MS14.5 - Moving Loads

The serviceability of a high-speed railway track depends on the limitation of the dynamic amplifications that occur for load velocities near the critical one, that is, it depends on the ability of its substructure to dissipate the energy transmitted by the transit of the moving loads. This substructure is composed of many stones of several sizes and shapes, interacting according to the laws of unilateral and frictional contact mechanics. In (Toscano Corrêa, Pinto da Costa, Simões, Finite element modelling of a rail resting on a Winkler-Coulomb foundation and subjected to a moving concentrated load, International Journal of Mechanical Sciences, 140, 432-445, 2018), a new foundation model with a non-smooth character nearer to the true frictional dissipative character of the ballast was proposed. In that study a time stepping algorithm specially designed to deal with non-smooth dynamical systems was for the first time applied to distributed frictional foundations and new conclusions on critical velocities, maximal displacements and dynamic amplification factors were drawn. In this work a finite element program is developed to compute the steady state solution of an Euler-Bernoulli beam under a moving load, on a foundation composed of a continuous distribution of linear elastic springs associated in parallel with a continuous distribution of Coulomb frictional dampers. The motion of the beam is governed by a partial differential inclusion that is semi-discretized in space, using the finite element method, as a system of ordinary differential inclusions and integrated using a special implementation of the Non-smooth Dynamics Method (NSD) adapted to distributed Coulomb friction. The steady state solutions are then obtained for different values of the maximum force per unit length of the frictional dampers and for different values of the load velocity at both subcritical and supercritical regimes. The goal of this study is to generalize, for more realistic behaviours, the analyses in the literature so that it can be of interest in terms of engineering analysis of high-speed railway tracks.

Ballasted track has been extensively employed in railway lines, even in high-speed railways. In recent years, with the increasing of train speed, the vibrations of the railway track become much more intense, which significantly accelerates the track deterioration, particularly leading to the excessive permanent settlement in the ballasted trackbed, consequently affecting the safety and comfort of train operation. Hence, comprehensive evaluations of the dynamic behaviors and the irreversible deformation of the granular trackbed under high-speed train loading are essential for track condition assessment and improving track maintenance practices. This study focuses on the distinct intense vibration of the track structure and the induced remarkable plastic deformation in the ballast layer under high-speed train loading, especially their particle-scale mechanisms, via a series of discrete element method (DEM) simulations. The DEM model of the granular trackbed is established with realistic polygon elements, and then validated with the measurements from full-scale model tests. Subsequently, the validated numerical model is used to simulate the response of railway ballast under different train speeds. Results indicate that the faster train speed motivates vigorous shaking of the ballast particles, manifesting as violent vibration of the track structure at the macroscopic level, thereby activating particles to move, leading to the instability of the inter-particle supporting structure in the ballast layer. Consequently, the migration and rearrangement of the ballast particles increases, and greater permanent deformation accumulates in the granular trackbed. Furthermore, the trackbed is becoming hard to stabilize with the increasing of the train speed especially when the shakedown threshold is reached, where the permanent deformation of railway ballast would rise nearly endlessly instead of presenting an obvious slow tendency. This paper discusses the dynamic response and cyclic settlement of railway ballast. These conclusions will guide the potential methods to alleviate the permanent deformation in high-speed railways.

Irregular interfaces between soil layers exist in the natural foundation. This paper proposes a thin layer method to calculate the three-dimensional (3D) ground vibration of layered soils with irregular interfaces by a moving load. Based on the double Fourier transform, the system governing equations in terms of the thin layer element for the elastic medium are obtained in the frequency-wavenumber domain; the stiffness matrices of the semi-infinite thin-layer element and the finite-length thin-layer element are derived through the modal superposition principle. The perfectly matched layers (PMLs) are subsequently introduced to simulate the wave propagation in the bottom half-space. Making use of the semi-infinite and the finite-length thin-layer elements as well as the PMLs, a calculation model is finally developed to obtain the 3D dynamic responses for a moving point load acting on a layered half-space with irregular interfaces. The accuracy of the proposed method is verified by comparing with the existing methods. Finally, the dynamic responses of the foundation with inclined layered interface induced by a moving harmonic load acting on the ground surface are investigated. The results show that the inclination of layer interfaces and the velocity of the moving load exhibits a significant effect on the ground vibration. The irregular interface needs to be considered in the evaluation of ground vibration generated by a moving load.