矩形巷道围岩应力解析解

Analytical solution of rectangular roadway surrounding rock stress

为得出矩形断面巷道围岩应力分布特征,采用复变函数解法对矩形巷道围岩弹性应力进行解析,得出了应力分量的曲线坐标表达式;分析了巷道高宽比和侧压对围岩应力的影响。结果表明,高宽相等时巷道最大应力最小,边界最大应力随侧压系数增大而增大。无论侧压和高宽比如何变化,四角附近区域应力集中系数均最大。同高宽比情况下,随侧压增加,矩形巷道径向应力的峰值近似呈线性增加,环向应力峰值减小,径向应力和环向应力峰值均向围岩内部迁移。相同侧压下,随巷道高宽比增大,径向应力和环向应力峰值均向围岩内部迁移。相同高宽比和侧压下,距离巷道右帮越远,径向应力越大,环向压应力先增后减。

In order to find the stress distributive features of a rectangular shape section coal mining roadway of the surrounding rocks,this paper attempts to apply the complex variable function method for analyzing the elastic stress of the roadway surrounded rocks so as to obtain a curve coordinate expression of the total stress of the said rocks. Through a careful analysis of the ratio of the roadway height and width and the effects of the side pressure on the surrounding rock stress,we have found that the maximum rectangular roadway boundary stress tends to increase first and then decrease with the ratio of height and width,and finally reaches the smallest,or the minimum stress of the roadway when the height becomes equal to the width at the same side pressure. On the other hand,the maximum rectangular roadway boundary stress tends to increase with the side pressure coefficient,when the effect of the side pressure coefficient on the maximum stress tends to be the minimum. What is more,the maximum roadway boundary stress tends to come out in the four corners and distributes symmetrically evenly,no matter how the side pressure coefficient and the ratio of the height to the width tend to vary. In addition,when the roadway boundary stress increases gradually from the middle to the right and from the left,to the central top and from the bottom plate to the four corners,the maximum radial stress of the rectangular roadway tends to increase approximately linearly,with the maximum circumferential stress decreasing and the maximum radial and circumferential stress migrating to the interior rocks at the same ratio of height and width with the side pressure coefficient. Furthermore,the circumferential tensile stress tends to appear on the two sides of the roadway when the side pressure coefficient approaches 2 with the ratio of height and width remaining unchanged. Moreover,at the same side pressure and the same ratio of height and width,the farther the distance from the right side of the roadway,the bigger the radial stress near the side pressure,and in turn,the circumferential stress also tends to increase first and then decrease,getting to be closer and closer to the far side of the vertical stress eventually. Under the same side pressure,both of the maximum radial and circumferential stress peak values tend to migrate to the interior proportionally with the ratio of the height and width.