Engineering Structures 27 (2005) 1981–1998 www.elsevier.com/locate/engstruct Investigation of ground vibrations induced by moving loads E. Celebi a,∗ , G. Schmid b a Faculty of Engineering, Department of Civil Engineering, Sakarya University, 54187 Esentepe-Sakarya, Turkey b Department of Civil Engineering, Ruhr University, D-44780 Bochum, Germany Received 14 September 2004; received in revised form 28 January 2005; accepted 19 May 2005 Available online 25 August 2005 Abstract The objective of this work indicates and discusses two mathematical models and numerical techniques for solving problems associated with wave propagation in the track and subsoil due to the passage of a train. The Thin Layer Method/Flexible Volume Method (TLM/FVM) and the Boundary Element Method (BEM) are used to analyse the three-dimensional dynamic response of the free field near railway lines induced by the moving loads acting on the surface of a homogeneous or layered half-space. Both simulation models employ the substructuring approach in the frequency domain. The validity of the methods are demonstrated by comparison with results of analytical solution. An extensive numerical investigation has been carried out to show the influence of different parameters on the effectiveness of vibration reduction through open trench barriers. © 2005 Elsevier Ltd. All rights reserved. Keywords: Wave propagation; Thin Layer Method/Flexible Volume Method; Boundary Element Method; Substructuring approach; Moving loads; Trench barrier 1. Introduction 1.1. General remarks and previous works The propagation of waves through a soil medium gener- ated by machine foundations, traffic loads or construction blasting may produce excessive ground vibrations which have recently received world-wide special attention because people are today more concerned about their life quality, comfort and safety. The increase in passenger transport with high speed, and the increased weight of high-speed trains with heavy-axle double-deck wagons, heavy-loaded freight traffics or giant lorries will produce strong ground and structural vibrations. Interest in this subject originates from the field of civil and railway engineering in association to design of the highway and railway track structures. Modern railways have become one of the most advanced and fast growing means of transport in Western Europe, and they are currently being developed further in order to reduce ∗ Corresponding author. Tel.: +90 2643460353; fax: +90 2643460351. E-mail address: ecelebi@sakarya.edu.tr (E. Celebi). 0141-0296/$ - see front matter © 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2005.05.011 even more the travelling time of the passengers, as reported by Banister and Hall [1], and Ford et al. [2]. The velocity increase brought a new problem to railway engineering as the high-speed trains may significantly amplify the train- track vibration. The rapid extension of the high-speed rail network in Europe in the last three decades has initiated a lot of research related to the development of numerical models to simulate and evaluate the dynamic interaction between rail tracks and subsoil [3–7]. It is well known in case of very soft ground, such as clay and peat soil zones, where surface wave velocities become very low, that very large values of displacement underneath a moving load will be reached if the speed of the moving load is equal to the propagation velocity of the surface wave. The speed for which this maximum amplification occurs is called the critical speed. In addition, some theoretical studies accomplished by Krylov [8,9] have indicated a substantial increase of the vibration level at the line side due to trains passing with high speed, which may exceed the surface wave velocity of the underlying soil. High-level vibrations, as caused by the passage of a high- speed train, especially if they run at speeds close to or