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

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.