M.F.M. Hussein

Using the PiP Model for Fast Calculation of Vibration from a Railway Tunnel in a Multi-layered Half-Space

This paper presents a new method for calculating vibration from underground railways buried in a multi-layered half-space. The method assumes that the tunnel’s near-field displacements are controlled by the dynamics of the tunnel and the layer that contains the tunnel, and not by layers further away. Therefore the displacements at the tunnel-soil interface can be calculated using a model of a tunnel embedded in a full space. The Pipe-in-Pipe (PiP) model is used for this purpose, where the tunnel wall and its surrounding ground are modelled as two concentric pipes using elastic continuum theory. The PiP model is computationally efficient on account of uniformity along and around the tunnel. The far-field displacement is calculated by using another computationally efficient model that calculates Green’s functions for a multi-layered half-space using the direct stiffness method. The model is based on the exact solution of Navier’s equations for a horizontally layered half-space in the frequency-wavenumber domain.

Prediction uncertainties and inaccuracies resulting from common assumptions in modelling vibration from underground railways

Underground railways produce significant ground-borne vibration that is reported to disturb people living or working near subways. Designers and engineers use numerical models to predict vibration levels so as to meet the increasingly strict vibration standards. These models commonly include simplifying assumptions to reduce the complexity and cost of the simulation. This paper reviews six commonly disregarded aspects of the underground railway environment and their respective effects on vibration prediction values: a second (twin) tunnel, piled foundations, track with discontinuous slabs, soil inhomogeneity, inclined soil layers, and irregular contact at the tunnel–soil interface. Results suggest that accounting for each of these simplifying assumptions can result in predictions that vary from the simplified cases by at least 5 dB and potentially up to 20 dB. This is a significant level of uncertainty and should be considered when estimating the predictive accuracy of numerical models using simplifying assumptions.

The use of sub-modelling technique to calculate vibration in buildings from underground railways

In this paper, a method is presented for the calculation of the vibration created in buildings by the operation of underground railways. The method is based on the sub-modelling approach which is used to couple a model of a building on a piled foundation to another model that calculates the vibration generated in the soil in underground railway tunnels. The method couples a building on a piled foundation to the soil at discrete points by satisfying equilibrium and compatibility requirements at those points. The method results in efficient numerical calculations. A two-dimensional frame made of beam elements is used to model the building and its piled foundation. The elements are formulated using a dynamic stiffness matrix which accounts for Euler–Bernoulli bending and axial behaviour. Vibrations created by a train moving in an underground tunnel are calculated using the well-known pipe-in-pipe (PiP) model. The model calculates the power spectral density (PSD) of the displacement in the soil. The excitation mechanism is the roughness of the rail and the PSD is calculated for a train moving on a floating-slab track in an underground railway tunnel for a stationary process. The current version of PiP accounts for a tunnel embedded in a half-space. The building frame is coupled in this paper at 90° to the tunnel’s centreline. The main result of this paper illustrates the significant contribution of the building’s dynamics to the displacement wave field received by the building. The example presented in this paper shows a decrease of more than 20 dB in the displacement PSDs at frequencies larger than 10 Hz when accounting for the change in this wave field.

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 Greens functions for a multi-layered half-space.

Influence of Preload and Nonlinearity of Railpads on Vibration of Railway Tracks under Stationary and Moving Harmonic Loads

In railway track dynamics, the stiffness and damping properties of railpads have a significant effect on track vibration, decay rates as well forces transmitted to the track supporting structure. Many studies have shown that railpads exhibit pronounced nonlinear behaviour, with preload and frequency dependent properties. This paper presents a three parameter railpad model, together with its differential equation of motion and the required model parameters obtained from experimental data. A time domain model of a rail discretely supported on these railpads is then formulated using the finite element method. The model is subjected to static and dynamic loading in order to study the effects of preload and frequency on its dynamic behaviour. Results are shown as time histories and frequency spectra for the track displacements and reaction forces for various preload levels. They emphasise the necessity of accounting for nonlinear behaviour based on the large disparities (up to 20 dB) observed between the linear and nonlinear cases for the parameters used in this study.

The effect of end bearings on the dynamic behaviour of floating-slab tracks with discrete slab units

ABSTRACT This article builds on previous work in the literature to investigate the dynamic effect of end bearings between consecutive slab units of floating-slab tracks. The work considers a floating-slab track with discrete units under the action of a harmonic moving load. A special periodic-structure model is developed for this purpose. The model performs calculations in the frequency domain and makes use of the periodicity condition resulting from the use of unit slabs as well as that due to the nature of applied loading. The article demonstrates the influence of vertical stiffness of end bearings and its effect on the dynamic responses of the tracks.

Recent developments in the pipe-in-pipe model for underground-railway vibration predictions

The Pipe-in-Pipe (PiP) model is a fast-running model that calculates vibration levels from an underground railway within a layered halfspace. This model contains many simplifying assumptions, but its fast computation time makes it useful as an early design tool.

A flexural crack model for damage detection in reinforced concrete structures

The use of changes in vibration data for damage detection of reinforced concrete structures faces many challenges that obstruct its transition from a research topic to field applications. Among these is the lack of appropriate damage models that can be deployed in the damage detection methods. In this paper, a model of a simply supported reinforced concrete beam with multiple cracks is developed to examine its use for damage detection and structural health monitoring. The cracks are simulated by a model that accounts for crack formation, propagation and closure. The beam model is studied under different dynamic excitations, including sine sweep and single excitation frequency, for various damage levels. The changes in resonant frequency with increasing loads are examined along with the nonlinear vibration characteristics. The model demonstrates that the resonant frequency reduces by about 10% at the application of 30% of the ultimate load and then drops gradually by about 25% at 70% of the ultimate load. The model also illustrates some nonlinearity in the dynamic response of damaged beams. The appearance of super-harmonics shows that the nonlinearity is higher when the damage level is about 35% and then decreases with increasing damage. The restoring force-displacement relationship predicted the reduction in the overall stiffness of the damaged beam. The model quantitatively predicts the experimental vibration behaviour of damaged RC beams and also shows the damage dependency of nonlinear vibration behaviour.

Re-Anchorage of a Ruptured Tendon in Bonded Post-Tensioned Concrete Beams: Model Validation

Many post-tensioned concrete bridges have been reported to have ruptured tendons due to corrosion [1] and the assessment of their residual structural capacity has to account for the possibility of re-anchorage of failed tendons. This paper presents an experimental programme to validate a numerical model developed by the authors for the re-anchorage of a ruptured tendon in post-tensioned concrete [2]. The experimental programme considered 33 post-tensioned concrete prisms, in which the rupture of tendon was simulated by releasing the tendon at one end. The full field displacement at concrete surface after release was measured using 3D Electronic Speckle Pattern Interferometry (ESPI). A wide range of parameters: tendon diameter, duct material, grout strength, concrete strength and shear reinforcement were investigated to validate the proposed model, which is found to be suitable for use in assessing post-tensioned concrete bridges with damaged tendons.

The dynamic interaction effects of railway tunnels: Crossrail and the Grand Central Recording Studios

In cities around the world, underground railways offer an environmentally friendly solution to society’s increasing demand for mass transport. However, they are often constructed close to sensitive buildings, where the resulting ground-borne noise and vibration can cause disturbance to both the occupants and the equipment. Such a scenario occurred in central London, where the new twin tunnels of Crossrail were bored beneath the Grand Central Recording Studios, causing an immediate concern. As a result, vibration in the studios’ building was monitored throughout the Crossrail construction period. Since Crossrail is yet to operate, the resulting data provide a unique opportunity to investigate the effect of new tunnels, acting as passive buried structures, on the existing vibration environment. This paper presents the results of such an investigation, together with complementary results from a theoretical four-tunnel boundary-element model. The data analysis, presented in the first half of the paper, indicates that the construction of the second Crossrail tunnel has led to an overall reduction in the noise and vibration levels beneath the studios, due to the operation of the nearby Central line trains of London Underground. This is predominantly due to a reduction of approximately 6 dB in the 63 Hz band-limited levels but accompanied by a slight increase, of approximately 2 dB, in the 125 Hz band. Further analysis indicates that any seasonal variations in vibration levels over the measurement period are negligible, adding weight to the conclusion that the observed changes are a causal effect of the tunnel. The second half of the paper presents results from the model, which aims to simulate the dynamic interaction between the Central line tunnels and those of Crossrail. With nominal parameter values, the results demonstrate qualitative similarities with the measurement findings, thereby adding to the growing body of evidence that dynamic interaction between neighbouring tunnels can be significant.