考虑衬砌截面协调变形约束的既有隧道受盾构下穿施工影响的Fourier能量变分解

Fourier energy variational solution of effects on existing tunnels induced by shield tunneling considering coordinated deformation of lining cross-section

目前关于新建盾构开挖诱发既有地铁隧道变形的理论研究,大多将既有隧道简化为不含接头的Euler-Bernoulli梁,而忽视了衬砌截面的剪切变形与管片接头的局部刚度削弱。此外,既有地基模型理论较少考虑衬砌管片与接触土体的协调变形约束。首先,采用Loganathan-Polous公式计算盾构开挖诱发的土体自由位移场,并将既有隧道视为考虑剪切变形的Timoshenko梁,基于沿轴线变化的抗弯与剪切刚度函数来描述管片接头的局部削弱作用;然后,结合能量变分原理与连续弹性体Mindlin解,建立考虑衬砌截面协同变形约束的隧道位移控制方程,将盾构开挖诱发的附加荷载施加于既有隧道,并使用Fourier级数方法求解既有隧道纵向变形;最后,将Fourier能量变分解与3组工程实测数据进行对比验证,取得了较好的一致性。此外,考虑隧道抗弯刚度、剪切刚度、接头刚度削弱作用、土体参数与隧道空间位置等因素的共同影响,使用抗弯系数、剪切系数及接头系数进行敏感性分析。结果表明,考虑截面变形协调约束的理论解更为符合实际,不考虑变形协调约束所得隧道位移结果偏大;衬砌接头局部刚度的削弱作用将造成隧道弯矩沿轴线在接头处发生明显锯齿状突变;抗弯系数与剪切系数的增长均导致隧道结构所受弯矩降低;剪切系数由低到高的增长将导致隧道变形模式发生“弯曲控制-弯剪混合-剪切控制”三阶段变化;隧道变形模式进入“剪切控制”阶段的过程中,抗弯刚度的变化对隧道内力影响逐渐降低;接头系数的增长将造成隧道所受弯矩降低,但隧道抗弯刚度较大时其影响逐渐减弱。

Current theoretical researches on shield tunneling induced existing metro tunnels deformation generally simplify the existing tunnels as Euler-Bernoulli beams without joints,neglecting the tunnel shear deformation and the local stiffness reduction caused by joints.Additionally,the existing foundation model theory rarely incorporates the coordination between lining cross-section and soil deformation.The study utilizes the Loganathan and Polous method to establish the shield tunneling-induced soil greenfield.To account for the local stiffness reduction,the paper then treats the existing tunnel as a Timoshenko beam,with the tunnel stiffness function varying along the axis.By combining the energy principle and the Mindlin solution,the paper stablishes the tunnel displacement equation considering the coordinated constraint between tunnel and soil.The soil greenfield is applied to the tunnel,resulting in longitudinal deformation,which is solved by Fourier series.Finally,the Fourier energy variational solution is verified by three sets of engineering data,achieving good consistency.To conduct parameter analysis,the relative effects among factors such as bending stiffness,shear stiffness,joint action,soil parameters and space relationship are also adopted.Analysis results indicate that the theoretical solution considering the coordinated constraints of cross-section aligns more closely with the field data.Tunnel displacement results obtained without considering the coordination constraints tend to be larger.The local stiffness weakening effect of joint will cause significant sudden variations in tunnel bending moments along the axis.The increase in both bending and shear stiffness coefficients leads to a decrease in the bending moment of the tunnel structure.Changes in shear stiffness coefficient from low to high would result in a three-stage process of the tunnel deformation mode,which is from bending controlled stage to bending-shear mixed stage and then to shear controlled stage.As the tunnel deformation mode enters the shear-controlled stage,the effect of bending stiffness coefficients gradually weakens.An increase in the joint coefficient generally causes a decrease in the bending moment of the tunnel,but the impact is slight as the bending coefficient increases.