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<p>Understanding the mechanical response of coal mine roofs under combined vertical overburden loads and horizontal lateral stresses is critical for assessing roof stability in longwall mining. In this study, the periodically weighting roof is idealized as a rectangular thin plate model with two adjacent sides clamped and the other two simply supported (CCSS), and a composite deflection function is constructed by coupling polynomial terms with trigonometric series. The Galerkin method is applied to convert the governing partial differential equation for the deflection function into an algebraic system, deriving an analytical solution that enables modal analysis of roof deflection and stress. Results show that the deformation is predominantly controlled by the superposition of the mode with one modal number in the <i>x</i> direction and one in the <i>y</i> direction, and the mode with one modal number in the <i>x</i>-direction and two in the <i>y</i>-direction, together contributing 96.67% of the global strain energy, with the latter mode alone contributing 61.5%. High tensile stress regions are found to spatially coincide with large deflection zones. The theoretical results show high consistency with the concentration of high energy microseismic events and the peak hydraulic support resistance observed at the 14321 longwall working face in the Gubei Mine, Huainan. This study establishes a new theoretical framework for analyzing the mechanical response of mine roofs and provides a reliable approach for accurate prediction of periodic weighting.</p>

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Analytical bending model and modal characteristics of coal mine roof under lateral stress

  • 期刊论文

  • 发表日期：

    2025年12月3日

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  • Can-Zhen Wu,
  • Ying Xu,
  • Qiang-Qiang Zheng,
  • Hao-Tian Xie

摘要

Understanding the mechanical response of coal mine roofs under combined vertical overburden loads and horizontal lateral stresses is critical for assessing roof stability in longwall mining. In this study, the periodically weighting roof is idealized as a rectangular thin plate model with two adjacent sides clamped and the other two simply supported (CCSS), and a composite deflection function is constructed by coupling polynomial terms with trigonometric series. The Galerkin method is applied to convert the governing partial differential equation for the deflection function into an algebraic system, deriving an analytical solution that enables modal analysis of roof deflection and stress. Results show that the deformation is predominantly controlled by the superposition of the mode with one modal number in the x direction and one in the y direction, and the mode with one modal number in the x-direction and two in the y-direction, together contributing 96.67% of the global strain energy, with the latter mode alone contributing 61.5%. High tensile stress regions are found to spatially coincide with large deflection zones. The theoretical results show high consistency with the concentration of high energy microseismic events and the peak hydraulic support resistance observed at the 14321 longwall working face in the Gubei Mine, Huainan. This study establishes a new theoretical framework for analyzing the mechanical response of mine roofs and provides a reliable approach for accurate prediction of periodic weighting.