Mathematical modelling for ground consolidation settlements induced by lining leakage of shield tunnel under train loading in viscoelastic porous soils

Abstract

The long-term leakage of lining under train loading has a significant impact on the consolidation settlements around shield tunnel and the rheological behaviour of viscoelastic porous soils will further exacerbate this consequence, which adversely affect the adjacent geo-environments and the subsidence of existing structures. At present, the assumptions of tunnel impermeable lining and liner-elastic clays are usually received to conduct on the consolidation settlements. Moreover, little attention is paid on the coupled influence of lining leakage and train loading. For better engineering serviceability in viscous porous clays, this paper presents a closed-form analytical solution for predicting the ground consolidation settlements under train loading considering the lining leakage and the rheological medium, with the scope of Terzaghi-Rendulic theory. By introducing semi-permeable boundary condition, the triangular cyclic loading is equivalently applied to the tunnel lining and the Boltzmann viscoelastic model is employed to simulate the rheological characteristic of the actual geology. The dissipation solution of excess pore water pressure and the ground responses in viscoelastic porous clays are derived using the conformal mapping. In addition, the accuracy of the analytical solutions is verified by comparisons with in-situ observed data and existing numerical simulation results from the engineering cases, showing reasonable alignments. The differences between the Kelvin and Boltzmann model are further analyzed to estimate the influences of rheological geology. Furthermore, a detailed sensitivity analysis is also implemented to investigate the performance of concerned parameters on the surface consolidation settlements, including the lining-soil permeability, the parameters of Boltzmann model (elasticity module Eh in the Hoek body, elasticity module Ek and viscosity coefficient ηk in the Kelvin body), and the train loading. The interesting point and ingenious approach in this study are tracing the corresponding analytical solutions on the consideration for not only the coupled influence of lining leakage and train loading but also the rheological behaviour in the viscoelastic porous soils.