中文摘要：

煤矿开采地质条件复杂以及不同煤层采煤方法的差异,导致采场顶板会有多种边界条件。在不同边界下,坚硬顶板的极限载荷和破断距必不相同。因此,建立5种不同边界（四边固支、三固一简、邻固邻简、对固对简及三简一固）下顶板的力学模型,利用塑性极限法求得各种边界下顶板极限载荷,分析得出极限载荷随k（推进距离与工作面长度比）的变化规律。顶板极限载荷在对边固支和对边简支边界下最大,四边固支边界次之,而在其他3种边界下接近相等。此外,以所求顶板极限载荷为基础,得到了各种边界条件下顶板的最小破断距,并采用数值试验方法进行了验证。

英文摘要：

Complex geological condition and different mining methods in coal mining will result in multi boundary condition of roof.Under different boundaries,limit load and broken pace of hard roof was different without fail.5 roof mechanics models with 5 different boundary conditions were set up.Roof limit load under different boundaries（4 sides fixed,3 sides fixed and 1 side simply supported,adjacent fixed and adjacent simply supported,opposite side fixed,3 sides simply supported and 1side fixed.） was obtained by plastic limit method.Variation rule of limit load with k（ratio of advance distance to mining face length） was analyzed.Roof limit load reached maximum under the condition of opposite side fixed and opposite side simply supported boundary.4 sides fixed boundary was secondary.Other 3 boundary conditions were almost equal.Minimum roof broken pace of every boundary condition was obtained on the basis of roof limit load,which was verified by numerical simulation.