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Effective measures are needed to strictly control soil displacement caused during the process of shield construction excavation for urban subway tunnels. When calculating the displacement of soil caused by loading or unloading, many previous analytical studies have assumed that the soil was a linear elastic body and ignored the viscosity of the soil. In this study, the Boltzmann viscoelastic model and the Mindlin basic solution were combined to consider the effects of the additional support pressures, the shield shell frictions, the grouting pressures, and the ground loss, and a three-dimensional viscoelastic solution for soil displacement caused by shield tunneling was derived. According to the calculation results of an example, the analytical solution was able to consider the asynchronous construction of the left and right tunnels and the mutual influence of the double shield tunnel. The rationality of the approach proposed in this study was verified by comparing the theoretical solution with the measured settlement values. In addition, the influence of differences in the viscoelastic parameters (the viscosity coefficient, the shear modulus of the elastic element, and the shear modulus of the viscous element) and the geometric parameters (the distance from the excavation surface, the calculated depth, and tunnel spacing) on soil displacement is discussed. The calculation method in this study provides a theoretical basis for predicting the three-dimensional soil deformation caused by shield tunneling, especially in soft clays.

Analytical Study of Soil Displacement Induced by Twin Shield Tunneling in Semi-Infinite Viscoelastic Ground