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基于Timoshenko理论的急倾斜特厚煤层顶板挠度精准计算方法

Accurate calculation method for roof deflection of steeply inclined extra-thick coal seams based on Timoshenko theory

  • 摘要: 为了解决急倾斜特厚煤层顶板稳定性表征中,传统梁理论因忽略剪切变形而难以精准计算顶板挠度的难题,本文采用可计入剪切变形的Timoshenko梁理论,针对急倾斜特厚煤层的煤层倾斜、厚度大、剪切变形影响显著的特征,构建顶板力学模型。基于Timoshenko梁理论,明确采场顶板的受力与边界条件,建立顶板挠度控制方程并求解,形成适用于该类煤层开采的顶板挠度计算方法。并分析顶板不同区段的挠度演化规律,与Euler-Bernoulli梁理论计算结果进行对比。同时开展岩体弹性模量、充填体强度等关键参数的分析,揭示影响顶板变形的主导因素,提出顶板控制技术路径。研究结果表明,在该类顶板挠度计算中,Timoshenko梁理论充分考虑剪切变形对顶板变形的影响,计算结果与数值模拟偏差仅为3.2%,远低于Euler-Bernoulli梁理论9.4%的偏差值,能精准地反映顶板实际变形与演化规律。研究完善了此场景下的顶板挠度计算理论体系,为类似地质条件下煤层顶板控制工程的设计、充填参数调控提供了重要的理论依据与参考。

     

    Abstract: To solve the problem that traditional beam theory ignores shear deformation and fails to accurately calculate roof deflection in characterizing roof stability of steeply inclined extra-thick coal seams, this study adopts the Timoshenko beam theory incorporating shear deformation. Aiming at the characteristics of such coal seams—steep inclination, large thickness and significant shear deformation impact—a roof mechanical model was established. Based on the Timoshenko beam theory, the stress and boundary conditions of the stope roof were clarified, and the governing equation of roof deflection was established and solved to form a calculation method for this type of coal seam mining. The deflection evolution of different roof sections was analyzed and compared with Euler-Bernoulli beam theory results. Key parameters including rock mass elastic modulus and filling body strength were analyzed to reveal dominant factors affecting roof deformation, and a technical path for roof subsidence control was proposed. Results show that the Timoshenko beam theory fully considers shear deformation’s influence on roof deflection: its deviation from numerical simulation is only 3.2%, much lower than the Euler-Bernoulli beam theory’s 9.4%, and it accurately reflects actual roof deformation and evolution. This study improves the roof deflection calculation theoretical system for such scenarios, providing important theoretical basis for support design and filling parameter regulation in coal seam roof control projects under similar geological conditions.

     

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