Identification of support conditions of buried pipes using a vibrating pig

This paper describes a method for monitoring the variation in support condition of pipelines using a vibration technique. The method is useful for detecting poor support of buried pipelines and for detecting spanning and depth of cover in sub-sea lines. Variation in the pipe support condition leads to increased likelihood of pipe damage. Under roadways, poorly supported pipe may be damaged by vehicle loading. At sea, spanned sections of pipe are vulnerable to ocean current loading and also to snagging by stray anchors in shallow waters. A vibrating `pig' has been developed and tested on buried pipelines. Certain features of pipe support, such as voids and hard spots, display characteristic responses to vibration, and these are measured by the vibrating pig. Post-processing of the measured vibration data is used to produce a graphical representation of the pipeline support and certain `feature characteristics' are identified. In field tests on a pipeline with deliberately constructed support faults, features detected by the vibrating pig are in good agreement with the known construction.

Probabilistic fault identification using vibration data and neural networks

Bayesian formulated neural networks are implemented using hybrid Monte Carlo method for probabilistic fault identification in cylindrical shells. Each of the 20 nominally identical cylindrical shells is divided into three substructures. Holes of (12±2) mm in diameter are introduced in each of the substructures and vibration data are measured. Modal properties and the Coordinate Modal Assurance Criterion (COMAC) are utilized to train the two modal-property-neural-networks. These COMAC are calculated by taking the natural-frequency-vector to be an additional mode. Modal energies are calculated by determining the integrals of the real and imaginary components of the frequency response functions over bandwidths of 12% of the natural frequencies. The modal energies and the Coordinate Modal Energy Assurance Criterion (COMEAC) are used to train the two frequency-response-function-neural-networks. The averages of the two sets of trained-networks (COMAC and COMEAC as well as modal properties and modal energies) form two committees of networks. The COMEAC and the COMAC are found to be better identification data than using modal properties and modal energies directly. The committee approach is observed to give lower standard deviations than the individual methods. The main advantage of the Bayesian formulation is that it gives identities of damage and their respective confidence intervals.

Feasibility of damage detection using vibration data in a population of cylinders

The feasibility of vibration data to identify damage in a population of cylindrical shells is assessed. Vibration data from a population of cylinders were measured and modal analysis was employed to obtain natural frequencies and mode shapes. The mode shapes were transformed into the Coordinate Modal Assurance Criterion (COMAC). The natural frequencies and the COMAC before and after damage for a population of structures show that modal analysis is a viable route to damage identification in a population of nominally identical cylinders. Modal energies, which are defined as the integrals of the real and imaginary components of the frequency response functions over various frequency ranges, were extracted and transformed into the Coordinate Modal Energy Assurance Criterion (COMEAC). The COMEAC before and after damage show that using modal energies is a viable approach to damage identification in a population of cylinders.

A three-dimensional tunnel model for calculation of train-induced ground vibration

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. © 2006 Elsevier Ltd. All rights reserved.

Ground vibration generated by trains in underground tunnels

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. © 2006 Elsevier Ltd. All rights reserved.

A computationally efficient software application for calculating vibration from underground railways

The PiP model is a software application with a user-friendly interface for calculating vibration from underground railways. This paper reports about the software with a focus on its latest version and the plans for future developments. The software calculates the Power Spectral Density of vibration due to a moving train on floating-slab track with track irregularity described by typical values of spectra for tracks with good, average and bad conditions. The latest version accounts for a tunnel embedded in a half space by employing a toolbox developed at K.U. Leuven which calculates Green's functions for a multi-layered half-space. © 2009 IOP Publishing Ltd.

The effect of a twin tunnel on the propagation of ground-borne vibration from an underground railway

Accurate predictions of ground-borne vibration levels in the vicinity of an underground railway are greatly sought after in modern urban centres. Yet the complexity involved in simulating the underground environment means that it is necessary to make simplifying assumptions about this system. One such commonly made assumption is to ignore the effects of neighbouring tunnels, despite the fact that many underground railway lines consist of twin-bored tunnels, one for the outbound direction and one for the inbound direction. This paper presents a unique model for two tunnels embedded in a homogeneous, elastic fullspace. Each of these tunnels is subject to both known, dynamic train forces and dynamic cavity forces. The net forces acting on the tunnels are written as the sum of those tractions acting on the invert of a single tunnel, and those tractions that represent the motion induced by the neighbouring tunnel. By apportioning the tractions in this way, the vibration response of a two-tunnel system is written as a linear combination of displacement fields produced by a single-tunnel system. Using Fourier decomposition, forces are partitioned into symmetric and antisymmetric modenumber components to minimise computation times. The significance of the interactions between two tunnels is quantified by calculating the insertion gains, in both the vertical and horizontal directions, that result from the existence of a second tunnel. The insertion-gain results are shown to be localised and highly dependent on frequency, tunnel orientation and tunnel thickness. At some locations, the magnitude of these insertion gains is greater than 20 dB. This demonstrates that a high degree of inaccuracy exists in any surface vibration prediction model that includes only one of the two tunnels. This novel two-tunnel solution represents a significant contribution to the existing body of research into vibration from underground railways, as it shows that the second tunnel has a significant influence on the accuracy of vibration predictions for underground railways. © 2011 Elsevier Ltd. All rights reserved.

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