初次来压前受超前增压荷载作用的坚硬顶板弯矩、挠度和剪力的解析解

ANALYTIC SOLUTION OF TIGHT ROOF′S BENDING MOMENT, DEFLECTION AND SHEAR FORCE UNDER ADVANCED SUPERCHARGER LOAD AND SUPPORTING RESISTANCE BEFORE FIRST WEIGHTING

坚硬顶板弯矩、挠度的理论解是矿山岩体力学中未曾获得较好解决的课题。初次来压坚硬顶板问题的超静定次数,比周期来压坚硬顶板问题的超静定次数要高1次。将煤层、直接顶按弹性地基处理,对初次来压前受均布荷载、荷载峰超前的增压荷载和支护阻力共同作用的,工作面中部煤壁前方和采空区单位宽坚硬顶板的挠度进行求解,采用潘岳等求解周期来压前坚硬顶板弯矩、挠度解中的部分结果,求得满足全部连续条件和自然边界条件的坚硬顶板的4段式挠度表达式中的所有系数。据所得表达式,采用Matlab软件计算和绘图得到的初次来压前坚硬顶板挠度、弯矩曲线在考察区间光滑连接,剪力曲线连续。对曲线进行分析可知:(1)荷载增减对顶板弯矩、挠度作用明显;(2)支护阻力可有效减小煤壁前方顶板和悬空顶板的弯矩、挠度及采空区顶板的剪力值;(3)单位宽顶板的特征长度由弹性地基系数、顶板抗弯刚度组成。在相同荷载下,只要特征长度相同,顶板弯矩分布完全相同,特征长度大者顶板弯矩大;(4)弹性地基系数小者,煤壁前方顶板挠度(下沉量)大。抗弯刚度小者,采空区顶板挠度(下沉量)大;(5)顶板弯矩峰位置在煤壁前方。顶板荷载大,支护阻力小,弹性地基系数大者,其弯矩峰与煤壁的距离近。在控顶区两端顶板剪力取最大值。所得硬顶板的关系式为理想坚硬顶板模型的解析解,其应用是从解析解算例中受到启发,获得参数变动时坚硬顶板弯矩、挠度和剪力变化的规律性认识,对采场顶板状况变化作出合理的定性判断,亦可为坚硬顶板断裂过程和断裂引发顶板应变能释放、冲击矿压能量来源及初次来压步距的量化分析提供基础。

Theoretical solution of bending moment and deflection about tight roof is a subject which has not been well solved in mining rock mechanics. Statically indeterminate times of the tight roof in the first weighting are one more higher than that in the periodic weighting. The coal seam and immediate roof are considered as an elastic ground to solve the deflection of the unit width tight roof in front of the coal face and over the gob at the middle part of working face which is under the combined action of uniform load, advanced supercharger load of the load peak and the support resistance is solved. Adopting some results of solution of tight roof＇s bending moment and deflection before periodic weighting obtained by PAN Yue et al., all coefficients of tight roof＇s four parts deflection expressions which are on the satisfaction of all continuity conditions and natural boundary conditionsare obtained. According to the expressions obtained, the tight roof deflection, bending moment curve and shear curve of the tight roof in the first weighting which was got by Matlab software＇s calculation and drawing functions was connected smoothly during the inspection. The following conclusions can be drawn from the curve analysis： （1） The increase or the decrease of the load has an obvious effect on bending moment and deflection of the roof. （2） The support resistance could effectively reduce the bending moment and deflection of the roof before the mine face and hanging roof and the shear stress of the gob roof. （3） Characteristic length of the unit width roof is composed of strata rigidity and flexural rigidity of the roof. With the same load, the bending moment of roof is completely the same if the characteristic length is identical; but the bending moment of the roof is larger when the characteristic length is larger. （4） When the elastic foundation coefficient is smaller, the deflection（subsidence value） of the roof ahead of coal face is larger. When the flexural rigidity is smaller, the deflection（subsidence value） of the gob roof is larger. （5） The peak position of the bending moment lies ahead of the coal face. The position of the bending moment peak is closer to coal face with the condition of large roof load, small the supporting resistance and large the elastic foundation coefficient. The roof shear is largest at the both sides of roof-control area. In this paper the expressions of tight roof 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 deflection and bending moment when the relational parameters are changed; and to make reasonable qualitative judgment on the changes of the mine roof status. Also the analytic solution can offer basis for further study about the fracture process of tight roof, the releases of the roof strain energy and the energy source ofrockburst caused by the fracture of tight roof.