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© 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

In this paper, a novel numerical methodology to deal with longitudinally invariant soil-structure interaction problems is proposed. The methodology uses the finite element method to model the structure and the singular boundary method to model the wave propagation in the soil, both formulated in the wavenumberfrequency domain. The versatility presented by the finite element method combined with the simplicity and computational efficiency of the singular boundary method results in a friendly, robust and accurate novel methodology to address the soil-structure interaction problems. The accuracy of the proposed method is assessed by comparing it against 2.5D FEM-MFS and 2.5D FEM-BEM approaches for two cases: a thin cylindrical shell and a star-like beam structure, both embedded in a full-space medium. Moreover, the computational efficiency of the proposed method is evaluated against 2.5D FEM-MFS and 2.5D FEM-BEM methods. In the final step, the applicability of the proposed method is studied through an example of a railway tunnel embedded in a layered half-space. The results presented in this work exhibit the advantages of the novel approach in modelling simplicity, numerical efficiency and robustness with respect to previous methodologies.

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The vibro-acoustic response of complex structures with uncertain properties is a problem of great concern for modern industries. In recent years, much research has been devoted to the prediction of this response in the mid-frequency range where, because neither finite element analysis nor statistical energy analysis are appropriate, a hybrid deterministic-statistical approach becomes a suitable solution. Despite its potential, the existence of systems with active components that are too complex to be modelled numerically can limit the application of the method. However, it may still be possible to measure the dynamical response of these structures experimentally. This paper is hence concerned with the possibility of integrating experimental data into a hybrid deterministic-statistical method. To explain the new methodology, two similar case studies, consisting of a deterministic source structure that is coupled to a statistical plate receiver using passive isolators, are used. For each case, the vibratory excitation, characterised using in-situ blocked force measurements, the source structure mobility, and the isolators stiffness are experimentally determined and inserted in the proposed hybrid model of the system. The paper explains the techniques used for obtaining the considered experimental data and the theoretical model proposed for describing the systems.To validate the proposed approach, the predicted vibration response of the receiver plate is compared to the one obtained by experimentally randomising the plate in both case studies. The results show that a good agreement is obtained, both for the ensemble average response of the receiver structure and for the ensemble variance of this response. Moreover, the upper confidence bounds predicted by the hybrid method enclose well the ensemble of experimental results. The cause of some narrow-band differences observed between the predicted response and the experimental measurements is finally discussed. It is therefore concluded that the capabilities of the hybrid deterministic-statistical method can be clearly enhanced through the incorporation of experimental data prescribing active sub-systems.