ICSV 14 Cairns • Australia 9-12 July , 2007 THE PiP MODEL , A SOFTWARE APPLICATION FOR CALCULATING VIBRATION FROM UNDERGROND RAILWAYS
Significant vibration in buildings near underground tunnels is attributed to moving trains. Vibration is generated due to irregularities of wheels and tracks and propagates to nearby buildings causing annoyance to people and malfunctioning of sensitive equipment. Modelling of vibration from underground railways is gaining more interest on account of the need for quick tools to design vibration countermeasures for both existing and newly constructed tunnels. This paper describes a software application for calculating vibration from underground railways, called the Pipe-in-Pipe (PiP) model. The software has a user-friendly interface and is available on the internet as a freeware for engineers in charge of designing of vibration countermeasures in railway tunnels. The PiP model accounts for a train running on a floatingslab track in a tunnel embedded in the ground. The software calculates the Power Spectral Density (PSD) of the vertical displacement at any selected point in the soil for a roughness excitation of a unit value (i.e. white noise). It also calculates the Insertion Gain (IG) which is the difference in decibel between the displacement PSD after and before changing parameters of the track, tunnel or soil. The latest version of the software plots the displacement contours around the tunnel and accounts for a bedrock layer below the tunnel using the mirror-image method. The software is computationally efficient as it calculates results accurately and quickly on a personal computer unlike other available models of vibration from underground railways which take much longer time and require huge computational resources. A full description of the current version of the software is given in this paper along with ongoing developments that will appear in future versions.
An insertion loss model for evaluating the performance of floating-slab track for underground railway tunnels
This paper discusses a comprehensive three-dimensional model of a deep underground railway tunnel. The model consists of Euler-Bernoulli beams to account for the rails and the slab track. These are coupled to an infinite continuum (pipe-inpipe) model, which accounts for the tunnel wall and the cylindrical cavity within an infinite soil domain. The track slab is coupled to the tunnel wall using slab-bearings along several lines. The coupling is performed in the wave number domain and results for soil displacements and velocities are obtained by transformation to the space domain. Random vibration theory is used to predict vibration levels in the soil due to an empirical rail roughness input. The model shows the importance of soft slab-bearings in decreasing the vibration levels by confining the energy in the slab. It also shows the effect of distribution of slab-bearings on the vibration isolation performance.
Noise and vibration from underground railway lines: Proposals for a prediction procedure
Abstract A procedure for predicting structure-borne noise and vibration from underground railway lines is discussed. Using a chain of transmission losses within the source-path-reciever system, one is enabled to make variable applications to numerous planning situations. The method is based on analytical techniques, laboratory tests and measurements in situ. The results show that an impedance analogy model could be used in the interpretation of measurements and for predicting the insertion loss of resilient track components.