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Uncertainty-aware stability analysis and reliability-oriented design of dual rectangular tunnels in rock masses
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DOI：10.1016/j.tust.2026.108020.png)
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Abstract
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The stability of closely spaced tunnels in rock masses is strongly influenced by geometric interaction, rock mass quality, and failure uncertainty, particularly for rectangular tunnel geometries where corner effects are pronounced. This study presents a unified physics-based and data-driven framework for the stability assessment of dual rectangular tunnels excavated in rock masses. A large, mechanically consistent dataset is generated using upper-bound adaptive finite element limit analysis incorporating the generalized Hoek–Brown criterion. Based on the numerical results, a refined five-mode failure taxonomy is proposed to describe the progressive transition from strongly interacting collapse to isolated tunnel behavior. To enable efficient prediction and uncertainty-aware interpretation, a physics-guided Bayesian neural network surrogate is developed by embedding the Hoek–Brown strength formulation as a mechanistic baseline while allowing the neural network component to flexibly learn data-driven corrections beyond the physical baseline. Under geological domain shifts, the physics-guided formulation reduced the root mean square error by 56–85% and the continuous ranked probability score by 41–88% relative to a purely data-driven Bayesian neural network, demonstrating substantially improved extrapolation robustness. By integrating probabilistic prediction, threshold-dependent reliability evaluation, sensitivity analysis, and reliability-oriented design exploration, the study reveals how tunnel interaction, geometry, and geological conditions jointly govern stability and risk under varying performance demands. The proposed framework thus provides an interpretable and practically applicable basis for reliability-informed assessment and design of interacting rectangular tunnel systems.
Keywords:
Dual rectangular tunnels
Finite element limit analysis
Tunnel interaction and failure modes
Physics-guided Bayesian modeling
Uncertainty-aware stability assessment
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