基于壳柱模型的饱和地基盾构隧道车致动应力计算理论研究

The study on the dynamic stress in ground caused by moving train is the basis of train-induced cumulative settlement calculation. However，there is no ideal theory for the calculation of dynamic stress in saturated foundation of shield tunnel yet. In this study, thin-walled cylindrical shell is used to simulate shield tunnel lining and saturated cylindrical soil is used to simulate saturated ground respectively. Then the vibration governing equations of shield tunnel and wave equations of porous saturated ground in cylindrical coordinate system are established. Through the coupling of tunnel and ground subsystems, a model for calculation of dynamic stress of saturated soil induced by train running in shield tunnel is eventually established, and the solution of train-induced dynamic stress of saturated ground is finally obtained. On this basis, further calculation and analysis of dynamic stress and its change laws with time and space will be done. Meanwhile, a vibration response model test of the subway tunnel is performed to test the dynamic stress of the ground caused by moving train by means of an annular vibration simulation test bench with a scale of 1:10, thus the distribution characteristics and the change laws of the dynamic stress can be revealed, and the reliability of the calculation results of the shell cylinder model for dynamic stress of saturated foundation of shield tunnel can be verified as well. This research results can be a theoretical support on train-induced cumulative settlement calculation for saturated soil under shield tunnel.

列车运行引起的地基动应力的研究是进行车载累积沉降计算的基础，然而，对于饱和地基盾构隧道车致动应力的计算，目前尚无理想的理论算法。本研究分别采用薄壁圆柱壳模拟盾构隧道衬砌和多孔饱和圆柱形土体模拟地基，建立盾构隧道振动控制方程和柱坐标系下多孔饱和地基的波动方程，通过将隧道与地基子系统进行耦合组装求解，最终建立饱和地基盾构隧道车致动应力壳柱法计算模型，进而获得饱和地基盾构隧道车致动应力解，在此基础上，进一步计算和分析饱和地基盾构隧道车致动应力及其时空变化规律。同时，借助1:10轨道交通环形振动模拟实验台，开展地铁隧道行车振动响应模型试验，测试列车运行引起的地基的动应力，进而揭示其分布特征与变化规律，并验证饱和地基圆形隧道车致动应力壳柱模型计算结果的可靠性。研究成果可为饱和黏性土地基盾构隧道的车载累积沉降计算及相关研究提供理论支撑。

列车运行引起的地基动应力的研究是进行车载累积沉降计算的基础，然而，对于饱和地基盾构隧道车致动应力的计算，目前尚无理想的理论算法。本项目从频域和时域两个角度出发，构建了三类隧道-土体系统车致振动响应分析方法，包括：（1）将土体视为饱和多孔介质，隧道衬砌和壁后注浆层视为双层圆柱壳，轨道板和钢轨视为Euler梁，地铁列车荷载视为一系列移动的轮载，建立了车辆-轨道-隧道土体动力响应壳柱法半解析模型。（2）推导了饱和半空间内和饱和分层半空间内作用单位集中简谐荷载和单位简谐流相点源的2.5维动力Green函数，建立了饱和半空间土-隧道系统车致动力响应的2.5维有限元-边界元耦合模型。（3）使用动态子结构法和半解析法，考虑轮轨非线性接触特性，在时域内建立了车辆-轨道-隧道-土体空间耦合分析模型。基于上述模型，分析了地铁隧道车致动应力的响应特征。.重要结论包括：.（1）定幅值（荷载频率f =0Hz）移动车辆荷载作用下，土体的响应是拟静态的，并未产生明显的波动现象。双线运行条件下，土体的动力响应较单线运行下的大，叠加效应明显，且土体位移和孔隙水压力的叠加效应比土体动应力的叠加效应更为明显。此外，土体的车致动力响应具有明显的转向架和车体特性，而轮对特性不明显。.（2）地铁车致地基附加正应力中，隧底土体竖向正应力τrr幅值最大，τθθ和τzz幅值接近，约为0.5τrr。饱和土体正应力及孔压幅值随着深度增大而减小，正应力中τθθ沿深度衰减最快，τrr最慢，剪应力τrz幅值随着深度增加先增大后减小，至注浆层底部以下9 m处，地基动应力衰减为最大值的20%左右。.（3）弹性土体与饱和弹性土体的动应力区别明显，如果忽略土中孔隙水的影响和荷载的叠加作用，会低估移动荷载作用下土体的附加动应力水平。因此，在分析车致动应力时需要考虑弹性地基和饱和地基的区别，车辆荷载和单个荷载的区别。地基土体的渗透性越差，隧底车致正应力τrr和孔压Pf幅值越大，剪应力τrz越小。