In Hungarian design practice, the Zimmermann-Eisenmann quasi-static design method is employed to dimension track structures with embedded rails. This method determines the mean values of deformations and stresses using an infinitely long elastically embedded beam as the static frame. After establishing these mean values, the effects of track condition and speed are considered through Eisenmann multiplication, enabling the definition of design values. Conversely, international practices include methods that calculate deformations and stresses based on dynamic models incorporating viscoelastic embedding, directly accounting for speed but not dynamic effects due to track characteristics. This paper presents a solution to the dynamic problem, extending it to studying rotating frames beyond the commonly considered uniaxial solution. Each factor's effect is separately analyzed for track structures with embedded rail tracks, leading to a recommendation for the value of the "load multiplication factor".

On behalf of MÁV Hungarian State Railways Ltd., the authors carried out a research and development (R&D) project on behalf of the Budapest University of Technology and Economics, Department of Highway and Railway Engineering, on the subject of “Research and investigation of the causes of gauge narrowing by finite-element modeling in running track and turnout, and under operational and laboratory conditions”. The main objective of the research was to investigate the causes of localized defects of gauge narrowing in railway tracks based on machine and manual track measurements, laboratory measurements, and theoretical considerations. The measures proposed as a consequence of identifying the causes could significantly contribute to reducing the number and extent of local defects in the future. Furthermore, the research aims to develop new theories in less scientifically mature areas and provide procedures and instructions that professional engineers and practitioners can easily apply. The main areas of research, which are not exhaustive, are as follows: (i) the evaluation of the measurement results provided by track geometry measuring and recording cars; (ii) on-site investigations in the railway track in terms of gauge and rail profile measurements; and, based on these, (iii) the selection of concrete sleepers, which were removed from the track and subjected to more detailed geometrical investigations in the laboratory, together with the components of the rail reinforcement; (iv) the track–vehicle connection, tight running in straight and curved track sections under track confinement; (v) modeling of the stability and deflection of the rail when the rail fastenings lose part of their supporting function; and (vi) finite element modeling of the concrete sleepers under operating conditions such as slow deformation of the concrete, temperature variation effects, and lateral support on the ballast. In the already-narrowed track section, the tight vehicle running is not the cause of the track gauge narrowing but a consequence, so it is not investigated in this paper.

This paper deals with the time-frequency characteristic analysis for track geometry irregularities using field data recorded by a comprehensive track inspection train. The parameters of the track gauge and the left and right rail alignment are considered to identify their characteristic wavelengths and the locations of their waveforms. In addition to the conventional time and frequency domain analysis, auto-adaptive signal decomposition techniques are used on four pre-selected track sections. During the time series analysis of the track gauge, the cumulative difference from the mean value is calculated, which makes it possible to distinguish the track section constructed with non-standard initial track gauges. The sensitive wavelengths of the track irregularities are obtained from the proper allocation of wavelength ranges in the Fourier Amplitude Spectrum of the original signal and the Fourier transform of the components detected by the Variational Mode Decomposition. This analysis can elucidate the wavelengths and positions of track irregularities that affect vehicle responses.