Time domain 3D finite element modelling of train-induced vibration at high speed

Abstract

The purpose of this paper is to investigate a 3D finite element (FE) coupled train-track model for the numerical modelling of the ground induced vibration due to the passage of a single high speed train locomotive. The track components such as the sleepers, the ballast and the subgrade are represented by 20 noded brick elements. The rail is modelled by using 3D beam-column elements. A quarter train model is coupled to the 3D railway track model, through the interaction points between the wheels and the rail, based on the nonlinear Hertzian contact theory. A damping model, based on Rayleigh damping approach, is used. The 3D FE model is capable of simulating multi-layered ground and radiation damping by using viscous boundary conditions. Material nonlinearity, especially of the ballast and subgrade layers can be taken into account as appropriate. Numerical experiments are carried out, using the proposed 3D FE coupled train-track model, to study the train fundamental passing frequency effect on the dynamic railway track response for train speeds belonging to the subcritical, critical and supercritical ranges. The influence of the soil material damping is also investigated. The results clearly show an increase in track deflection with train speed. The material damping model allows a realistic prediction of the track vibration and train body dynamics at high speeds.

Introduction

During the past decades, important developments have taken place to provide guidance on a safe and cost effective design for constructing high speed trains. This is driven by the increase in the train speed, axle loads and the construction of new high speed lines, and their resulting vibration effects on the track and nearby buildings due to the waves transmitted through the soil. In soft ground sites, high levels of vibration can be produced, when the train speed exceeds the ground Rayleigh wave speed. Understanding the related wave propagation problems becomes necessary, when looking at mitigation strategies, to allow the safe and reliable operation of high-speed trains over poor ground.

Various models have been developed to predict the generation and propagation of ground vibration due to train passage. Most of the early works are based on analytical or semi-analytical approaches and deal with moving point load induced ground vibration (see Refs. [1], [2], [3], [4], [5], [6], [7], [8], [9], e.g.). Further related bibliography references can be found in [10] and [11]. With the rapid progress of computer technologies, models based on the finite element method, the boundary element method, or coupled together, become more suited for solving soil dynamic problems. The FE method can be used in problems with complex geometry. However, when dealing with infinite domains, absorbing boundary conditions may be implemented to avoid wave reflection.

The objective of the present work is to numerically enhance a 3D FE coupled train-track model which predicts the ground vibration of high speed train and heavy axle load conditions. References on advanced models incorporating the dynamic excitation are given in the research work of Galvín et al. [12], where a coupled finite element – boundary element model is used. This model incorporates the train-track interaction and solves non-linear coupled equations using an implicit time integration scheme. This involves assembling the global coupled system matrices, which requires large computational memory capacity.

The model proposed in this paper also takes into account the train-track interaction mechanisms and the sleeper-ballast interaction. It also accounts for the spread of the moving load on the adjacent sleepers via the rail and afterwards into the multi-layered subgrade. This model may deal with material nonlinearity, multi-layered ground and material damping. Moreover, this 3D FE model combines explicit time stepping with an element-by-element storage procedure and hence it does not require significant memory allocation and may be more suited for parallelization. The rail is represented by 3D Euler–Bernoulli beam elements. A multi degrees of freedom vehicle dynamic model [13] is incorporated and coupled to the 3D track model, based on the non linear contact theory. The program can also look at ground vibration generated due to track irregularities, such as those from short or long wavelength track faults, or from irregularities on the rail surface.

The structure of this paper is as follows. The next section details the presentation of the numerical model. This includes a brief description of the vehicle dynamic model, the material damping approach, the finite elements used in the approximation of the track model and the adopted explicit time integration scheme. Validation results based on the analytical solution of the Boussinesq’s problem, where a homogeneous half space is subjected to a static constant point load, are presented. Finally, numerical tests are performed to study the influence of the train’s fundamental passing frequency for different train speeds including the subcritical and supercritical ranges. The effect of material damping model is also presented.