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<p>The escalating utilization of urban underground space frequently necessitates the construction of surface structures in close proximity to subterranean tunnels. This study investigates the bearing capacity of rigid strip footings above dual square tunnels in Hoek–Brown rock masses under inclined loading. Utilizing rigorous Finite Element Limit Analysis (FELA) with adaptive mesh refinement, the true ultimate bearing capacity is bracketed with a strict upper and lower bound error margin of less than 3%. The analysis systematically quantifies the influence of key parameters across extensive ranges: tunnel depth ratio (<i>H/D</i> ∈ [1.5, 3.0]), spacing ratio (<i>S/D</i> ∈ [1, 6], Geological Strength Index (<i>GSI</i> ∈ [50, 100]), and intact rock constant (<i>m</i><sub>i</sub> = 7, 10, 15, 17, 25). A pivotal contribution is the precise identification of a load “critical angle” threshold, ranging from arctan(0.4) to arctan(0.5) depending on the tunnel depth. Below this angle, the failure mechanism is a deep-seated, tunnel-coupled mode; beyond it, the system transitions abruptly to a shallow, surface-controlled sliding failure where the tunnels have negligible impact. Furthermore, the study establishes quantitative engineering guidelines: narrow pillar spacings (<i>S/D</i> = 1) pose an extreme risk of catastrophic failure, whereas dual-tunnel interaction becomes negligible at <i>S/D</i> ≥ 4. Crucially, to bridge the gap between theoretical numerical analysis and practical application, a deep learning-based algorithm was employed to distill the extensive simulation dataset into an explicit, highly accurate, and interpretable predictive formula. Incorporating all investigated variables, this intelligent formula-alongside the comprehensive dimensionless failure envelopes-equips geotechnical engineers with a robust tool for rapid stability evaluations and design optimization.</p>

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Bearing capacity of inclined-loaded footings above dual tunnels in rock masses

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月25日

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  • Yuda Huang,
  • Xingyu Kang,
  • Donghong Dai,
  • Gaoqiao Wu

摘要

The escalating utilization of urban underground space frequently necessitates the construction of surface structures in close proximity to subterranean tunnels. This study investigates the bearing capacity of rigid strip footings above dual square tunnels in Hoek–Brown rock masses under inclined loading. Utilizing rigorous Finite Element Limit Analysis (FELA) with adaptive mesh refinement, the true ultimate bearing capacity is bracketed with a strict upper and lower bound error margin of less than 3%. The analysis systematically quantifies the influence of key parameters across extensive ranges: tunnel depth ratio (H/D ∈ [1.5, 3.0]), spacing ratio (S/D ∈ [1, 6], Geological Strength Index (GSI ∈ [50, 100]), and intact rock constant (mi = 7, 10, 15, 17, 25). A pivotal contribution is the precise identification of a load “critical angle” threshold, ranging from arctan(0.4) to arctan(0.5) depending on the tunnel depth. Below this angle, the failure mechanism is a deep-seated, tunnel-coupled mode; beyond it, the system transitions abruptly to a shallow, surface-controlled sliding failure where the tunnels have negligible impact. Furthermore, the study establishes quantitative engineering guidelines: narrow pillar spacings (S/D = 1) pose an extreme risk of catastrophic failure, whereas dual-tunnel interaction becomes negligible at S/D ≥ 4. Crucially, to bridge the gap between theoretical numerical analysis and practical application, a deep learning-based algorithm was employed to distill the extensive simulation dataset into an explicit, highly accurate, and interpretable predictive formula. Incorporating all investigated variables, this intelligent formula-alongside the comprehensive dimensionless failure envelopes-equips geotechnical engineers with a robust tool for rapid stability evaluations and design optimization.