A Geological Approach for the Estimation of the Confined Elastic Modulus of Rock Based on the Hoek–Brown $${{\varvec{m}}}_{{\varvec{i}}}$$ Constant

The elastic modulus of rock is a fundamental parameter in geomechanical design; however, its stress dependency is often overlooked when a single unconfined value is adopted. Laboratory experiments, case histories, and numerical studies consistently indicate that rock stiffness increases with confining pressure, and reliance on unconfined elastic modulus values can lead to biased displacement predictions. This research develops a geology-based empirical relationship for the confined intact modulus of rock, incorporating uniaxial compressive strength, confining stress, and the Hoek–Brown constant $${m}_{i}$$ . Validation against a diverse set of published data sets confirms a strong correlation between confinement and modulus evolution. The extension of the confinement-dependent relationship to rock masses is achieved by substituting $${m}_{i}$$ with the Hoek–Brown rock-mass constant $${m}_{b}$$ ​. Benchmarking against existing models for confined rock-mass modulus reveals close agreement, with the proposed relationship predicting values within the observed field ranges. Implementation in numerical modelling highlights reduced displacement predictions compared to constant unconfined elastic modulus approaches, supporting the practical value of the proposed relationship for excavation design. The formulation provides a simple, generalisable, and conservative method for incorporating confinement effects into modulus estimates, with future work recommended to expand validation across geological settings and to exploit emerging Artificial Intelligence and Machine Learning techniques.