基于软化地基和弹性地基假定的坚硬顶板力学特性分析

 传统矿压分析中将坚硬顶板下部软岩的支承作用简化为Winkler弹性地基，要较精确地分析覆岩的力学特性，该简化不能满足要求。鉴于软岩对顶板支承力峰位于煤壁前方的实际，对煤壁到支承力峰为软化地基、支承力峰前方为弹性地基支承的周期来压前坚硬顶板模型的力学特性进行分析。注意到软化地基与弹性地基交界处地基反力保持连续，是引入软化地基分析顶板问题的关键，提出一个软化地基支承力峰值确定法和2个支承力峰值精度验证法。据所提出的软化地基对顶板支承力表达式写出软化地基区段顶板挠度方程形式解，求得五段式顶板挠度方程形式解中全部积分常数。在算例中获得软化地基对顶板支承力峰值并对其精度予以验证，将分析结果与基于全弹性地基支承假定的顶板力学特性进行比较。得到如下认识：200～300 m埋深下全弹性地基支承假定的顶板在煤壁处受到的地基反力，是煤壁附近为软化地基支承的顶板在煤壁处所受地基反力的4倍。煤壁附近强大反力的支承使顶板弯曲程度小，弯曲范围小，弯矩峰超前煤壁的距离小，煤壁前方应变能储存区域及储存量小；软化地基支承的顶板在煤壁处的地基反力为前者的1/4。煤壁附近反力小使顶板通过加大弯曲程度和弯曲变形范围去抵抗顶板上覆荷载，这使得弯矩峰值和弯矩峰超前煤壁的距离有较大增加，煤壁前方应变能储存区域和储存量大为增加，顶板挠度比全为弹性地基支承的顶板挠度有全面、大幅度增加。煤壁前方顶板弯矩峰位置与顶板超前断裂距有关，基于软化地基和弹性地基假定计算的顶板弯矩峰位置，与现场监测到的顶板断裂位置接近，相应的顶板的内力、应变能和挠度特性描述，比基于全弹性地基支承假定的顶板力学特性更为贴近实际。

MECHANICAL PROPERTIES OF HARD ROOF BASED ON ASSUMPTIONS OF SOFTEN FOUNDATION AND ELASTIC FOUNDATION

In traditional ground control theory，supporting action of soft rock under hard roof was often simplified as the Winkler elastic foundation. To accurately analyze the mechanical characteristics and activity of overlying strata，this simplification cannot be contented with the actual requirements. In view of peak of abutment pressure in front of the coal wall，mechanics properties of hard roof model that was thought as soften foundation between coal wall and the peak of abutment pressure and elastic foundation ahead of the peak of abutment pressure were analyzed before the periodic weighting. Methods for determinating peak value of the abutment force were presented. Examples were given to illustrate how to calculate the peak value of the abutment and verify the accuracy using the development approaches. Analysis results were compared with mechanics properties of roof based on full elastic foundation. The research results are shown as follows：Reaction force near the coal wall to the roof obtained by full elastic foundation is 4 times as big as that of the roof calculated by the soften foundation in the depths of 200–300 m. Bending degree of roof，scope of the bend，the distance between peak of bending moment and the coal wall，storage area of strain energy and storage capacity become small near the coal wall，which result from the powerful reaction near coal wall. Reaction near the coal wall to the roof，which is caused by the soften foundation is a fourth as big as that of the former. Owning to the small reaction near coal wall，bending degree of roof and scope of the bend become increase for resisting on overly roof，which lead to the peak of bending moment and the distance between peak of bending moment and the coal wall increase remarkably. Meanwhile，storage area of strain energy and storage capacity outstanding aggrandize in front of coal wall. Then the roof?s deflection increase overall and remarkably when compared with the roof supported by full elastic foundation. Position of peak of bending moment in front of coal wall is related to the location of roof fracture. Position of roof fracture that calculated based on the assumption of soften foundation and elastic foundation is closer to the actual，and the corresponding internal force，strain energy and deflection are closer to the actual when compared to full elastic foundation.