Abstract
The procedure presented in this work aims at providing a framework for studying settlement of ballast in zones with stiffness variation of the railway track support. The proposed procedure results from expanding an existing infinite periodic model of a railway track to account for variations in the stiffness of the foundation. Ballast is simulated via a linear lattice, whose dynamic response differs from that of a continuum. The expanded model is composed of three regions: a left region, which is semi-infinite and periodic; a mid-region, of finite length and where the properties of the foundation can change; and a right region, which is also semi-infinite and periodic and whose properties can differ from those of the left region. The equations of motion of the mid-region are written directly in the time domain, with the rail being described by finite elements. On the other hand, the left and right semi-infinite regions are treated semi-analytically in the frequency domain, and afterwards their responses are converted to the time domain, resulting in convolution integrals prescribed at the boundaries of the mid-region that simulate non-reflective boundaries. The final model only contains the degrees of freedom corresponding to the mid-region (which can be as short as the region where the stiffness variation is present), and that leads to faster calculations than if the boundaries were placed further away to dissipate undesired reflections. The method is cast in the time domain, and all elements are assumed to behave linearly. In the future, the model will be expanded to incorporate non-linear behaviour of the ballast. The presented method is validated by means of simple examples, and afterwards applied to a real scenario in which a culvert crosses a railway track. As presented, the method can be used to study the linear dynamics of transitions zones, study mitigation measures, and infer about indicators like force transmitted and energy dissipated, which might be useful to assess the development of settlement of the ballast.
Highlights
Previous studies and measurements indicate that differential ballast settlement occurs at a faster pace in regions where railway tracks experience variations in their support stiffness than in regions with homogeneous support [1,2]
Studies focusing on settlement of ballast can be categorized into field measurements and condition monitoring [3,4], in which the position of rails and the geometry of ballast are measured and monitored in the period between maintenance operations; lab tests [5,6,7], in which ballast layers are cyclically loaded and the evolution of its geometry is recorded; and numerical simulations, in which more or less complex mathematical models are formulated to predict the response of the track
Lab tests allow for a better control of the loading process and in this way are useful to derive constitutive laws for the ballast, but for studying railway track support stiffness changes this approach becomes unfeasible due to the space required to accommodate such features
Summary
Previous studies and measurements indicate that differential ballast settlement occurs at a faster pace in regions where railway tracks experience variations in their support stiffness than in regions with homogeneous support [1,2]. Faragau and K.N. van Dalen disruptions of the train schedules These regions of stiffness variation are of interest to railway researchers, since understanding the phenomena behind the accelerated degradation helps designing solutions to mitigate the issue. Lab tests allow for a better control of the loading process and in this way are useful to derive constitutive laws for the ballast (which can include mitigation measures such as geogrids [8] or binding polymers [9]), but for studying railway track support stiffness changes this approach becomes unfeasible due to the space required to accommodate such features.
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