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<p>Tunnel linings are generally designed considering primary overburden stresses, while footing–tunnel interaction and foundation-induced stress bulb effects are often overlooked in secondary support design. This study optimizes tunnel-lining thickness to minimize its influence on the ultimate bearing capacity of overlying strip footings using finite-element limit analysis (FELA). The effects of tunnel depth, offset distance, and rock strength parameters are evaluated using a non-dimensional footing-stability improvement factor (<i>I</i><sub><i>f</i></sub>), defined as the ratio of UBC with and without tunnel-lining, to quantify lining effects on footing–tunnel interaction. The results show that footing–tunnel interaction becomes negligible when the tunnel depth exceeds three times the footing width or the tunnel offset distance reaches six times the footing width. The required lining thickness decreases significantly with increasing tunnel depth and offsets distance. For the case where the tunnel offset distance is equal to the footing-width, the optimum lining-thickness ratio is approximately five percent of the footing width for tunnel depths between one-half and one-and-a-half-times the footing width, two percent for depths between one-and-a-half and two times, and one percent for depths between two and two-and-a-half times the footing width. Beyond this depth range, <i>I</i><sub>f</sub> approaches unity, indicating negligible footing–tunnel interaction. Variations in rock strength parameters have negligible effects on <i>I</i><sub><i>f</i></sub>, whereas increasing lining thickness effectively mitigates footing–tunnel interaction and changes the failure mechanism. To predict <i>I</i><sub><i>f</i></sub>, several soft-computing models were developed. The artificial neural network demonstrated the highest accuracy (<i>R</i><sub>2</sub>=0.99, MSE=0.0000094). Among the regression-based models, the Optimizable Gaussian Process Regression and Bi-layered Neural Network showed strong training performance (<i>R</i><sup>2</sup>≥0.97, RMSE≤0.044), while the Trilayered Neural Network achieved the best testing performance (<i>R</i><sup>2</sup>=0.95, RMSE=0.079). The study presents a performance-based FELA–ML framework for determining optimum tunnel-lining thickness and developing predictive design tools to minimize footing–tunnel interaction in horseshoe-shaped tunnels in rock masses.</p>

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Performance-based tunnel lining design and recommendations for horseshoe tunnels in rock mass using limit analysis

  • 期刊论文

  • 发表日期：

    2026年7月29日

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  • Aayush Kumar,
  • Vinay Bhushan Chauhan

摘要

Tunnel linings are generally designed considering primary overburden stresses, while footing–tunnel interaction and foundation-induced stress bulb effects are often overlooked in secondary support design. This study optimizes tunnel-lining thickness to minimize its influence on the ultimate bearing capacity of overlying strip footings using finite-element limit analysis (FELA). The effects of tunnel depth, offset distance, and rock strength parameters are evaluated using a non-dimensional footing-stability improvement factor (If), defined as the ratio of UBC with and without tunnel-lining, to quantify lining effects on footing–tunnel interaction. The results show that footing–tunnel interaction becomes negligible when the tunnel depth exceeds three times the footing width or the tunnel offset distance reaches six times the footing width. The required lining thickness decreases significantly with increasing tunnel depth and offsets distance. For the case where the tunnel offset distance is equal to the footing-width, the optimum lining-thickness ratio is approximately five percent of the footing width for tunnel depths between one-half and one-and-a-half-times the footing width, two percent for depths between one-and-a-half and two times, and one percent for depths between two and two-and-a-half times the footing width. Beyond this depth range, If approaches unity, indicating negligible footing–tunnel interaction. Variations in rock strength parameters have negligible effects on If, whereas increasing lining thickness effectively mitigates footing–tunnel interaction and changes the failure mechanism. To predict If, several soft-computing models were developed. The artificial neural network demonstrated the highest accuracy (R2=0.99, MSE=0.0000094). Among the regression-based models, the Optimizable Gaussian Process Regression and Bi-layered Neural Network showed strong training performance (R2≥0.97, RMSE≤0.044), while the Trilayered Neural Network achieved the best testing performance (R2=0.95, RMSE=0.079). The study presents a performance-based FELA–ML framework for determining optimum tunnel-lining thickness and developing predictive design tools to minimize footing–tunnel interaction in horseshoe-shaped tunnels in rock masses.