Pipe in Pipe PiP

PiP software is a powerful computational tool for calculating vibration from underground railways and for assessing the performance of vibration countermeasures. The software has a user-friendly interface and it uses the state-of-the-art techniques to perform quick calculations for the problem. The software employs a model of a slab track coupled to a circular tunnel embedded in the ground. The software calculates the Power Spectral Density (PSD) of the vertical displacement at any selected point in the soil. Excitation is assumed to be due to an infinitely-long train moving on a slab-track supported at the tunnel bed. The PSD is calculated for a roughness excitation of a unit value (i.e. "white noise"). The software also calculates the Insertion Gain (IG) which is the ratio between the PSD displacement after and before changing parameters of the track, tunnel or soil. Version 4 of the software accounts for important developments of the numerical model. The tunnel wall is modelled as a thick shell (using the elastic continuum theory) rather than a thin shell. More importantly, the numerical model accounts now for a tunnel embedded in a half space rather than a full space as done in the previous versions. The software can now be used to calculate vibration due to a number of typical PSD roughnesses for rails in good, average and bad conditions.

The effects of a second 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 in modern urban centers. Yet the complexity involved in simulating the underground environment means that it is necessary to make simplifying assumptions about this environment. One such commonly-made assumption is to model the railway as a single tunnel, despite many underground railway lines consisting of twin-bored tunnels. A unique model for two tunnels embedded in a homogeneous, elastic full space is developed. The vibration response of this two-tunnel system is calculated using the superposition of two displacement fields: one resulting from the forces acting on the invert of a single tunnel, and the other resulting from the interaction between the tunnels. By partitioning of the stresses into symmetric and anti-symmetric mode number components using Fourier decomposition, these two displacement fields can by calculated with minimal computational requirements. The significance of the interactions between twin-tunnels is quantified by calculating the insertion gains that result from the existence of a second tunnel. The insertion-gain results are shown to be localized and highly dependent on frequency, tunnel orientation and tunnel thickness. At some locations, the magnitude of these insertion gains is greater than 20dB. This demonstrates that a high degree of inaccuracy exists in any surface vibration-prediction model that includes only one of the two tunnels. © 2012 Springer.

Monitoring offshore pipelines using forced transverse vibration: Data analysis

Vibration methods are used to identify faults, such as spanning and loss of cover, in long off-shore pipelines. A pipeline `pig', propelled by fluid flow, generates transverse vibration in the pipeline and the measured vibration amplitude reflects the nature of the support condition. Large quantities of vibration data are collected and analyzed by Fourier and wavelet methods.