Tunnel-soil-pile interaction in the prediction of vibration from underground railways: validation of the sub-models

ABSTRACT: This paper proposes a method for calculating the vibration levels from an underground tunnel, adjacent to a piled-foundation, embedded in a homogeneous half-space on the basis of strong coupling. The method relies on superposing the vibration field generated by the tunnel with that generated by the piled-foundation. The soil in this paper is modelled utilising the boundary element method, while the tunnel is modelled using thin-shell theory and the piled-foundation is modelled by adopting the elastic bar and Euler beam theories. Only the results of the sub-models (tunnel and piled-foundation) are presented herein and compared with previous work in the literature. The current tunnel model is contrasted to the well-known PiP model whereas the piled-foundation model is validated against a previous boundary element model. The comparisons reveal good agreement between the results of the current model and those of the previous models. The robustness of the current model has been highlighted by examining the responses of the tunnel at points on the free surface when it is subject to a point harmonic load at its invert. The responses of the piled-foundation to horizontal and vertical point loads on the pile-head are also investigated, in addition to the displacement field on the free surface due to a vertical point load. KEY WORDS: Ground-borne vibration; Boundary element method; Soil-structure interaction, Tunnel; Piled-foundation 1 INTRODUCTION Underground railway noise and vibration can be a major source of disturbance to occupants in close proximity. Vibration is generated at the wheel-rail interface, due to wheels and track irregularities, and propagates through soil to nearby buildings. Whilst these vibrations may not induce structural damage, their effects can impair human comfort and activity leading to long-term implications [1, 2] or can cause malfunctioning of sensitive equipment. The problem of ground-borne vibration has caught the attention of researchers during the past decades. To better understand the transmission of vibration from underground railways, different numerical simulation techniques have been exploited. These techniques are essentially aimed at identifying ways to tackle unacceptable levels of vibration from existing as well as future railway lines. In the literature, there exist a number of models to calculate vibration from railways that are based on space discretisation and superposition of elastic waves. Models based on space discretisation employ boundary element (BE) and finite element (FE) methods to simulate the dynamic soil-tunnel interaction, where the FE method is used to model the tunnel’s wall, and the surrounding soil is simulated by the BE method. In the last decade, these methods were often coupled together to provide more rigorous, efficient computation. This was achieved by assuming homogeneity in the track direction allowing for the implementation of a two-and-a-half-dimensional (2.5D) or wavenumber FE-BE model [3], or by incorporating periodicity of the tunnel and soil with the Floquet transform [4, 5]. The periodicity approach was also utilised within the context of a BE method to model soil-piled foundations dynamic interaction [6]. Models based on superposition of elastic waves, on the other hand, are deemed to provide computationally efficient tools. A model that is particularly popular is the pipe-in-pipe (PiP) model, which is a semi-analytical three-dimensional (3D) model accounting for the dynamic soil-tunnel interaction [7, 8]. The main model accounts for a tunnel embedded in a full-space by using the elastic wave equations for two concentric pipes with infinite length. The PiP model has been also augmented to consider a tunnel embedded in a half-space or a multi-layered half-space [9]. Despite the research effort devoted to the topic of underground railway vibration, simplifying assumptions remain necessary in all numerical models due primarily to computational limitations. A common simplifying assumption is to neglect the interaction between neighbouring structures. It must be mentioned, however, that there exist in the literature a few studies investigating the dynamic interaction between neighbouring tunnels [10, 11], and between an underground tunnel and strip-foundations [12] or piled-foundations [13, 14]. In the studies of tunnel/piled-foundations interaction [13, 14], a sub-domain modelling approach was adopted in which the displacements and tractions generated by the tunnel’s vibration were used as input variables for the piled-foundations. Put differently, the presence of piles in the soil was neglected when calculating vibration field due to the movement of a train in a tunnel. This approach results in a weak coupling, and it thereby does not predict accurately the behaviour of the coupled system. This paper reports on a novel technique for modelling the dynamic interaction of a fully coupled underground tunnel and a piled-foundation embedded in a homogeneous half-space. The surrounding soil is modelled using the BE method adopting half-space Green’s functions, whereas the thin-shell