椭圆形溶洞对邻近深埋圆形隧洞的影响分析

将深埋溶洞-隧洞所处的地下空间转换为平面应变情况下的弹性半空间，溶洞为似椭圆形；由于圆形断面隧洞埋深与孔径相比比较大从而不考虑重力梯度影响，考虑隧洞衬砌法向支撑力的影响，且考虑溶洞先于隧洞形成等因素，利用复变函数中的柯西积分法结合Schwarz交替法求解出弹性半空间内椭圆形溶洞及圆形隧洞周边任意一点处的应力值和位移值解析解的具体显式表达式。采用有限元分析对理论推导的椭圆形溶洞-圆形隧洞体系的解析解进行验证。

Analysis solution for tunnels due to the influence of adjacent ellipse karst cave

Problems of karst collapse may often occur in railway and highway construction.How to evaluate the influence of existed karst on adjacent tunnels reasonably is meaningful to design of tunnel engineering in karst regions.Considering a simplified cave as ellipse shape section and tunnel as circular,a simplified analysis solution for stresses and deformation characteristic of tunnel due to the influence of adjacent ellipse karst cave is proposed in the paper.Schwarz's alternating method was used to derive the formulas for calculating the stress and displacement of the surrounding rocks.Since the depth is larger than the size of the tunnel,the effect of gravity gradient is ignored,and gravity loads are simplified as uniform normal loads along far-field boundary.Comparison between the results from the closed solutions and those from numerical analysis by two-dimensional finite element method indicates that the closed solution is reliable and applicable for the stress and displacement field around circular tunnels adjacent to the influence of an ellipse karst cave at great depth.