Critical velocity modelling of high-speed rail lines
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Increased train speeds result in elevated railway track vibrations. This is undesirable because high track deflections can cause rapid track degradation and safety concerns. To understand the relationship between train speed and track vibrations and to investigate remedial measures, this thesis presents three computational approaches. The first method is intended for use during the early design stage of a new line, and is capable of predicting the speed at which track deflections will be greatest (aka the ‘critical speed’). The method analyses the dispersion relationships of the track and the soil and uses their intersection to compute the critical speed. It is advantageous because the procedure is fast and fully automated, thus removing the need for two dimensional image processing, which is often required for dispersion analysis. The model is validated using larger 2.5D finite element simulations. Using the method, a variety of track-soil variables is investigated to determine their influence on the critical speed, including: track type, track depth, track mass, railpad stiffness and soil layer configuration. The second approach is intended for use on sections of new high speed line, where the train speed is found to be greater than 50% of the critical speed (e.g. calculated using the first approach). It is designed to calculate the relationship between train speed and track deflection, known as the dynamic amplification function. It, therefore, allows designers to determine track displacements for a range of speeds and the effect of changing different track-soil properties. The proposed method is semi-analytical, and couples a thin layer finite element formulation for the soil with an analytical approach for the track. The model is validated using field data from the Ledsgård site, Sweden, and then used to investigate axle spacing, train passage direction, slab tracks and soil stiffness. The third approach is intended for detailed analyses of complex critical velocity sites and for cases where mitigation measures require appraisal. The model is a three dimensional finite element model developed using the commercial software ABAQUS. It is a fully coupled train-track-soil system which considers train-track interaction. It is validated using field data from two European sites (Ledsgård, Sweden and Carregado, Portugal) and strong agreement is found. The method is then extended to simulate potential remediation measures such as stone columns and slab track. The three approaches are used to conclude that, in general, increasing rail bending stiffness and railpad stiffness results in an increased critical velocity for ballasted track. However, for concrete slab tracks, these variables have minimal effect because slab track already has a significant bending stiffness. It is also found that soil saturation results in a reduced critical velocity and that if the soil has a deep uppermost layer, the critical speed is equal to the shear velocity of that layer. In terms of vibration levels, it is concluded that increasing the stiffness of the supporting soil results in a significant reduction in track vibration. This is particularly true for the case study of Ledsgård, Sweden, which has a low stiffness layer sandwiched between two stiffer layers. For vibration mitigation methods, it is found that the use of stone columns is an effective method to reduce track deflections, and that they should be deployed to a depth covering the softest soil layers.