carlo uncertainty analysis confirms the robustness of the approach, particularly for crystalline and well-cemented formations. The method offers a cost-effective and theoretically grounded alternative for preliminary design and rock characterization where triaxial testing is impractical, thereby enhancing the applicability of the Hoek–Brown criterion in routine engineering practice.