中文摘要：

根据坚硬顶板孤岛工作面的特点,选取四面采空的孤岛工作面为研究对象,建立了孤岛工作面的坚硬顶板力学模型,将坚硬顶板视为弹性薄板,利用瑞利-里兹法进行了分析计算,研究了四面采空孤岛工作面坚硬顶板初次破断前后的能量特征,推导得出了孤岛工作面坚硬顶板的弯曲应变能简化公式,并利用典型冲击地压案例进行了验证分析,揭示了冲击地压发生的能量原因。研究表明：孤岛工作面坚硬顶板初次破断前的弯曲应变能在顶板见方时最大,且与采空区悬顶面积的三次方成正比;坚硬顶板初次破断后的弯曲应变能最大值出现在煤壁处,且与采空区悬顶长度的五次方成正比;经案例解算,孤岛工作面坚硬顶板初次破断前后的能量释放率达95.4%,具有强烈的冲击危险性,孤岛工作面冲击地压所释放的能量主要来自于悬空坚硬顶板破断的弹性能,采取及时有效的断顶卸压措施对于坚硬顶板孤岛工作面的冲击地压防治具有重要作用。

英文摘要：

According to the characteristics of the island working face with hard roof, 4 island working face with all round gobs was selected as research object, the mechanical model of hard roof in island working face was established, regarding the hard roof as elastic thin plate. Then Rayleigh - Ritz method was used to calculate and analyze energy characteristics of hard roof before and after the first fracture in island working face with all round gobs, the simplified formulas of bending strain energy for hard roof before and after the first fracture was deduced, using which the bending strain energy for the typical case of rock burst was estimated, the energy cause of rock burst was revealed. The result shows that： The maximum bending strain energy of hard roof before the first fracture in island working face appears when the roof is square, which is in direct proportion to cubic of the hanging roof area; that after first fracture in island working face appears at the coal face, which is in direct proportion to power of five of the hanging roof length. By the case, the release rate of bending strain energy for hard roof before and after the first fracture was 95.4% , which has the strong risk of rock burst. The energy of rock burst in is mainly from the elastic energy of the hanging hard roof, timely and＇ effective roof breakage is significant for the prevention and controlling of rock burst in the island working face with hard roof.