Analytical Solution for Pipeline Settlement Law Using Shield Tunnel Excavation Underneath Based on Vlasov–Timoshenko Model Considering Lateral Soil Action

Abstract

This study used a two-stage method to derive an analytical solution for assessing the vertical displacement of an existing pipeline caused by the undercrossing construction of a shield tunnel. The aim was to evaluate the impact of shield excavation on adjacent pipelines. A Timoshenko beam lying on a Vlasov foundation was adopted to model the existing pipeline subjected to soil disturbance induced by underneath tunneling. The model considered the shear stiffness of the pipeline and the vertical nonuniformity of the foundation parameters. The lateral soil action was considered in the force analysis to develop a prediction model for pipeline settlement. The proposed analytical solution was tested against project examples and field measurements collected from a construction site. The prediction results of our new model, the Vlasov–Timoshenko beam model, exhibited greater consistency with field monitoring data than those of the existing models, such as the Euler–Bernoulli beam model. The model with lateral soil action exhibited higher prediction accuracy than that without lateral soil action. Furthermore, parametric analyses evaluated the influences of different factors; for instance, when the pipe and tunnel angles decrease and pipe shear stiffness reduces, the tunnel radius increases, the pipe settlement increases, and the growth rate gradually increases. When the tunnel depth increases, the pipe settlement decreases. For the same calculation example, the maximum value of the pipe settlement and the range of the settlement trough increase after considering the lateral soil action on the pipeline. In a further parametric comparison analysis, when Poisson’s ratio increases, the settlement deformation of the pipeline decreases, and when the volume loss and elasticity modulus of the soil increase, the maximum settlement value of the pipeline increases and the growth rate gradually decreases. Hence, the reasonableness of the proposed method for calculating the settlement of adjacent pipelines by considering both the shear stiffness of the pipeline and the lateral soil action is demonstrated.