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<p>This study presents a semi-analytical solution for analyzing the dynamic response of rectangular tunnel linings subjected to SH-wave excitation within a quarter-space. The proposed approach integrates the image method with the conformal mapping technique to address the challenges of modeling the lining's rectangular geometry under dual free-surface boundaries. A rigorous wave-function expansion framework is developed, satisfying all stress and displacement continuity conditions at the lining-rock interfaces, with the inner boundary of the lining modeled as a stress-free surface. The model is validated against degenerate circular lining solutions. A comprehensive parametric analysis reveals the underlying mechanisms governing the dynamic stress concentration, particularly highlighting the emergence of periodic high-stress bands near the free-surface corners and a frequency-dependent reversal effect in the influence of lining-rock stiffness ratio. These findings, which deviate significantly from predictions of conventional half-space models, provide critical insights and a theoretical basis for the seismic design of tunnel linings in steep terrains, including the optimization of lining stiffness and the avoidance of resonance-prone configurations.</p>

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Semi-Analytical Study on SH-Wave Scattering by a Lining Structure of a Rectangular Tunnel in a Quarter-Space

  • 期刊论文

  • 发表日期：

    2026年7月10日

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  • Ni An,
  • Chunhui Yang,
  • Han Gao,
  • Zishi Li

摘要

This study presents a semi-analytical solution for analyzing the dynamic response of rectangular tunnel linings subjected to SH-wave excitation within a quarter-space. The proposed approach integrates the image method with the conformal mapping technique to address the challenges of modeling the lining's rectangular geometry under dual free-surface boundaries. A rigorous wave-function expansion framework is developed, satisfying all stress and displacement continuity conditions at the lining-rock interfaces, with the inner boundary of the lining modeled as a stress-free surface. The model is validated against degenerate circular lining solutions. A comprehensive parametric analysis reveals the underlying mechanisms governing the dynamic stress concentration, particularly highlighting the emergence of periodic high-stress bands near the free-surface corners and a frequency-dependent reversal effect in the influence of lining-rock stiffness ratio. These findings, which deviate significantly from predictions of conventional half-space models, provide critical insights and a theoretical basis for the seismic design of tunnel linings in steep terrains, including the optimization of lining stiffness and the avoidance of resonance-prone configurations.