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Within the SILVARSTAR project, a user-friendly frequency-based hybrid prediction tool is developed to assess the environmental impact of railway induced vibration. This will be implemented in the existing noise mapping software IMMI. The vibration level in a building in each frequency band is expressed as the product of source, propagation and receiver terms. A hybrid approach is used that combines experimental data with numerical predictions, providing increased flexibility and applicability. The train and track properties can be selected from a database or as numerical values. The user can select soil impedance and transfer functions from a database, pre-computed for a wide range of parameters with the MOTIV and TRAFFIC models. An experimental database of force densities, transfer functions, free field vibration and input parameters is also integrated into the new tool. The building response is estimated by means of empirical correction factors. Assumptions within the modelling approach can influence the prediction accuracy and the present paper aims to quantify these. We focus on the influence of train speed and soil properties on the compliance of the track-soil system, the dynamic axle loads, and the free field response, as well as on the load transfer between track and soil.

To improve the accuracy of railway induced ground vibration predictions, the influence of surrounding buildings should be considered. For this reason, a fast semi-analytical model is developed to investigate the vibration of the ground and the influence of a nearby building. The model contains two sub models: a finite element model which can simulate the building, and a semi-analytical model which can simulate the infinite free-field ground. The dynamic stiffness matrix method is used to simulate the ground as a homogeneous or layered half-space. The ground model works in the frequency-wavenumber domain and is based on the Green's functions developed for a half-space. Focusing on a building with a piled foundation, the coupling forces due to soil-structure interaction at coupled pile nodes are calculated assuming that the soil and pile displacements are identical. The results from the proposed model show that the vertical modes of the building, especially those that involve the vertical movement of the floors, can significantly influence the vibration of the surrounding ground. The findings suggest that when predicting the ground surface response induced by the railway, the surrounding buildings and their vertical modes should be included in the calculations.

In previous in-situ measurements of metro trains it has been found that the velocity level on the track or tunnel wall may vary significantly between different train passages, even though the measuring section, the type of trains and the track and tunnel conditions are identical. An investigation is carried out into the sources of this variability, using a 3D train-track numerical model. This is built using the software SIMPACK and ABAQUS, and is connected through one-way coupling to a finite element model of the tunnel and soil. These models are used to study the influence of various train parameters, including the wheel and rail unevenness, train speed and degree of train loading. For comparison, in-situ measurements were made of the dynamic response of the rail and tunnel wall. The rail roughness at the site as well as the wheel unevenness of all 48 wheels for one train were measured. The results from the model indicate that the wheel unevenness affects the rail velocity level in the frequency region between 25 and 250 Hz and tunnel wall vibration above 5 Hz. The rail velocity level can vary by up to 20 dB due to wheel unevenness, with the largest variations occurring in the frequency bands 50–63 Hz. Variations in passenger loading affect the train-induced vibration by up to 4.5 dB, mainly in the low frequency region. When the train speed varies within a range of ±20% relative to the nominal speed 60 km/h, the frequencies of the peaks are shifted and the level in some frequency bands can change by as much as 10 dB. However, the largest influence is that of the wheel unevenness. It is concluded that the variation in these parameters, especially the wheel and rail unevenness, should be considered to achieve reliable predictions of train-induced vibration.

The environmental impacts of noise and vibration are becoming increasingly important in the assessment of new and upgraded railway routes. Vibration from railways propagates through the ground to nearby buildings where it may cause annoyance as feelable vibration or as re-radiated noise. To tackle the adverse effects of ground-borne noise a range of possible interventions are available, including softer rail pads, under-sleeper pads and under-ballast mats. The installation costs of such interventions are generally higher for the higher-performing track types. Additionally, there are potential effects on track maintenance costs which may be positive or negative, for example by reducing sleeper damage or increasing the need for ballast tamping. This study presents a socio-economic analysis of the effects of several interventions to reduce ground-borne noise. By selecting a whole route, the installation and whole-life costs are assessed using Network Rail’s Vehicle-Track Interaction Strategic Model (VTISM) and these are offset against benefits in terms of reduced social costs. Ground-borne noise is predicted at various distances from the alignment using the Modelling of Train Induced Vibration (MOTIV) model and the effect of track interventions is determined as insertion loss spectra. The re-radiated noise within a typical domestic building is then estimated using generic building transfer functions. Geographic Information System tools are used to estimate the population affected by ground-borne noise and their expected level of exposure. The methodology is illustrated using a case study route between Brighton and Portsmouth in the South of England.

There is a great need to develop rail networks over long distances and within cities as more sustainable transport options. However, noise and vibration are seen as a negative environmental consequ...

Railway crossings are an important source of localized ground vibration. Models are required for identifying ways to tackle unacceptable levels of vibration from existing as well as future railway lines. Yet, the use of a prediction model that directly allows for the non-Hertzian wheel-rail contact dynamics and also includes three dimensional calculations of the ground response would be computationally expensive. In order to reduce the computational cost without affecting the accuracy of the predictions, a hybrid approach is proposed for the prediction of ground-borne vibration due to impacts at railway crossings. The approach combines the simulation of the vertical wheel-rail contact force in the time domain and the prediction of ground vibration levels in the far field using a linear wavenumber-frequency-domain approach. The proposed hybrid approach is used to investigate the influence of different vehicle speeds, crossing designs and wheel profiles on predicted ground vibration levels in the free field.

The dynamic properties of the rail fastening system affect the damping of the rail and the degree of coupling between the rail and the foundation. It is well known that the rate of decay of vibration along the rail is closely linked to the noise performance of the track. For this reason, the track decay rate (TDR) is used as an important measurable input quantity for models that predict railway rolling noise. This paper investigates whether the TDR can be estimated correctly from laboratory measured dynamic properties of rail fastening systems. The system studied in this work is a commercial two-stage baseplate system that is mounted on a slab track fitted with 60E1 rail. Four different types of rail pads were fitted during the track decay rates measurements. The TWINS model was used to predict the rolling noise using the measured and calculated track decay. The comparison has shown a good agreement between the measured and predicted TDR.

A number of different track forms are studied from one tramway system including tracks in ballast, on slab, and embedded rail in grass. Measurements have been carried out of rail roughness, wheel roughness and track decay rate, which are used as input data for the noise prediction model TWINS. The rail vibration and exterior noise of trams in operation have also been measured for comparison with the prediction model. The model is used to identify the relative contributions of noise radiated by the track and the wheels. The differences between different track forms are determined and the reasons for them are identified.

Tramway noise can be significant even though the speeds are relatively low. The influence of track design on the rolling noise is studied through a systematic comparison of different tracks on a single network. These include a slab track with embedded sleeper blocks, a ballasted track and a track with embedded rails. Measurements have been taken of rail vibration and noise during tram passages at approximately 55 km/h; the rail and wheel roughness have also been measured. Comparisons are made in terms of track decay rate, rail vibration and pass-by noise. After normalising to the same roughness, the slab track is found to be the noisiest and the ballasted track the quietest. Theoretical models of the various track forms are also presented to give insight into the differences in acoustic performance. The models allow the relative contributions of the track and wheels to the pass-by noise to be identified. In addition the effect of rail dampers added to the slab track is assessed. These attenuate the noise at higher frequencies due to the increase in decay rate, but an increase in radiation is noted at 500 Hz and below, possibly linked to differences in effective roughness.

The prediction of the ground vibration transmitted from tunnels to neighbouring buildings is a vital step in the assessment of the ground-borne noise in buildings. In empirical models it is commonly assumed that the level of ground vibration reduces monotonically with the distance away from the tunnel alignment. In reality, a ‘shadow’ zone is observed above the tunnel. This is first illustrated using measurements made above an operational railway line. To understand and characterise this effect, a study has then been carried out using various simulation models. Using an analytical model for the response to a point force acting in a homogeneous full-space, it is shown that the response is principally in the form of shear waves which radiate to the side rather than compressional waves which radiate in the direction of the load. This leads to a ‘shadow’ zone forming above a certain frequency, even in the absence of a tunnel and the absence of a free ground surface. The ground surface is next introduced by considering the response of a half-space to a point force, using a semi-analytical model. This is shown to exhibit similar behaviour although with differences caused by the free ground surface. Finally, a numerical 2.5-dimensional finite element/boundary element model is used to determine the response of a half-space ground to a force acting at the bottom of a concrete tunnel. The extent of the shadow is defined as the width to the point of maximum response. This depends largely on the depth of the excitation force and the shear wave speed of the soil. Although similar features are found with or without the tunnel, the presence of the tunnel structure causes a reduction in the shadow width, and the level difference within the shadow region is slightly increased. A tunnel with a smaller diameter leads to an increase in the frequency at which a given shadow effect occurs, but the tunnel lining thickness has negligible influence. The existence of shadow effect should be taken into account when making predictions of ground vibration using empirical models.

When a train runs on soft ground it can approach or even exceed the speed of surface waves in the ground. Under such conditions the amplitudes of the track response increase considerably. Moreover, a resonance-like phenomenon can occur in which a clear oscillation trail can be observed behind the moving axle loads. An investigation is presented of this resonance frequency and the critical speed effect for a track on a layered half-space subject to a moving load. Three different methods are used to investigate this resonance frequency: (i) the spectrum of the response to a moving load, (ii) analysis of the dispersion curves of the ground, and (iii) frequency analysis of the response to a stationary load. A parameter study is presented of a layered half-space ground with different P-wave speeds, S-wave speeds, and depth of the upper layer. The critical speeds are found in each case; in such a layered ground, the critical speed is greater than the Rayleigh wave speed of the soft upper layer due to the influence of the underlying half-space. The oscillating frequencies are shown to vary with the speed of the moving load, tending to reduce when the load speed increases. The P-wave speeds of both the upper layer and the underlying half-space are found to have negligible influence on the critical velocity and on the oscillating frequency; the S-wave speed of the half-space has only a small influence. Larger differences are found when the depth of the layer is varied. Finally, a formula for calculating this resonance frequency is proposed.

A numerical model is presented for the ground-borne vibration produced by trains running in tunnels. The model makes use of the assumption that the geometry and material properties are invariant in the axial direction. It is based on the so-called two-and-a-half dimensional (2.5D) coupled Finite Element and Boundary Element methodology, in which a two-dimensional cross-section is discretised into finite elements and boundary elements and the third dimension is represented by a Fourier transform over wavenumbers. The model is applied to a particular case of a metro line built with a cast-iron tunnel lining. An equivalent continuous model of the tunnel is developed to allow it to be readily implemented in the 2.5D framework. The tunnel structure and the track are modelled using solid and beam finite elements while the ground is modelled using boundary elements. The 2.5D track-tunnel-ground model is coupled with a train consisting of several vehicles, which are represented by multi-body models. The response caused by the passage of a train is calculated as the sum of the dynamic component, excited by the combined rail and wheel roughness, and the quasi-static component, induced by the constant moving axle loads. Field measurements have been carried out to provide experimental validation of the model. These include measurements of the vibration of the rail, the tunnel invert and the tunnel wall. In addition, simultaneous measurements were made on the ground surface above the tunnel. Rail roughness and track characterisation measurements were also made. The prediction results are compared with measured vibration obtained during train passages, with good agreement.

This paper presents a methodology for studying ground vibration in which the railway track is modelled in the space-time domain using the finite element method (FEM) and, for faster computation, discretisation of the ground using either FEM or the boundary element method (BEM) is avoided by modelling it in the wavenumber-frequency domain. The railway track is coupled to the ground through a series of rectangular strips located at the surface of the ground; their vertical interaction is described by a frequency-dependent dynamic stiffness matrix whose elements are represented by discrete lumped parameter models. The effectiveness of this approach is assessed firstly through frequency domain analysis using as excitation a stationary harmonic load applied on the rail. The interaction forces at the ballast/ground interface are calculated using the FE track model in the space-time domain, transformed to the wavenumber domain, and used as input to the ground model for calculating vibration in the free field. Additionally, time domain simulations are also performed with the inclusion of nonlinear track parameters. Results are presented for the coupled track/ground model in terms of time histories and frequency spectra for the track vibration, interaction forces and free-field ground vibration. For the linear track model, the results from the mixed formulation are in excellent agreement with those from a semi-analytical model formulated in the wavenumber-frequency domain, particularly in the vicinity of the loading point. The accuracy of the mixed formulation away from the excitation point depends strongly on the inclusion of through-ground coupling in the lumped parameter model, which has been found to be necessary for both track dynamics and ground vibration predictions.

Environmental noise is an issue that has seen increased awareness in recent years. In this chapter, the various sources of noise and vibration are summarised and methods to control them are discussed. The main source of noise from the railway system is rolling noise from the wheel-rail contact. Models for this are described leading to an overview of potential methods to control it. In addition, impact noise due to wheel flats and rail joints and squeal noise in sharp curves are considered. At high speed, aerodynamic noise becomes dominant due to its higher speed dependence. All these sources of noise can be transmitted to the vehicle interior as well as radiated to the wayside; both structure-borne and airborne transmission paths need to be considered. Ground vibration is also produced, which can be experienced as feelable vibration and as low-frequency re-radiated noise. Methods to control ground-borne noise include resilient track forms; feelable vibration is more difficult to control, although it is important to minimise the vehicle unsprung mass. Finally, ride comfort and the influence of the vehicle suspension are discussed.

Transport infrastructure produces many externalities. Increased accessibility and the resultant economic development are among the most notable positive ones. Accidents, air and noise pollution and other environmental issues, such as impacts on biodiversity, landscape and townscape, are the most important negative ones. In the case of railway infrastructure, noise impacts have a key effect on net social benefit. Noise reduction is crucial to achieve greater social benefits. Against this background, the University of Southampton has been undertaking the Track to the Future (T2F) project, which is assessing, among other issues, how to produce a quiet ballasted track system that at the same time is cheaper to maintain and renew.This paper considers combinations of engineering interventions that could reduce rail-related noise, including under sleeper pads, rail dampers and noise barriers which all reduce noise emissions. It extends previous analysis of under sleeper pads to compare their costs and benefits with those of rail dampers and noise barriers in the context of a UK-based installation case study.

With the development of non-ballasted track forms (often referred to as slab tracks) over the few last decades, it is important to understand their behaviour with respect to ground-borne vibration compared with the traditional ballasted tracks. This is important in deciding between the use of the two track forms. The present work aims to quantify the differences between slab tracks and ballasted tracks numerically by using the MOTIV model. This is a general and fully coupled three-dimensional model that works in the wavenumber-frequency domain. It can predict the vibration levels of the track and the ground due to the gravitational loading of a passing train and the wheel and rail unevenness. A comparative analysis between the two track types is presented in terms of ground vibration with emphasis given to the influence of the stiffness and inertial parameters of the two track forms. It is shown that, for the same fastener stiffness there are only small differences in ground vibration behaviour, with the mass of the track slab leading to reductions of 1–3 dB at frequencies above 16 Hz. However, if softer rail fasteners are used in the slab track, as is usual, this leads to further reductions above 63 Hz. The critical velocity on soft soil is also considered. Although there is little difference between the different tracks for a homogeneous ground, for grounds with a soft surface layer the critical velocity is increased by the slab bending stiffness. The maximum rail displacement is also smaller for a slab track than the equivalent ballasted track. The work described here has been supported by the EPSRC under the programme grant EP/M025276/1, ‘The science and analytical tools to design long life, low noise railway track systems (Track to the Future)’ and the MOTIV project (Modelling of Train Induced Vibration), grants EP/K005847/2 and EP/K006002/1. All data published in this article are openly available from the University of Southampton repository at https://doi.org/10.5258/SOTON/D1001. Scopus

A novel computational modelling approach for prediction of environmental vibration is introduced. The model is formulated in both moving and fixed frames of reference, with a mixed frame of reference formulation introduced to couple the two frames of reference. The resulting system is able to model a vehicle travelling on an infinite railway track, formulated in a moving frame of reference, interacting via the soil with a structure (i.e. building), formulated in a fixed frame of reference. The method utilizes a semi-analytical soil model with the structures modelled using three-dimensional finite elements. Two solution procedures of the full system are proposed: partial coupling, where some secondary effects from reflected waves propagating through soil are disregarded, and full coupling, where the vehicle–track–soil–structure is modelled as a fully coupled system. Both proposed solution procedures offer a one-step approach for solving the whole system in the frequency–spatial domain. The usage of the model is demonstrated in two example cases: one analysing a simple building structure near a railway track, using the partial coupling solution procedure, and another one analysing the behaviour of a vehicle model traversing over a rigid block embedded inside the soil, using the full coupling solution procedure. The introduced modelling approach offers a computationally efficient solution procedure, at the same time being applicable to a wide array of application cases.

Transport infrastructure produces many externalities. Increased accessibility and the resultant economic development are among the most notable positive ones. Accidents, air and noise pollution, and other environmental issues, such as impacts on biodiversity, landscape and townscape, are the most important negative ones. In the case of railway infrastructure, noise and vibration impacts have a key effect on net social benefit. Noise and vibration reduction is crucial to achieve greater social benefits. In this context, the University of Southampton has been working on the Track to the Future (T2F) project, which is assessing, among other issues, how to produce a quiet ballasted track system that is also cheaper to maintain and renew. This paper considers combinations of engineering interventions that could reduce noise and vibration. These include under sleeper pads which attenuate ground vibration, rail dampers and noise barriers which reduce airborne noise. The effects on noise and vibration of under sleeper pads are determined using detailed engineering models. The overall benefits are then assessed for a notional section of track based on a typical route in the UK.

A trench can act as a barrier to ground vibration and is a potential mitigation measure for low frequency vibration induced by surface railways. However, to be effective at very low frequencies the depth required becomes impractical. Nevertheless, for soil with a layered structure in the top few metres, if a trench can be arranged to cut through the upper, soft layer of soil, it can be effective in reducing the most important components of vibration from the trains. This study considers the possibility of using such a realistically feasible solution. Barriers containing a soft fill material are also considered. The study uses coupled finite element / boundary element models expressed in terms of the axial wavenumber. It is found to be important to include the track in the model as this determines how the load is distributed at the soil's surface which significantly affects the insertion loss of the barrier. Calculations are presented for a range of typical layered grounds in which the depth of the upper soil layer is varied. Variations in the width and depth of the trench or barrier are also considered. The results show that, in all ground conditions considered, the notional rectangular open trench performs best. The depth is the most important parameter whereas the width has only a small influence on its performance. More practical arrangements are also considered in which the sides of the trench are angled. Barriers consisting of a soft fill material are shown to be much less effective than an open trench but still have some potential benefit. It is found that the stiffness of the barrier material and not its impedance is the most important material parameter. 2016 Elsevier Ltd. The results presented in this paper have been obtained within the EU FP7 project RIVAS (Railway Induced Vibration Abatement Solutions) under grant agreement No. 26575 . The project coordinator was UIC (International Union of Railways). The sixth and seventh authors are post-doctoral fellows of the Research Foundation Flanders (FWO). The financial support is gratefully acknowledged. All data published in this paper are openly available from the University of Southampton repository at http://dx.doi.org/10.5258/SOTON/394807 . Scopus

A new state-space model is formulated for the dynamic analysis of sandwich beams that are made of two thin elastic layers continuously joined by a shear-type viscoelastic (VE) core. The model can accommodate different boundary conditions for each outer layer and accounts for the rate-dependent constitutive law of the core through additional state variables. The mathematical derivation is presented with the Standard Linear Solid (SLS) model (i.e., a primary elastic spring in parallel with a single Maxwell element) and then extended to the generalized Maxwell (GM) model. The kinematics equations are developed by means of Galerkin-type approximations for the fields of axial and transverse displacements in the outer layers, and imposing the pertinent compatibility conditions at the interface with the core. Numerical examples demonstrate the accuracy and versatility of the proposed approach, which endeavors to represent the effects of the VE memory on the vibration of composite beams.

A case study on a small-scale laboratory vehicle frame is used to investigate the variability of the updated finite element (FE) models that arises from model and measurement errors and demonstrate the effect of this variability on response predictions. Conventional weighted modal residuals and recently introduced multi-objective identification methods for structural model updating are used to provide the entire spectrum of Pareto optimal FE models consistent with the measured modal data. Similarities and differences between the two model updating methods are explored and the advantages of the multi-objective identification methods are emphasized. A significant variability in Pareto optimal models is observed, which is indicative of the uncertainty in the updated FE models. The dependence of the variability of the Pareto models on the information contained in the measured data and the size of model and measurement errors is explored by varying the number of measured modes, number of sensors, FE mesh discretization sizes, and number of model parameters. The effectiveness of the updated Pareto optimal models and their predictive capabilities are assessed. Frequency response functions and fatigue lifetime predictions are used as example of structural performance variables in order to demonstrate the variability in the response predictions that arises from the variability in the Pareto optimal models. A large variability in the response predictions is observed that cannot be ignored in decisions based on updated FE models. The multi-objective optimization method provides the general framework for properly accounting for model uncertainty in model-based response predictions consistent with measured data.

A methodology is proposed for estimating damage accumulation due to fatigue in the entire body of a metallic structure using output-only vibration measurements from a sensor network installed at a limited number of structural locations. Available frequency domain stochastic fatigue methods based on Palmgren-Miner damage rule, S-N fatigue curves on simple specimens subjected to constant amplitude loads, and Dirlik's probability distribution of the stress range are used to predict the expected fatigue damage accumulation of the structure in terms of the power spectral density (PSD) of the stress processes. The PSD of stresses at unmeasured locations are estimated from the response time history measurements available at the limited measured locations using Kalman filter and a dynamic model of the structure. The effectiveness and accuracy of the proposed formulation is demonstrated using a multidegree-of-freedom spring-mass chain model and a two-dimensional truss model arising from structures that consist of members with uniaxial stress states

The dynamic characteristics of two representative R/C bridges on Egnatia Odos motorway in Greece are estimated based on low amplitude ambient and earthquake-induced vibrations. The present work outlines the instrumentation details, algorithms for computing modal characteristics (modal frequencies, damping ratios and modeshapes), modal-based finite element model updating methods for estimating structural parameters, and numerical results for the modal and structural dynamic characteristics of the two bridges based on ambient and earthquake induced vibrations. Transverse, bending and longitudinal modes are reliably identified and stiffness-related properties of the piers, deck and elastomeric bearings of the finite element models of the two bridges are estimated. Results provide qualitative and quantitative information on the dynamic behavior of the bridge systems and their components under low-amplitude vibrations. Modeling assumptions are discussed based on the differences in the characteristics identified from ambient and earthquake vibration measurements. The sources of the differences observed between the identified modal and structural characteristics of the bridges and those predicted by finite element models used for design are investigated and properly justified.

In this paper, a mixed model for studying ground vibration generated from surface railway tracks is presented. A ballasted track with nonlinear resilient components is modelled in the time domain using the Finite Element method. The ground is modelled as a linear homogeneous half-space in the wavenumber domain for faster computation. The interaction between the track and the ground is incorporated into the track model through a lumped parameter model representing the vertical dynamic stiffness of the ground. The coefficients of the components of the lumped parameter model are obtained by curve fitting of the transfer function of the half-space for a load applied at its origin. The coupled equation of motion for the track/ground system is formulated with excitation from a stationary point load-consisting of static and dynamic partsacting at the centre of the rail. The coupled equation is solved by numerical integration. The calculated interaction forces at the ballast/ground interface from the space-time domain track model are Fourier transformed to the wavenumber domain and used as excitation to the ground model in order to calculate free-field surface vibration of the ground. Results are presented for the vertical dynamic stiffness for the ground, and for the track and ground displacement in the vicinity of the track and in the free-field. A comparative study between the mixed formulation with the lumped parameter model for the ground, and a fully coupled wavenumber domain model is conducted for linear parameters. Using the fully coupled model as a benchmark, it is observed that the inclusion of the lumped parameter ground model in the track model gives good estimation of the transmitted forces, and hence ground vibration, both in the near and far fields. Finally, the effect of nonlinear track components is briefly investigated for different levels of static preload.

In this paper, the dynamic pile-soil-pile interaction (PSPI) in a multi-layered half-space is in-vestigated for the prediction of the response of piled foundations due to railway vibrations. Two methods of modelling piled foundations in a multi-layered half-space are presented. The first is an efficient semi-analytical model that calculates the Green’s functions of the multi-layered half-space soil using the thin layer and the dynamic stiffness matrix methods. The second is a fully-coupled model that utilises the boundary element (BE) method to simulate the soil, where the Green’s functions are calculated using the ElastoDynamics Toolbox (EDT). The paper aims to investigate the accuracy and the efficiency of the semi-analytical model by comparing the predictions of the two methods. A set of comparisons is performed, including the driving point response of a single pile and the interaction between two piles. The comparisons reveal that, at most frequencies, the semi-analytical model can predict the driving point response and the dynamic interaction with acceptable accuracy and computational efficiency. The model is then used for predicting the response of a pile-group due to the vibration field generated by a railway in varying distance from the piles. The vibration field generated by the railway is mod-elled as the superposition of the response due to harmonic loadings generated at the wheel-rail interface and the vibration response is examined at different points on the free surface away from the piles. The comparisons highlight the efficiency and accuracy of the semi-analytical model and illustrate its practical application

Companies which manage railway networks have to cope continually with the problem of operating safety and maintenance intervention issues related to rail surface irregularities. A lot of experience has been gained in recent years in railway applications but the case of tramways is quite different; in this field there are no specific criteria to define any intervention on rail surface restoration. This paper shows measurements carried out on some stretches of a tram network with the CAT equipment (Corrugation Analysis Trolley) for the principal purpose of detecting different states of degradation of the rails and identifying a level of deterioration to be associated with the need for maintenance through rail grinding. The measured roughness is used as an input parameter into prediction models for both rolling noise and ground vibration to show the potential effect that high levels of roughness can have in urban environment. Rolling noise predictions are also compared with noise measurements to illustrate the applicability of the modelling approach. Particular attention is given to the way the contact filter needs to be modelled in the specific case of trams that generally operate at low speed. Finally an empirical approach to assess vibration levels in buildings is presented.

A bridge health monitoring system is presented based on vibration measurements collected from a network of acceleration sensors. Sophisticated structural identification methods, combining information from the sensor network with the theoretical information built into a finite element model for simulating bridge behaviour, are incorporated into the system in order to monitor structural condition, track structural changes and identify the location, type and extent of damage. This work starts with a brief overview of the modal and model identification algorithms and software incorporated into the monitoring system and then presents details on a Bayesian inference framework for the identification of the location and the severity of damage using measured modal characteristics. The methodology for damage detection combines the information contained in a set of measurement modal data with the information provided by a family of competitive, parameterized, finite element model classes simulating plausible damage scenarios in the structure. The effectiveness of the damage detection algorithm is demonstrated and validated using simulated modal data from an instrumented R/C bridge of the Egnatia Odos motorway, as well as using experimental vibration data from a laboratory small-scaled bridge section.

A multi-objective identification method for structural model updating based on modal residuals is presented. The method results in multiple Pareto optimal structural models that are consistent with the experimentally measured modal data and the modal residuals used to measure the discrepancies between the measured and model predicted modal characteristics. These Pareto optimal models are due to uncertainties arising from model and measurement errors. The relation between the multi-objective identification method and the conventional single-objective weighted modal residuals method for model updating is investigated. Using this relation, an optimally weighted modal residuals method is also proposed to rationally select the most preferred model among the alternative multiple Pareto optimal models for further use in structural model prediction studies. Computational issues related to the reliable solution of the resulting multi-objective and single optimization problems are addressed. The model updating methods are compared and their effectiveness is demonstrated using experimental results obtained from a three-story laboratory structure tested at a reference and a mass modified configuration. The variability of the Pareto optimal models and their associated response prediction variability are explored using two structural model classes, a simple 3-DOF model class and a higher fidelity 546-DOF finite element model class. It is demonstrated that the Pareto optimal structural models and the corresponding response and reliability predictions may vary considerably, depending on the fidelity of the model class and the size of measurement errors.

A multi-objective identification method for model updating based on modal residuals is proposed. The method results in multiple Pareto optimal structural models that are consistent with the measured modal data, the class of models used to represent the structure and the modal residuals used to judge the closeness between the measured and model predicted modal data. The conventional single-objective weighted modal residuals method for model updating is also used to obtain Pareto optimal structural models by varying the values of the weights. Theoretical and computational issues related to the solution of the multi-objective and single optimization problems are addressed. The model updating methods are compared and their effectiveness is demonstrated using experimental results obtained from a three-story laboratory structure tested at a reference and a mass modified configuration. The variability of the Pareto optimal models and their associated response prediction variability are explored using two structural model classes, a simple 3-DOF model class and a higher fidelity 546-DOF finite element model class. It is shown that the Pareto optimal structural models and the corresponding response predictions may vary considerably. The variability of Pareto optimal structural model is affected by the size of modelling and measurement errors. This variability reduces as the fidelity of the selected model classes increases.

This work outlines the optimization algorithms involved in integrating system analysis and measured data collected from a network of sensors. The integration is required for structural health monitoring problems arising in structural dynamics and related to (1) model parameter estimation used for finite element model updating, (2) model-based damage detection in structures and (3) optimal sensor location for parameter estimation and damage detection. These problems are formulated as single- and multi-objective optimization problems of continuous or discrete-valued variables. Gradient-based, evolutionary, hybrid and heuristic algorithms are presented that effectively address issues related to the estimation of multiple local/global solutions and computational complexity arising in single and multi-objective optimization involving continuous and discrete variables.

When modelling the railway induced vibration in a building, three main aspects of the problem have to be considered: the vibration generation at the moving vehicle-track interaction points, the vibration propagation in the underlying infinite soil, and the vibration reception inside the building. This study proposes a computational modelling approach for predicting the full vibration propagation path from the train vehicles up to the building structure. The method includes a moving train model that is directly coupled to a stationary building structure, with interaction between them through the underlying soil using a single step solution procedure. A semi-analytical model is utilized to model the soil to which rigid objects and structures modelled by finite elements (FE) are coupled. The system is excited by a multi-body vehicle model passing over an irregular track. The proposed modelling approach uses the frequency-domain solution with some parts, such as the railway track, formulated in the moving frame of reference (FOR) and other parts, such as building structures, formulated in a fixed FOR. The coupling terms between the two FORs are found by utilizing an analytical formulation of receptance between the two FORs. It is shown that due to the coupling between the fixed and moving FORs, the previously uncoupled discrete frequencies become coupled through the other FOR as a result of the Doppler effect and wave scattering. Two solution procedures of the full system are pro-posed: partial coupling, where some secondary effects from reflected waves propagating through soil are disregarded, and full coupling, where the vehicle, track, soil and structure are modelled as a fully coupled system. Both proposed solution procedures offer a single-step approach for solving the whole system in the frequency-spatial domain. The application of the model is demonstrated and validated in two example cases: one analyzing a simple building structure near a railway track, using the partial coupling solution procedure, and another analyzing the behaviour of a vehicle model passing over a rigid block embedded inside the soil, using the full coupling solution procedure.