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.
本研究旨在揭示煤矿回采工作面顶板在垂向覆岩荷载与水平侧向应力耦合作用下的弯曲行为与破断机理。研究将周期来压的顶板简化为两邻边固支两邻边简支约束(CCSS)矩形薄板模型;构造多项式与重三角级数乘积形式的复合挠度函数,采用伽辽金法将挠度函数偏微分方程转化为代数方程组,求解挠度函数解析式,对顶板挠度、应力进行模态分析。结果表明:顶板变形由x方向模态数m为1、y方向模态n数为1与x方向模态数m为1、y方向模态数n为2的叠加模态主导,二者叠加应变能之和占全局应变能96.67%,x方向模态数m为1、y方向模态数n为2的单模态应变能占全局应变能的61.5%;且顶板高拉应力区与大挠度区在空间上具有一致性。该理论结果与淮南顾北矿14321回采工作面现场微震监测的高能量事件密集区及液压支架工作面阻力峰值区高度吻合。本研究为矿山顶板力学响应分析提供了新的理论框架,并为周期来压的精准预测提供了可靠方法。
基金
supported by the Natural Science Research Project of Colleges and Universities in Anhui Province(Grant No.2024AH050374)
Anhui Provincial Natural Science Foundation(Grant No.2508085QE186)
Research Foundation for Postdoctoral of Anhui Province(Grant No.2024B817)
National Natural Science Foundation of China(Grant No.52074009).
