Modeling Brittle-to-Ductile Transitions in Rock Masses: Integrating the Geological Strength Index with the Hoek–Brown Criterion

Abstract

Many studies focus on brittle–ductile transition stress in intact rocks; however, in real life, we deal with rock mass which contains many discontinuities. To fill this gap, this research focuses on the brittle–ductile transition stress of rock mass by considering the influence of different Geological Strength Index (GSI) values on the brittle–ductile transition stress of rock mass. In other words, the Hoek–Brown failure criteria for rock mass were reformulated mathematically including the ductility parameter (d), which is defined as the ratio of differential stress to minor stress. Then, the results were analyzed and plotted between σ3*σc and GSI, considering different (d) and Hoek–Brown material constant (mi) values. The brittle–ductile transition stress, σ3*, was determined by intersecting the Hoek–Brown failure envelope with Mogi’s line, with ductility parameters d ranging from 3.4 (silicate rocks) to 5.0 (carbonate rocks). Numerical solutions were derived for σ3*σc as a function of GSI using Matlab, and the results were fitted with an exponential model. The analysis revealed an exponential relationship between σ3*σc and GSI for values above 32, with accuracy better than 3%. Increased ductility reduces rock mass strength, with higher d values leading to lower σ3*σc. The diminishing returns in confinement strength at higher GSI values suggest that rock masses with higher GSI can sustain more confinement but with reduced effectiveness as GSI increases. These findings provide a framework for predicting brittle–ductile transitions in rock engineering.