基于改进壳-柱模型的盾构隧道饱和地基动应力解

Solution for Dynamic Stress of Saturated Soil Surrounding Shield Tunnel Based on Modified Shellcylinder Model

摘要:

针对现有壳柱模型无法考虑盾构隧道壁后注浆层的问题，分别采用无限长的双层圆柱壳模拟盾构隧道衬砌和壁后注浆层，中空圆土柱模拟饱和地基，基于Flügge圆柱壳理论和Biot波动理论，结合边界条件，求解隧道内作用固定简谐荷载时饱和地基中的动应力，并分析其分布规律及注浆层对土体动应力的影响.结果表明：隧道注浆层底部土体径向正应力τrr和孔压Pf幅值随着与荷载的轴向距离增大而减小，剪应力τrz随距离增加先增大后减小，至3D(隧道直径)时地基动应力接近于0；土体的渗透性越差，径向正应力和孔压幅值越大，但当土体渗透系数k小于10-5 m?s-1时，渗透系数的进一步减小对地基动应力幅值的影响不大；隧道壁后注浆层能减小土体径向正应力和孔压(约5%~8%)；注浆层下方同一点土体径向正应力和孔压幅值均随着注浆层厚度增加而线性减小；而注浆层的弹性模量在一定范围内(50~650 MPa)变化时对其几乎无影响.

Abstract:

To investigate the influence of grouting layer of shield tunnel on dynamic stresses of saturated soil under a harmonic loading, a modified shellcylinder model is established. The lining and grouting layer of the shield tunnel are conceptualised as a double cylindrical shell and the saturated soil is conceptualised as a hollow cylinder with infinite radial extent. Based on the Flügge’s shell theory and Biot’s wave equations, the dynamic stresses of the soil induced by a stationary harmonic point load in the tunnel are analyzed. The results show that: The amplitude of radial normal stress τrr and porepressure Pf of the soil beneath the grouting layer decreases with the increase of the longitudinal distance measured from the load point, and the amplitude of shear stress τrz of the soil increase firstly and then decrease with the increase of the longitudinal distance measured from the load point, which attenuate to zero as the longitudinal distance is approximately 3D (D is the diameter of the tunnel). A worse permeability of the soil leads to a greater amplitude of radial normal stress and porepressure. However, when the soil permeability coefficient k is approximately smaller than 10-5 m?s-1, the effect of the soil permeability on the amplitude of dynamic stresses is limited. The grouting layer can reduce the radial normal stress and porepressure of the surrounding soil (approximately 5%~8%); the magnitude of radial normal stress and porepressure of soil beneath the grouting layer decrease linearly with the increases of the thickness of grouting layer. However, the changes of the Young’s modulus of the grouting layer within a certain range of 50~650 MPa almost have no effect on the dynamic stresses of the saturated soil.