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.
Ground vibration generated by trains in underground tunnels
Abstract A popular method used to reduce vibration transmitted from underground railways into nearby buildings is floating-slab track, whereby a concrete slab supporting the two rails is mounted on rubber bearings or steel springs to isolate it from the tunnel invert. This paper adds a track model to a previously developed three-dimensional tunnel model in order to assess the effectiveness of floating-slab track. A slab beam coupled to the tunnel in the wavenumber domain, with the slab bearings represented by an elastic layer, is examined first. A second beam representing the two rails together is then coupled to the slab, and axle masses representing a train are added to the rail beam. Power-spectral densities and RMS levels of soil vibration due to random roughness-displacement excitation between the masses and the rail beam are calculated. Analytical techniques are used to minimise the computational requirements of the model. The results demonstrate the inadequacy of simple mass–spring and Winkler-beam models with rigid foundations for the assessment of the vibration-isolation performance of railway track. They suggest that the achievable insertion loss is modest and that floating the track slab may in fact cause increased transmission of vibration under certain conditions.
Control of ground-borne noise and vibration
Abstract Ground-borne noise and vibration created by train operations is one of the major environmental problems faced by rail transit systems. In the past 10–20 years there have been a number of developments in the control and prediction of ground-borne noise and vibration although it is evident that further research is needed. In this paper the focus is on two methods of controlling the vibration radiated by the transit structure. First is the use of floating slab trackbeds, a method that has proven to be very effective at reducing vibration at frequencies above the resonance frequency of the floating slab system. Second is to modify the design of transit car bogies such that the wheel/rail forces are reduced. Although this method is still in the exploratory phase it has been shown that proper design of the bogie suspension can significantly reduce the levels of ground-borne noise and vibration.