Analytical solution for vibrations of a curved tunnel on viscoelastic foundation excited by arbitrary dynamic loads. (February 2022) - Yu, Haitao; Li, Xinxi; Li, Pan
Graphical abstract: Highlights: Solution for curved tunnel on viscoelastic foundation to arbitrary loads is given. Both curved and straight tunnel segments are considered in the dynamic problem. The modal superposition method is employed to decouple governing equations. The radius of curvature has significant effect on dynamic response of curve tunnel. Abstract: The paper proposes a new analytical solution for the dynamic response of a curved tunnel resting on a viscoelastic foundation subjected to dynamic loads in arbitrary forms. For the derivation, the governing differential equations and boundary conditions of the problem are established based on the Hamilton principle and the dynamic equilibrium theory. The modal superposition method is employed to obtain the explicit formulations of tunnel response, including deflection, velocity, acceleration, bending moment and shear force. The proposed solution is verified by providing comparisons between its results and those from the Finite Element program ABAQUS. Further parametric analysis explore the influence of radius of curvature and soil-structure relative stiffness ratio on the dynamic response of the tunnel. The proposed solution can be used by practitioners for the design of curved tunnels or pipelines.