A Computational Approach to Preliminary Tunnel Design: Integrating Kirsch Equations and the Generalized Hoek–Brown Criterion

Reliable preliminary assessment of stress redistribution and rock mass stability is a critical step in tunnel design, providing guidance before detailed numerical modeling and support design are undertaken. This study presents RockStressCalc, a Python-based computational framework that integrates classical elastic stress–displacement analysis with empirical rock mass strength evaluation for circular tunnels within a transparent analytical workflow. The tool combines Kirsch’s closed-form solution for stress redistribution around a circular opening under anisotropic in situ stress conditions with the generalized Hoek–Brown criterion to enable spatially resolved evaluation of elastic strength reserve. The framework assumes a homogeneous, isotropic, linear–elastic rock mass under plane strain conditions and introduces a Stability Factor as a stress-based indicator of proximity to initial yield. The analytical implementation is verified against finite-element simulations performed in Plaxis2D under equivalent elastic assumptions. The maximum stress difference at the excavation boundary remained below 10%, while displacement deviations were below approximately 4%. In addition, comparison between the analytical far-field Stability Factor and the numerical strength reduction multiplier demonstrated close agreement, confirming consistency between the analytical and finite-element formulations under uniform stress conditions. The results show that RockStressCalc provides a computationally efficient analytical baseline suitable for rapid parametric evaluation, sensitivity studies, educational use, and independent verification of numerical models in early-stage tunnel design. By emphasizing explicit coupling of stress redistribution and strength evaluation within a reproducible framework, rather than introducing new constitutive models, the proposed approach offers practical engineering value as a screening and benchmarking tool and provides a foundation for future probabilistic or extended tunnel stability analyses.