周期来压前受超前隆起分布荷载作用的坚硬顶板弯矩和挠度的解析解

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摘要将煤壁前方煤层和直接顶视为弹性地基，鉴于坚硬顶板的损伤、破裂从工作面中轴线的超前部位开始，在工作面煤壁中央取单位宽度的岩层结构研究，建立受均布荷载、超前隆起分布荷载和支护阻力共同作用的坚硬顶板超静定挠度微分方程组。在满足所有自然边界条件和连续条件的基础上，导得周期来压前煤壁前方和采空区坚硬顶板的挠度、弯矩表达式。据所得表达式，用Matlab的算例和绘图，对顶板荷载、支护阻力、地层刚度、单位宽顶板抗弯刚度及悬顶步距变化时坚硬顶板的挠度、弯矩进行分析，所得到的4段式弯矩、挠度曲线在考察区间内光滑连接，弯矩峰值位置在煤壁前方，顶板下沉量计算值在现场经验范围内。所得坚硬顶板弯矩、挠度的关系式为理想模型的解析解，其应用是从解析解算例中受到启发，获得参数变动时顶板弯矩、挠度变化的规律性认识，对实际采场顶板状况的变化作出由合理的定性判断，并可为坚硬顶板损伤断裂，为因断裂引发顶板应变能释放及冲击矿压能量来源的研究提供基础。

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关键词 ：采矿工程, 坚硬顶板, 周期来压, 弹性地基, 隆起荷载, 挠度, 弯矩

Abstract：Coal seam and immediate roof ahead of the coal face are considered as an elastic foundation；and because of that the damage and fracture of tight roof start at the advanced position of the middle axis of working face，so unit width rock stratum structure at middle part of the working surface can be taken to study and then the indeterminate deflection simultaneous differential equations of tight roof which are under the combined action of uniform load，advanced swelling distributive supporting load and support resistance are established. On the basis of all natural boundary conditions and continuity conditions being satisfied，the expressions about tight roof?s deflection，bending moment are derived ahead of the coal face and over the gob before the periodic weighting. According to these expressions obtained above，using Matlab software?s calculation and drawing functions，tight roof?s deflection and bending moment with the change of load，strata rigidity，flexural rigidity，support resistance and gob span are analyzed. Both the obtained four-part bending moment and deflection curves connect smoothly above the investigation interval，the peak positions of the bending moments lie ahead of the coal face and the tight roof?s subsidence values are coincident with the field experimental data. The expressions of tight roof?s deflection and bending moment are only theoretical solutions under ideal roof model，which can be used to be aroused from the calculation example of the theoretical solutions and to obtain regularity understanding for the variation in the roof?s deflection and bending moment when the relational parameters are changed；and to make reasonable qualitative judgment on the changes of the mine roof status. The analytic solution can also offer basis for further study about the damage and fracture of tight roof before the periodic weighting，the releases of the roof strain energy and the energy source of rockburst caused by the fracture of tight roof.

Key words： mining engineering tight roof periodic weighting elastic foundation swelling loading deflection bending moment

收稿日期: 2012-03-19

引用本文:

潘岳1，顾士坦2，戚云松1. 周期来压前受超前隆起分布荷载作用的坚硬顶板弯矩和挠度的解析解[J]. 岩石力学与工程学报, 2012, 31(10): 2053-2063.
PAN Yue1，GU Shitan2，QI Yunsong1. ANALYTIC SOLUTION OF TIGHT ROOF?S BENDING MOMENT AND DEFLECTION UNDER SWELLING DISTRIBUTIVE SUPPORTING PRESSURE. , 2012, 31(10): 2053-2063.

链接本文:

http://www.rockmech.org/CN/Y2012/V31/I10/2053

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