Randomly-fluctuating heterogeneous continuum model of a ballasted railway track

Abstract

This paper proposes a description of a granular medium as a stochastic heterogeneous continuum medium. The heterogeneity of the material properties field recreates the heterogeneous stress field in a granular medium. The stochastic approach means that only statistical information, easily available, is required to construct the model. The heterogeneous continuum model is calibrated with respect to discrete simulations of a set of railway ballast samples. As they are continuum-based, the equilibrium equations can be solved on a large scale using a parallel implementation of an explicit time discretization scheme for the Finite Element Method. Simulations representative of the influence on the environment of the passage of a train on a ballasted railway track clearly show the influence of the heterogeneity. These simulations seem to correlate well with previously unexplained overly damped measurements in the free field.

Dispersion analysis in ballasted railway tracks and Anderson localization in granular media

“…First, the setup of the model is described. Then, we provide some [46,4], where waves should propagate non-dispersively with the velocity of a Rayleigh wave. In a setting including a homogeneous ballast layer, the situation would be more complex, and probably involve dispersive waves in the waveguide [46].…”

“…Indeed, the latter produce vibration levels away from the track that are much larger than experimentally measured, while the former are too numerically expensive for such applications. Recently, a randomly-fluctuating heterogeneous continuum model of the ballast was proposed [4]. This model is based on continuum mechanics, so that it is parameterized with Lamé parameters and density, which are constant within the domain in classical models.…”

“…This model is based on continuum mechanics, so that it is parameterized with Lamé parameters and density, which are constant within the domain in classical models. In the proposed model, however, they fluctuate at the scale of the grains, which allows to recover the strong heterogeneity of the stress field, characteristic of granular media and very influential on its dynamic behavior [5,4]. Finally, the fluctuations of the mechanical parameters are modeled as random fields and parameterized with statistical parameters (average, variance, correlation length).…”

Stability of an explicit high‐order spectral element method for acoustics in heterogeneous media based on local element stability criteria

“…The analysis revealed the origin of instabilities that are often observed when the stability limit derived for homogeneous materials is adapted by simply using the lowest local velocity in Equation . The main limitation of the analysis presented in the preliminary work is the link between the periodicity of the material properties and the element size of the mesh, which precludes its application to a large class of problems, including those where the mechanical properties are modeled as realizations of random fields …”

“…The main limitation of the analysis presented in the preliminary work 18 is the link between the periodicity of the material properties and the element size of the mesh, which precludes its application to a large class of problems, including those where the mechanical properties are modeled as realizations of random fields. [19][20][21][22][23] The objective of this work is to obtain a stability criterion that is accurate for a general heterogeneous medium. The strategy follows a methodology commonly employed in a finite element context (or by other element-based methods) that consists of bounding the eigenvalues of a global matrix by the eigenvalues of the elemental matrices (Irons-Treharne theorem).…”