A dynamical model of a double-deck circular tunnel embedded in a full-space

This thesis presents a three-dimensional dynamic model of a double-deck circular tunnel embedded in a full-space. The model uses the receptance method to obtain the response of the complete structure from the response of its parts. The considered subsystems are the interior floor and the tunnel-soil coupled system. The classical thin plate theory is considered to represent the behaviour of the first and the Pipe in Pipe model is chosen to describe the second. Because the complete model is assumed to be geometrically invariant in the train circulation direction, the coupling of both systems is performed in the wavenumber-frequency domain. After the model formulation, some important issues about its numerical computation are detailed and the obtained results are discussed. The response of a double-deck tunnel to a dynamic and to a quasistatic excitation is compared to the response obtained for a simple tunnel. The first comparison is done performing a power flow study of both tunnel structures when a harmonic line load is applied on them. The main differences between their radiation magnitudes and patterns are identified and discussed. The second comparison is done calculating the total amount of energy crossing a certain surface when a static load moving at a constant speed is considered. Results for a wide range of load speeds and radial distances are presented. A complete track-tunnel-soil model is finally obtained coupling a superstructure model to the interior floor model previously presented.Postprint (published version

An energy flow study of a double-deck tunnel under quasi-static and harmonic excitations

© 2016. This version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper presents a comparison between the vibration energy flow radiated by a double-deck tunnel and the one radiated by a simple tunnel when both are excited by constant or by harmonic moving loads. For both cases, the radiated energy is computed using a three-dimensional semi-analytical model of the system. The total energy radiated upwards is presented for a wide range of load speeds, when a constant moving load is considered, and for a wide range of excitation frequencies, when the excitation is a harmonic moving load. Significant differences have been obtained, first, for constant loads moving at very high speeds and, second, for harmonic loads moving at typical speeds for underground trains.Peer ReviewedPostprint (author's final draft

A 2.5D automatic FEM-SBM method for the evaluation of free-field vibrations induced by underground railway infrastructures

This paper presents an efficient method to predict underground railway-induced vibrations. The method uses the finite element method (FEM) to model the railway tunnel structure and the singular boundary method (SBM) to model the wave propagation in the surrounding soil. The FEM mesh and the distribution of SBM collocation points at the tunnel/soil interface are generated using an automatic meshing strategy. The presented method is one of the main components of VIBWAY, a user-friendly prediction tool to address railway-induced vibration problems. This paper presents three calculation examples in which the soil response due to forces applied on the tunnel structure are computed in terms of transfer functions. The results obtained for each one of the calculation examples are compared with those computed using a model based on a 2.5D FEM-BEM approach. The presented comparisons show that the proposed approach is a suitable strategy for predicting underground railway-induced vibrations, both in terms of accuracy and computational efficiency. Moreover, the use of an automatic meshing strategy and the SBM formulation not only eases the implementation of the approach but it also makes it easier to use, which is one of the key features of the VIBWAY tool.Peer ReviewedPostprint (published version

Dynamic response of a double-deck circular tunnel embedded in a full-space

© 2016. This version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/A three-dimensional dynamic model for calculating the ground-borne vibrations generated by harmonic loads applied on the interior floor of a double-deck circular tunnel is developed. The response of the system is obtained coupling the interior floor subsystem and the tunnel-soil subsystem in the wavenumber-frequency domain. The interior floor is modeled as a thin plate of infinite length in the train circulation direction and the tunnel-soil system is described using the Pipe in Pipe model. Some numerical instabilities of the resulting expressions are overcome by using analytic approximations. The results show that the dynamic behavior of the interior floor clearly influences the magnitude of the coupling loads acting on the tunnel structure. The soil response to a harmonic load acting on the double-deck tunnel is compared to the one obtained for the case of a simple tunnel finding significant differences between them for the whole range of frequencies studied. The proposed model extends the prediction of train-induced vibrations using computationally efficient models to this type of tunnel structure.Peer ReviewedPostprint (author's final draft

Control of ground-borne underground railway-induced vibration from double-deck tunnel infrastructures by means of dynamic vibration absorbers

The aim of this study is to investigate the efficiency of Dynamic Vibration Absorbers (DVAs) as a vibration abatement solution for railway-induced vibrations in the framework of a doubledeck circular railway tunnel infrastructure. A previously developed semi-analytical model of the track-tunnel-ground system is employed to calculate the energy flow resulting from a train pass-by. A methodology for the coupling of a set of longitudinal distributions of DVAs over a railway system is presented as a general approach, as well as its specific application for the case of the double-deck tunnel model. In the basis of this model, a Genetic Algorithm (GA) is used to obtain the optimal parameters of the DVAs to minimize the vibration energy flow radiated upwards by the tunnel. The parameters of the DVAs set to be optimized are the natural frequency, the viscous damping and their positions. The results show that the DVAs would be an effective countermeasure to address railway induced ground-borne vibration as the total energy flowradiated upwards fromthe tunnel can be reduced by an amount between 5.3 dB and 6.6 dB with optimized DVAs depending on the type of the soil and the train speedPostprint (updated version

An efficient experimental methodology for the assessment of the dynamic behaviour of resilient elements

The assessment of the dynamic behaviour of resilient elements can be performed using the indirect method as described in the standard ISO 10846-3. This paper presents a methodology for control the error on the estimation of the frequency response functions (FRF) required for the application of the indirect method when sweep sine excitation is used. Based on a simulation process, this methodology allows for the design of the sweep sine excitation parameters, i.e., the sweep rate and the force amplitude, to control three types of errors associated to the experimentally obtained FRF in the presence of background noise: a general error of the FRF in a selected frequency range, and the errors associated to the amplitude and the frequency of the FRF resonance peak. The signal processing method used can be also tested with this methodology. The methodology has been tested in the characterisation of two different resilient elements: an elastomer and a coil spring. The simulated error estimations has been found to be in good agreement with the errors found in the measured FRF. Furthermore, it is found that for large signal-to-noise ratios, both sweep rate and force amplitude significantly affect the FRF estimation error, while, for small signal-to-noise ratios, only the force amplitude can control the error efficiently. The current methodology is specially interesting for laboratory test rigs highly used for the dynamic characterisation of resilient elements which are required to operate efficiently, since it can be used for minimising test times and providing quality assurance. Moreover, the application of this methodology would be specially relevant when characterisation is done in noisy environmentsPostprint (published version

A hybrid SBM-MFS methodology to deal with wave propagation

In this paper, a novel hybrid 2.5D SBM-MFS approach is formulated and developed in the frequency domain. This approach inherits the accuracy of MFS while keeping the robustness presented by the SBM. The MFS is employed to study the smooth portion of the boundary, while the complex segments are analysed through the SBM. For the sake of presenting the potential of the proposed hybrid approach, a square-shaped boundary excited by a unit point load is considered. The performance of the hybrid method is thoroughly assessed against 2.5D BEM, MFS, and SBM methods, in terms of convergence error analysis. Since the considered problem does not have a known analytical solution, the 2.5D FEM-BEM approach with a highly refined mesh is taken as the reference in the error analysis. The convergence error is calculated in terms of receptances at two circular distributions of evaluation points. In the hybrid method, 70 percent of the virtual sources are allocated on an auxiliary virtual boundary (MFS sources) while the remaining 30 percent are allocated on the physical boundary (SBM sources). The convergence plots obtained by four methods show that the accuracy of the hybrid method is significantly higher than the one of MFS and, in some cases, even higher than the one of BEM. While MFS requires a large number of nodes per wavelength to achieve acceptable results, the 2.5D SBM-MFS presents a high convergence rate, even for a small number of nodes per wavelength. The main benefit of the hybrid method is not solely its accuracy, compared with the BEM and SBM methods, but also its computational efficiency is another achievement. Moreover, in contrast to integration-based methods, such as BEM, the implementation of the new procedure is quite simple. It can be concluded that the hybrid 2.5D SBM–MFS is an adequate alternative prediction tool for elastodynamic problems.Peer ReviewedPostprint (published version

VIBWAY: A user-friendly computational tool for the prediction of railway-induced ground-borne noise and vibration

This paper aims to introduce preliminary statement of methods of a computationally efficient and user-friendly toolbox, called VIBWAY, able to predict vibration and re-radiated noise levels in two situations. On the one hand, it can predict levels in existing buildings due to new lines or after the application of mitigation measures in existing operational railway infrastructures. Thus, it can be used to assess the performance of vibration countermeasures applied at the track, at the soil and/or at the building. On the other hand, it can predict levels in new buildings to be constructed close to an existing railway line from vibration measurements in the surface of the ground where the building will be constructed. The VIBWAY toolbox is based on a non-interface 2.5D FEM-SBM approach for the wave propagation on the soil, on semi-analytical approaches for the track and the building and on rigid multibody dynamics modelling of the train vehiclePostprint (published version