非均布荷载作用下煤柱-顶板系统的失稳分析

针对实际工程中作用在煤柱-顶板系统上的荷载为非均布荷载的现象，研究了煤柱-顶板系统在非均布荷载下的失稳机制。基于温克尔假设，把坚硬顶板视为弹性梁，把煤柱等效为连续均匀分布的支撑弹簧，从而形成煤柱-顶板相互作用系统的力学模型；基于尖点突变理论，对采空区煤柱-顶板系统失稳机理进行了探索，导出了该系统失稳的充要力学判据，并得出了顶板破坏的临界厚度；同时，分析了影响系统失稳的主要参数，并给出了若干工程建议；最后以甘肃省某煤矿为例，计算了该矿体的临界顶板厚度。所得结果为进一步研究煤柱-顶板系统的失稳机制和制定相关规范提供了参考。

Instability Analysis of Coal Pillar and Roof System Under Non-uniformly Distributed Loading

Since the loads on the coal pillar and roof system were non-uniformly distributed, the instability mechanism of the system under non-uniformly distributed loading was studied. Based on the Winkler＇s hypothesis, the stiff roof was assumed as an elastic beam and the coal pillars were equal to continuously and uniformly distributed support springs, which formed the mechanical model of the pillar and roof interaction system. Then the instability mechanisms of the coal pillar and roof system were explored, the instability mechanical criterion was deduced and the critical thickness of roof was obtained based on the catastrophe theory. Furthermore, some suggestions for application were given according to the parametric analysis. At last, taking a coal mine in Gansu Province as an example, the exact critical thickness of roof was calculated. The result is useful for the further research of the stability of the pillar and roof system and designing of relevant codes.