Computational Upper- and Lower-Bound 3D Limit Analysis Using the Hoek–Brown Yield Criterion

Abstract

The Hoek–Brown failure criterion has been widely applied to predict the strength of rock masses, demonstrating its relevance in diverse geotechnical contexts. This paper presents a novel 3D numerical implementation of the Hoek–Brown criterion in a finite-element limit analysis code. The proposed formulation is unique in its ability to produce strict upper and lower bounds for 3D problems, providing more accurate and reliable predictions of failure mechanisms compared to previous formulations. The validity of the formulation is demonstrated through comparisons with known analytical solutions or other authors’ numerical solutions. Furthermore, the proposed numerical tool is used to determine the stability of shallow circular tunnels in rock masses, highlighting its practical applicability in engineering design.