Abstract
This paper discusses the dynamical behavior of a randomly-fluctuating heterogeneous continuum model of the ballast. The Young’s modulus is modeled as a random field parameterized by its average, its variance and a correlation model representing non-interpenetrating spheres. A numerical model of the ballast and the surrounding soil is then constructed based on an efficient implementation of an explicit spectral element solver on a large cluster of computers. This model allows to describe numerically the wave field generated in the ballast and soil by the passage of a train, as well as to construct dispersion equations for the ballast-soil model. The influence of heterogeneity is discussed by comparison with a similar model where the ballast is assumed homogeneous. Different values of the soil mechanical parameters are considered and compared. Finally, potential consequences for the design of the ballast are discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aki K (1969) Analysis of the seismic coda of local earthquakes as scattered waves. J Geohysical Res 74(2):615–631
Al Shaer A, Duhamel D, Sab K, Foret G, Schmitt L (2008) Experimental settlement and dynamic behavior of a portion of ballasted railway track under high speed trains. J Sound Vib 316(March):211–233
Alleyne D, Cawley P (1991) A two-dimensional Fourier transform method for the measurement of propagating multimode signals. J Acoust Soc Am 89(3):1159–1168
Arlaud E, D’Aguiar S, Balmes E (2014) Validation of a reduced model of railway track allowing long 3D dynamic calculation of train-track interaction. Comput Methods Recent Adv Geomech 193:1193–1198
Bagi K (2003) Statistical analysis of contact force components in random granular assemblies. Granular Matter 5(1):45–54
Bian X, Cheng C, Jiang J, Chen R, Chen Y (2015) Numerical analysis of soil vibrations due to trains moving at critical speed. Acta Geotech 11(2):281–294
BITRE (2003) Rail Infrastructure Pricing: Principles and Practice. Technical report, Bureau of Infrastructure, Transport and Regional Economics
Cohen G (2001) Higher-Order Numerical Methods for Transient Wave Equations., Scientific Computation Springer, New York
Connolly DP, Kouroussis G, Laghrouche O, Ho CL, Forde MC (2014) Benchmarking railway vibrations - track, vehicle, ground and building effects. Constr Build Mater
Correa L. de Abreu, Cottereau R, Quezada JC, Costa d’Aguiar S, Voivret C (2016b) Randomly-fluctuating heterogeneous continuum model of a granular medium. Comput Mech (submitted for publication)
Drescher A, De Jong GD (1972) Photoelastic verification of a mechanical model for the flow of a granular material. J Mech Phys Solids 20(5):337–340
Festa G, Vilotte JP (2005) The Newmark scheme as velocity-stress time-staggering: an efficient PML implementation for spectral element simulations of elastodynamics. Geophys J Int 161(3):789–812
Freitas da Cunha, JP (2013) Modelling of Ballasted Railway Tracks for High-Speed Trains. Ph.D. thesis, Universidad do Minho
Goddard JD (1990) Nonlinear elasticity and pressure-dependent wave speeds in granular media. Proc R Soc A Math Phy Eng Sci 430(1878):105–131
Guerin N (1996) Approche expérimentale et numérique du comportement du ballast des voies ferrées (in French)
Guillot L, Aubry L, Le Piver F, Mariotti C, Sèbe O, Thauvin E, Odonbaatar C, Ulziibat M, Demberel S, Sukhbaatar S (2014) Numerical simulation of seismic wave propagation: site effects. Chocs 45:29–36
Hoang TM, Alart P, Dureisseix D, Saussine G (2011) A Domain Decomposition method for granular dynamics using discrete elements and application to railway ballast. Ann Solid Struct Mech 2(2–4):87–98
Jacob X, Aleshin V, Tournat V, Leclaire P, Lauriks W, Gusev VE (2008) Acoustic probing of the jamming transition in an unconsolidated granular medium. Phys Rev Lett 100(158003):1–4
Jehel P, Cottereau R (2015) On damping created by heterogeneous yielding in the numerical analysis of nonlinear RC frame elements. Comput Struc 154:192–203
Jia X, Caroli C, Velicky B (1999) Ultrasound propagation in externally stressed granular media. Phys Rev Lett 82:1863–1866
Knopoff L (1964) A matrix method for elastic wave problems. Bull Seismol Soc Am 54(1):431–438
Komatitsch D (2005) The spectral-element method in seismology. Geophys Monogr Ser 157(55):205–227
Lagasse PE (1973) Higher-order finite-element analysis of topographic guides supporting elastic surface waves. J Acoust Soc Am 53(4):1116–1122
Lawney BP, Luding S (2014) Frequency filtering in disordered granular chains. Acta Mech 225:2385–2407
Leibig M (1994) Model for the propagation of sound in granular materials. Phys Rev E 49(2):1647–1656
Liu C-H, Nagel SR, Schecter DA, Coopersmith SN, Majumdar S, Narayan O, Witten TA (1995) Force fluctuations in bead packs. Science 269(5223):513–515
Paludo LC, Bouvier V, Cottereau R (2016) Scalable parallel scheme for sampling of Gaussian random fields over large domains. Int J Numer Meth Engrg, In preparation
Rosenblatt M (1952) Remarks on a multivariate transformation. Ann Math Stat, 470–472
Sheng X, Jones CJC, Thompson DJ (2004) A theoretical study on the influence of the track on train-induced ground vibration. J Sound Vib 272:909–936
Shinozuka M, Deodatis G (1991) Simulation of stochastic processes by spectral representation. Appl Mech Rev 44(4):191–204
Suiker ASJ (2002) The Mechanical Behaviour of Ballasted Railroad Tracks. Delft University of Technology, TU Delft
Ta Q-A, Clouteau D, Cottereau R (2010) Modeling of random anisotropic elastic media and impact on wave propagation. Eur J Comput Mech 19(1–3):241–253
Wellmann C, Wriggers P (2012) A two-scale model of granular materials. Comput Methods Appl Mech Eng 205–208:46–58
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
De Abreu Correa, L., Cottereau, R., Bongini, E., Costa d’Aguiar, S., Faure, B., Voivret, C. (2018). Impact of the Heterogeneity of the Ballast on the Dynamical Behavior of the Ballast-Soil System. In: Diez, P., Neittaanmäki, P., Periaux, J., Tuovinen, T., Bräysy, O. (eds) Computational Methods and Models for Transport. ECCOMAS 2015. Computational Methods in Applied Sciences, vol 45. Springer, Cham. https://doi.org/10.1007/978-3-319-54490-8_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-54490-8_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-54489-2
Online ISBN: 978-3-319-54490-8
eBook Packages: EngineeringEngineering (R0)