隧道沉降引起的轨道结构变形与脱空

Deformation and Cavity of Track Structure Due to Tunnel Settlement

从微元体的平衡出发推导轨道结构变形的非线性控制微分方程。假设盾构隧道沉降遵从正态曲线,并引入阶梯函数描述轨道与基底的脱开状态,导出求解轨道变形的级数解。对支承块式道床轨道结构进行实例计算和对比分析。结果表明:级数解计算的道床沉降与实测数据一致;隧道沉降不大时,轨道结构的轴力对计算结果的影响可以忽略;隧道沉降槽宽度一定时,轨道结构的沉降、脱空范围及内力均随隧道沉降量的增加而增大;在沉降槽宽度小、沉降值较大时,钢轨与道床间以及道床与隧道底板间将产生沉降差及脱空。对隧道底板沉降槽半宽为3m的实例计算结果表明:在扣件失效条件下,隧道底板沉降值达到4mm时钢轨与道床间产生沉降差和脱空;在扣件正常连接条件下,隧道底板沉降值达到12mm时道床与隧道底板间产生沉降差和脱空;道床沉降值达到30mm时钢轨与道床间产生明显的沉降差;道床沉降值达到50mm时支承块与道床间产生脱空。

Based on the equilibrium of infinitesimal segment,a nonlinear governing differential equation of track structure deformation was derived.The vertical settlement of shield tunnel was assumed to follow a Gaussian curve,and Heaviside step function was employed to describe the detachment state between the track and the bottom plate of the tunnel.Then a Fourier series solution was derived to calculate the deformation of track structure.At last,case study and comparison were conducted upon a bearing block track structure.Results show that the computed settlement of the track bed is in good accordance with insitu measured data.The influence of the axial force of the track structure on the calculation results can be ignored as the tunnel settlement is not large.When the width of tunnel settlement trough is fixed,the settlement,cavity scope and internal force of track structure increase with the increase of tunnel settlement.When the width of tunnel settlement trough is small and the settlement value is large,the settlement difference and cavity will occur between the rail and track bed as well as between the track bed and the bottom plate of tunnel.The calculation results of an example,i.e.the settlement trough with the half width 3 mof tunnel bottom plate show that,under the condition of fastener failure,the settlement difference and cavity between the rail and track bed will occur when the settlement of bottom plate reaches4 mm.Under the normal connection of fasteners,the settlement difference and cavity between track bed and bottom plate will occur when the settlement of bottom plate reaches 12 mm.There will be an obvious settlement difference between the rail and track bed when the settlement of track bed reaches 30 mm.There will be a cavity between the supporting block and track bed when the settlement of track bed reaches50 mm.