Using the PiP model for fast calculation of vibration from a railway tunnel in a multi-layered half-space

Abstract

This paper presents a new method for calculating vibration from underground railways buried in a multi-layered half-space. The method assumes that the tunnel's near-field displacements are controlled by the dynamics of the tunnel and the layer that contains the tunnel, and not by layers further away. Therefore the displacements at the tunnel-soil interface can be calculated using a model of a tunnel embedded in a full space. The Pipe-in-Pipe (PiP) model is used for this purpose, where the tunnel wall and its surrounding ground are modelled as two concentric pipes using elastic continuum theory. The PiP model is computationally efficient on account of uniformity along and around the tunnel. The far-field displacement is calculated by using another computationally efficient model that calculates Green's functions for a multi-layered half-space using the direct stiffness method. The model is based on the exact solution of Navier's equations for a horizontally layered half-space in the frequency-wavenumber domain. The results and computation time of the new method are compared with those of an alternative coupled Finite-Element-Boundary-Element (FE-BE) method that accounts for a tunnel in a multi-layered half-space. It is shown that the results of the two methods are in a good agreement for typical parameter values of a tunnel. The new method is computationally more efficient, i.e. requires significantly less running-time on a personal computer with much less use of memory. © 2008 Springer-Verlag Berlin Heidelberg.