The dynamic response of a Hyperloop tube embedded in soft soils

Abstract

The hyperloop system is a new transportation mode, which consists a magnetic levitating capsule-like hyperloop pod and a vacuum tube. Due to small air hindrance, the hyperloop pod is conceived to have a maximum speed of 333 m/s. If such a hyperloop system is to be built underground in soft soils, the hyperloop speed can easily reach the wave propagation speeds in the soil. Strong wave radiation is expected when the hyperloop is travelling at wave propagation speeds, which are called the critical speeds.

The first objective is to analyse the dynamic influence from the hyperloop. A linear elastic half-space with an infinitely long concrete tunnel buried at a certain depth has been modeled. The excitation of the system is a hyperloop modeled as a moving constant load acting at the tunnel invert. In this thesis, a so-called indirect boundary element method (BEM) is applied. Indirect boundary integrals are formed which rely on the fundamental solutions for the interior medium, the two-and-a-half dimensional Green's functions. These 2.5D Green's functions are essentially the steady state solutions of the half-space subjected to a spatially varying line load. The space is assumed to be infinitely long and invariant in the direction parallel to the axis of the tunnel.

Before implementing the BEM model, two improvements have been made to the 2.5D Green's functions: a better convergence of the Green's function surface-related terms and a better satisfaction of stress-free boundary conditions at the free surface. The accuracy and correctness of the boundary element model using the improved Green's functions have been verified by intensive case studies. Firstly, the scattering of 3D harmonic seismic P waves by a cavity and a tunnel in a linear elastic half-space is analysed. Results are validated by comparing to those from literature. Secondly, the BEM model is employed for the moving load problem. The embedded concrete tunnel is modeled using the Donnell's theory for thin shells. A coupled form of the indirect boundary integrals is formulated. Using the same model parameters, the results obtained by the BEM are in good agreements with those from literature. Moreover, a parametric study has been conducted to study the effect of moving load velocity, tunnel depth and thickness of concrete lining on the dynamic response.

As a second objective of the current thesis work, the BEM model is compared with a finite element method (FEM) based model, developed by Movares B.V. The models are compared in both accuracy and computational efficiency. In the FEM model, the moving load is considered as a series of consecutive short pulses. The contributions from all the pulses are synthesized using a convolution. Furthermore, since the space is invariant in the direction parallel to the tunnel axis, it is possible to apply just one stationary impulse load in the finite element model. Using this method, a constant moving load and a moving load with acceleration are modeled. The FEM results are found to have close agreements with those by the BEM. Besides the Rayleigh wave speed in the soil, a second critical velocity which is related to the wave propagation in the tunnel is found. Furthermore, the case where a hyperloop runs constantly at the Rayleigh wave speed is more crucial than the case where the hyperloop accelerates and passes the Rayleigh wave speed.