Keywords: moving load, soil structure interaction, railway dynamics, boundary element method, finite element method, wave propagation.

This paper describes a method to compute the dynamic response of culverts under high-speed-train lines. The importance of the subject is related to the observed resonance of simply supported bridges of short span when traversed by modern European high-speed-trains. The resonance is such that important vertical accelerations are produced, conducting to the ballast liquefaction and the corresponding safety loss problem.

The technical solution is the use of box-type structures that enforce the play of important soil-structure interaction effects mobilising radiation damping effects and changes in the structural natural frequencies.

The rigorous analysis of the problem is complex and expensive. From a practical engineering point of view the structure is not very important if compared with large or medium span bridges. So the practising engineer is faced with the decision of using simple methods, which accuracy is unknown or to dedicate an enormous amount of computational effort to a structure which cost does not justify it.

In this paper we try to develop a method based on simple modelling that only uses everyday classical tools and that has been calibrated against more refined computational techniques.

The main idea is the assumption that the most important soil effects are related to rigid modes of the structure, while the flexible modes are reduced as much as possible to reduce the computational effort.

In this way the soil-structure interaction effects can be obtained using well established methods of engineering practice or studying models that doesn't need to include the flexibility of the structure. The last one is then studied separately using a model of 5 or 6 degrees of freedom (d.o.f).

The paper proposes a Boundary Element Approach for the first part of the analysis (dynamic stiffness of soil induced by harmonic unit displacement of the structure considered as a rigid body) and a specific analysis of the 6 d.o.f. flexible structure that combines the interaction of the culvert with the soil and natural embankments through the culvert supported in a Winkler type foundation.

The model has been tested for different cases and show promising results that could be used to organise parametric studies and synthesise practical recommendations.

1

Novak, M.; "Effect of Soil on Structural response to Wind and Earthquake"; Earthquake Engineering and Structural Dynamics; Vol. 3 69-76. 1974. doi:10.1002/eqe.4290030107

2

Fang, H.Y.; "Foundation Vibrations. Foundation Engineering Handbook"; Van Nostrand; ISBN: 0-442-22487-7; 1991

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