深埋双隧洞开挖的解析延拓法求解

ANALYTIC CONTINUATION SOLUTION OF DEEP TWIN-TUNNELS

将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,考虑两隧洞开挖次序的影响,利用解析延拓法及Schwarz交替法求解出弹性半空间内2个任意形状任意尺寸的双隧洞在任意相对位置下其半空间内任意一点的应力解和位移解的隐式表达式。将双圆形隧洞作为特例,考虑到隧洞埋深与孔径相比比较大,从而不考虑重力梯度的影响,将重力化为作用在边界上的均布外荷载,考虑2个隧洞衬砌法向反力的影响,求解出弹性半空间内圆形双隧洞任意一点处的应力值和位移值解析解的具体显式表达式。最后利用二维有限元分析对理论推导的两圆形孔洞解析解进行验证,表明解的可靠性。

Considering the sequence of two-tunnel excavation,converting the underground space of tunnel to the case of elastic half-space under plane strain,an analytical solution is presented for stress and displacement of twin-tunnels with arbitrarily shape and size using analytic continuation method and Schwarz alternating method in an elastic half-plane.Because the depth is larger than the size of the tunnel,thus the effect of gravity gradient is ignored,and gravity loads are simplified as uniform normal loads along far-field boundary.As a special case,a close solution for stress and displacement field around circular twin-tunnels at great depth considering the influences of lining forces of tunnels is given.Circular twin-tunnels are subjected to uniform internal pressure and their construction sequences are properly taken into consideration.Comparison between the results of numerical analysis by two-dimensional finite element method and those from the closed solutions indicates that the closed solution is reliable and applicable for the stress and displacement field around the twin-tunnels at great depth.