Mathematical Modelling for Interaction Between Soft Ground and Small Curvature Shield Tunneling Considering Viscoelastic Characteristics Influences

The current analytical solutions for predicting the ground settlements induced by small curvature tunneling in soft ground are generally conducted on the assumption of linear elastic foundation and provide little attention on the soil rheology. This paper introduces a mathematical model to estimate the small curvature tunneling induced adjacent ground settlement considering the soil viscoelasticity. By introducing the Boltzmann viscoelastic ground model under the Laplace transform, the time domain parameters converted from Poisson's ratio and shear modulus are derived to further obtain the viscoelastic ground loss solution and the Mindlin solution. Then, the proposed viscoelastic solutions are employed for the ground settlement caused by the overexcavation and imbalanced loads for the small curvature tunnel, which accounts for the soil rheology influence. The accuracy of the mathematical model is then verified by comparisons with in-situ observed data and 3D numerical simulation results, as well as good agreement is obtained. Finally, the parametric analyses are performed to estimate the influence for transverse and longitudinal surface settlements, including tunnel curvature radius, shield cutterhead face radius, over-excavation value, creep time and shear modulus ratio of viscoelastic ground.