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<p>Large deformation in soft rock tunnels remains a critical challenge in mining and underground engineering, with conventional rigid supports prone to overstressing and failure due to limited deformation compatibility. Although yielding supports with resistance limiters such as inflatable airbags and circular steel bellows (CSBs) provide improved adaptability, current design approaches remain largely empirical or overly simplified. As a result, they lack a unified constitutive framework that can quantitatively describe their multi-stage mechanical behavior and effectively link it to performance-based design. To address this gap, this study develops and experimentally validates a novel constitutive model that characterizes yielding supports through three explicit phases: elastic yielding (initial stiffness <i>k</i><sub>o</sub> = 0.18–0.25 kN/mm), post-yield hardening (hardening stiffness <i>k</i><sub><i>h</i></sub> = 0.42–0.68 kN/mm), and locking (ultimate resistance <i>F</i><sub><i>L</i></sub> = 2.0–2.4 kN). To enable quantitative performance assessment, eight dimensionless indices are introduced, including the yielding ductility ratio (<i>μ</i>), deformation capacity envelope (Ω), plasticity index (ψ), strain localization index (<i>L</i><sub><i>Ɛ</i></sub>), strain uniformity index (<i>U</i><sub><i>Ɛ</i>)</sub>, support adaptability index (SAI), and energy-reaction coupling coefficient (<i>η</i>). Large-scale model tests demonstrate that airbag limiters reduce vertical deformation by approximately 35% relative to rigid supports and exhibit superior early-stage adaptability (Ω ≈ 0.46), whereas CSBs provide higher energy dissipation (<i>E</i><sub><i>d</i></sub> = 50–55&#xa0;J), greater strain uniformity (<i>U</i><sub><i>ε</i></sub> ≈ 0.79), and enhanced stability through post-yield hardening. The proposed framework further integrates these indices into practical design tools, including stability maps based on stiffness ratios (<i>α</i> = <i>k</i><sub>o</sub>/<i>k</i><sub><i>r</i></sub>, <i>β</i> = <i>k</i><sub>h</sub>/<i>k</i><sub><i>r</i></sub>) and the Yield-Hardening Design Surface (YHDS), enabling performance-based selection and optimization of yielding supports under squeezing conditions. This work provides a validated, mechanics-based, and metrics-driven approach to mining and tunnel support design, effectively bridging the gap between constitutive modeling and practical engineering application.</p>

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A unified constitutive model for yielding single-lining tunnel supports with resistance limiters under large deformation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月23日

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  • Muhammad Zohaib,
  • Qiu Wenge,
  • Muhammad Awais Hussain,
  • Weipeng Pan,
  • Muhammad Akbar,
  • Tarek Salem Abdennaji,
  • Aymen Flah

摘要

Large deformation in soft rock tunnels remains a critical challenge in mining and underground engineering, with conventional rigid supports prone to overstressing and failure due to limited deformation compatibility. Although yielding supports with resistance limiters such as inflatable airbags and circular steel bellows (CSBs) provide improved adaptability, current design approaches remain largely empirical or overly simplified. As a result, they lack a unified constitutive framework that can quantitatively describe their multi-stage mechanical behavior and effectively link it to performance-based design. To address this gap, this study develops and experimentally validates a novel constitutive model that characterizes yielding supports through three explicit phases: elastic yielding (initial stiffness ko = 0.18–0.25 kN/mm), post-yield hardening (hardening stiffness kh = 0.42–0.68 kN/mm), and locking (ultimate resistance FL = 2.0–2.4 kN). To enable quantitative performance assessment, eight dimensionless indices are introduced, including the yielding ductility ratio (μ), deformation capacity envelope (Ω), plasticity index (ψ), strain localization index (LƐ), strain uniformity index (UƐ), support adaptability index (SAI), and energy-reaction coupling coefficient (η). Large-scale model tests demonstrate that airbag limiters reduce vertical deformation by approximately 35% relative to rigid supports and exhibit superior early-stage adaptability (Ω ≈ 0.46), whereas CSBs provide higher energy dissipation (Ed = 50–55 J), greater strain uniformity (Uε ≈ 0.79), and enhanced stability through post-yield hardening. The proposed framework further integrates these indices into practical design tools, including stability maps based on stiffness ratios (α = ko/kr, β = kh/kr) and the Yield-Hardening Design Surface (YHDS), enabling performance-based selection and optimization of yielding supports under squeezing conditions. This work provides a validated, mechanics-based, and metrics-driven approach to mining and tunnel support design, effectively bridging the gap between constitutive modeling and practical engineering application.