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.
A three-dimensional tunnel model for calculation of train-induced ground vibration
Abstract The frequency range of interest for ground vibration from underground urban railways is approximately 20 to 100 Hz. For typical soils, the wavelengths of ground vibration in this frequency range are of the order of the spacing of train axles, the tunnel diameter and the distance from the tunnel to nearby building foundations. For accurate modelling, the interactions between these entities therefore have to be taken into account. This paper describes an analytical three-dimensional model for the dynamics of a deep underground railway tunnel of circular cross-section. The tunnel is conceptualised as an infinitely long, thin cylindrical shell surrounded by soil of infinite radial extent. The soil is modelled by means of the wave equations for an elastic continuum. The coupled problem is solved in the frequency domain by Fourier decomposition into ring modes circumferentially and a Fourier transform into the wavenumber domain longitudinally. Numerical results for the tunnel and soil responses due to a normal point load applied to the tunnel invert are presented. The tunnel model is suitable for use in combination with track models to calculate the ground vibration due to excitation by running trains and to evaluate different track configurations.
Physics-based Model and Neural Network Model for Monitoring Starter Degradation of APU
An electric starter provides the initial power to run the Auxiliary Power Unit (APU) during the startup process. With the starter degradation, its output power declines, which affects the APU starting performance, and eventually leads to the starting failure. Previous works have attempted to estimate the starter degrading trend, however a clear symptom for the starter degradation is not provided, which can be instrumental for the preventive maintenance. This paper develops a physics-based transient model to assess the starter degradation using the gas-path measurements of the APU. To overcome shortcomings for the lack of component characteristics, a generic modeling approach is adopted. For the comparative study, a back-propagation, feedforward neural network model is structured, trained and tested. Both models are implemented in the nominal and degraded conditions, and their capabilities as monitoring tools for the starter degradation are verified. The physics-based approach provides more accurate results for the cases with degraded starters, whereas the neural network model shows superior results with the starters in healthy condition.