Title:

Models for vehicle/track/ground interaction in the time domain

Due to the demands of increasing population and environmental concerns, the highspeed train has become an important means of transportation in many countries. However, severe vibration induced by highspeed trains can occur when train speeds approach the speed of waves in the ground and track deflections can then become large. Consequently, the track and ground may no longer behave linearly. The aim of this work is to develop a threedimensional model of vehicle/track/ground interaction in the time domain that can include the consideration of soil nonlinearity. A threedimensional timedomain model of a coupled vehicle, track and ground has been developed in the finite element (FE) software ABAQUS. A new analysis approach has been adopted for modelling the moving vehicle without the need for a userdefined subroutine. The results from a track on a hemispherical ground model surrounded by infinite elements show good agreement with the results from a wavenumber finite element/boundary element method at lower speeds. However, significant differences are found for load speeds close to the critical speed for a homogeneous ground. This has been shown to be due to a relatively long transient in the numerical simulation that requires a considerable distance to achieve convergence to steadystate results. As a result, a very long model is required to derive the steadystate results. However, this becomes expensive because of the model geometry. Moreover, the results from the hemispherical model contain incorrect wholebody displacements due to the use of the infinite elements that make the ground model become unconstrained. Therefore, a cuboid model with a fixed boundary at the bottom is used for the further simulations to prevent these incorrect phenomena. Two different cuboid models, with or without the infinite elements at the sides, are compared. Finally, a wider cuboid model with fixed boundaries is used with appropriate Rayleigh damping which shows the best results and efficiency. A very long model, around 150~300 m, is required when the load speed is equal to the critical speed for a homogeneous soft ground. However, a shorter model is sufficient to obtain the steadystate results for a layered halfspace. For a load moving close to the critical speed on a layered halfspace, the track oscillates with a certain dominant frequency. An investigation is presented into the dependence of the oscillating frequency on the ground properties, taking account of the dispersive surface waves. Three different methods are used to investigate this oscillating frequency for a layered halfspace ground and a parametric study is carried out. The oscillating frequency is found to vary with the speed of the moving load and tends to decrease when the load speed increases. It mainly depends on the shear wave speed of the upper soil layer and the depth of this layer. A formula is introduced to estimate this oscillating frequency in a layered halfspace. Finally, soil nonlinearity is introduced in the FE model through a userdefined subroutine. The nonlinearity is specified in terms of the shear modulus reduction as a function of octahedral shear strain, based on data obtained from laboratory tests on soil samples. The model is applied to the soft soil site at Ledsgård in Sweden, from which extensive measurements are available from the late 1990s. It is shown that the use of a linear model based on the smallstrain soil parameters leads to an underestimation of the track displacements when the train speed approaches the critical speed, whereas the nonlinear model gives improved agreement with the measurements. However, the results are quite sensitive to the choice of nonlinear model. In addition, an equivalent linear model is considered in which the equivalent soil modulus is derived from the laboratory curve of shear modulus reduction using an 'effective' shear strain. It is shown that the predictions are improved by using a value of 20% of the maximum strain as the effective strain rather than the value of 65% commonly used in earthquake studies.
