Skip to main content
SpringerLink
Log in

Shakedown analysis of ballasted track structure using three-dimensional finite element techniques

  • Research Paper
  • Published:
Acta Geotechnica Aims and scope Submit manuscript

Abstract

Shakedown analysis is an attractive method for determining the capacity of geostructures to sustain repeated loads involving a large number of cycles, e.g. rolling and sliding train wheel loads. Its main advantage is that it comes at a significantly reduced computational cost, compared to standard time-domain analyses. An essential component of shakedown analysis is the derivation of closed-form solutions to compute stresses due to the external repeated loads, a task that is not always feasible for complex problems as the ballasted rail track discussed herein. To tackle this, we present in this paper the use of finite element tools to obtain a quasi-lower-bound shakedown load numerically. The proposed method is based on the computation of the three-dimensional elastic stress field numerically, and the estimation of the shakedown load iteratively via an optimisation subroutine implemented in ABAQUS. Following a short presentation of this concept, we compare the elastic stress fields from models featuring varying degree of complexity, with the aim of identifying an optimal discretisation of the problem. This approach can be used for optimising the design of ballasted track structure, and this concept is briefly presented via a parametric study.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. American Railway Engineering and Maintenance-of-Way Association (2012) AREMA manual for railway engineering, vol 1. American Railway Engineering and Maintenance-of-Way Association, Landover

    Google Scholar 

  2. Bocciarelli M, Cocchetti G, Maie G (2004) Shakedown analysis of train wheels by Fourier series and nonlinear programming. Eng Struct 26:455–470

    Article  Google Scholar 

  3. Boulbibane M, Weichert D (1997) Application of shakedown theory to soils with non-associated flow rules. Mech Res Commun 24(5):516–519

    Article  Google Scholar 

  4. Brown SF, Yu HS, Juspi S, Wang J (2012) Validation experiments for lower-bound shakedown theory applied to layered pavement systems. Géotechnique 62(10):923–932

    Article  Google Scholar 

  5. Chazallon C, Allou F, Hornych P, Mouhoubi S (2009) Finite elements modelling of the long-term behaviour of a full-scale flexible pavement with the shakedown theory. Int J Numer Anal Meth Geomech 33(1):45–70

    Article  Google Scholar 

  6. China Railway Ministry (2010) Code for design of high-speed railway (for trial implementation). China Railway Publishing House, Beijing

    Google Scholar 

  7. Eason G (1965) The stresses produced in a semi-infinite solid by a moving surface force. Int J Eng Sci 2(6):581–609

    Article  Google Scholar 

  8. Galvin P, Romero A, Dominguez J (2010) Fully three-dimensional analysis of high-speed train–track–soil-structure dynamic interaction. J Sound Vib 329:5147–5163

    Article  Google Scholar 

  9. Ghadimi B, Nikraz H, Rosano M (2016) Dynamic simulation of a flexible pavement layers considering shakedown effects and soil-asphalt interaction. Transp Geotech 7:40–58

    Article  Google Scholar 

  10. Hadda N, Wan R (2018) Micromechanical analysis of cyclic and asymptotic behaviors of a granular backfill. Acta Geotech. https://doi.org/10.1007/s11440-018-0733-7

    Article  Google Scholar 

  11. Ishikawa T, Sekine E, Miura S (2011) Cyclic deformation of granular material subjected to moving-wheel loads. Can Geotech J 48(5):691–703

    Article  Google Scholar 

  12. Johnson KL (1985) Contact mechanics. Cambridge University Press, Cambridge

    Book  Google Scholar 

  13. Kapoor A, Williams JA (1996) Shakedown limits in rolling-sliding point contacts on an anisotropic half-space. Wear 191(1):256–260

    Article  Google Scholar 

  14. Koiter WT (1960) General theorems for elastic–plastic solids. In: Sneddon IN, Hill R (eds) Progress in solid mechanics. North Holland, Amsterdam, pp 165–221

    Google Scholar 

  15. Krabbenhøft K, Lyamin AV, Sloan SW (2007) Shakedown of a cohesive-frictional half-space subjected to rolling and sliding contact. Int J Solids Struct 44(11–12):3998–4008

    Article  Google Scholar 

  16. Krylov VV, Ferguson C (1994) Calculations of low-frequency ground vibrations from railway trains. Appl Acoust 42:199–213

    Article  Google Scholar 

  17. Langueh AMG, Brunel JF, Charkaluk E, Dufrénoy P, Tritsch JB, Demilly F (2013) Effects of sliding on rolling contact fatigue of railway wheels. Fatigue Fract Eng Mater Struct 36(6):515–525

    Article  Google Scholar 

  18. Li HX (2010) Kinematic shakedown analysis under a general yield condition with non-associated plastic flow. Int J Mech Sci 52:1–12

    Article  Google Scholar 

  19. Li HX, Yu HS (2006) A nonlinear programming approach to kinematic shakedown analysis of frictional materials. Int J Solids Struct 43:6594–6614

    Article  Google Scholar 

  20. Makino T, Kato T, Hirakawa K (2012) The effect of slip ratio on the rolling contact fatigue property of railway wheel steel. Int J Fatigue 36(1):68–79

    Article  Google Scholar 

  21. Melan E (1938) Theorie Statisch Unbestimmter Tragwerke aus idealplastischem Baustoff. Sitzungsbericht der Akademie der Wissenschaften (Wien) Abt IIA 195:145–195

    Google Scholar 

  22. Naeimi M, Li Z, Petrov R, Dollevoet R, Sietsma J, Wu J (2014) Substantial fatigue similarity of a new small-scale test rig to actual wheel-rail system. World Acad Sci Eng Technol 8:1830–1838

    Google Scholar 

  23. Nejad RM, Farhangdoost K, Shariati M (2015) Numerical study on fatigue crack growth in railway wheels under the influence of residual stresses. Eng Fail Anal 52:75–89

    Article  Google Scholar 

  24. Nguyen AD, Hachemi A, Weichert D (2008) Application of the interior-point method to shakedown analysis of pavements. Int J Numer Meth Eng 75(4):414–439

    Article  Google Scholar 

  25. Nguyen K, Goicolea JM, Galbadon F (2014) Comparison of dynamic effects of high-speed traffic load on ballasted track using a simplified two-dimensional and full three-dimensional model. Proc Inst Mech Eng F J Rail Rapid Transit 228(2):128–142

    Article  Google Scholar 

  26. Paixão A, Fortunato E, Calçada R (2015) The effect of differential settlements on the dynamic response of the train-track system: a numerical study. Eng Struct 88:216–224

    Article  Google Scholar 

  27. Raad L, Weichert D (1995) Stability of pavement structures under long term repeated loading. In: Mroz Z, Weichert D, Dorosz S (eds) Inelastic behaviour of structures under variables loads. Kluwer Academic Publishers, Dordrecht, pp 473–496

    Chapter  Google Scholar 

  28. Raad L, Weichert D, Najm W (1988) Stability of multilayer systems under repeated loads. Transp Res Rec 1207:181–186

    Google Scholar 

  29. Ringsberg JW, Franklin FJ, Josefson BL, Kapoor A, Nielsen JC (2005) Fatigue evaluation of surface coated railway rails using shakedown theory, finite element calculations, and lab and field trials. Int J Fatigue 27(6):680–694

    Article  Google Scholar 

  30. Selig ET, Waters JM (1994) Track geotechnology and substructure management. Thomas Telford, London

    Book  Google Scholar 

  31. Sharp RW, Booker JR (1984) Shakedown of pavements under moving surface loads. J Transp Eng 110(1):1–14

    Article  Google Scholar 

  32. Suiker AS, de Borst R (2003) A numerical model for the cyclic deterioration of railway tracks. Int J Numer Meth Eng 57(4):441–470

    Article  Google Scholar 

  33. Taraf M, Zahaf EH, Oussouaddi O, Zeghloul A (2010) Numerical analysis for predicting the rolling contact fatigue crack initiation in a railway wheel steel. Tribol Int 43:585–593

    Article  Google Scholar 

  34. Van KD, Maitournam MH (2003) Rolling contact in railways: modelling, simulation and damage prediction. Fatigue Fract Eng Mater Struct 26(10):939–948

    Article  Google Scholar 

  35. Wei X, Wang G, Wu R (2016) Prediction of traffic loading-induced settlement of low-embankment road on soft subsoil. Int J Geomech 17(2):06016016

    Article  Google Scholar 

  36. Yu HS (2005) Three-dimensional analytical solutions for shakedown of cohesive-frictional materials under moving surface loads. Proc R Soc A Math Phys Eng Sci 461:1951–1964

    Article  MathSciNet  Google Scholar 

  37. Zhao X, Li Z (2015) A three-dimensional finite element solution of frictional wheel–rail rolling contact in elasto-plasticity. Proc Inst Mech Eng J J Eng Tribol 229(1):86–100

    Article  Google Scholar 

  38. Zhao J, Sloan SW, Lyamin AV, Krabbenhøft K (2008) Bounds for shakedown of cohesive-frictional materials under moving surface loads. Int J Solids Struct 45(11):3290–3312

    Article  Google Scholar 

  39. Zhuang Y, Wang KY (2017) Three-dimensional shakedown analysis of ballasted railway structures under moving surface loads with different load distributions. Soil Dyn Earthq Eng 100:296–300

    Article  Google Scholar 

Download references

Acknowledgements

The financial support of National Key R&D Program of China (No. 2016YFC0800200), the financial support sponsored by Qing Lan Project, A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (Grant No. 1105007138), the Open Fund of National Engineering Laboratory of Highway Maintenance Technology (No. kfj180106, Changsha University of Science and Technology), and the Fundamental Research Funds for the Central Universities (Grant No. 2242018K40133) is acknowledged. The first author would like to acknowledge the support from China Scholarship Council and the support provided to him by the ARC Centre of Excellence for Geotechnical Science and Engineering at The University of Newcastle, NSW Australia.

Author information

Authors and Affiliations

  1. School of Civil Engineering and Architecture, Zhejiang University of Technology, Hangzhou, 310014, China

    Kangyu Wang

  2. Key Laboratory for RC and PRC Structures of Education Ministry, School of Civil Engineering, Southeast University, No. 2 Sipailou, Nanjing, 210096, Jiangsu, China

    Yan Zhuang

  3. National Engineering Laboratory of Highway Maintenance Technology, Changsha University of Science and Technology, Changsha, 410114, Hunan, China

    Yan Zhuang

  4. ARC Centre of Excellence for Geotechnical Science and Engineering, Faculty of Engineering and Built Environment, The University of Newcastle, Callaghan, NSW, 2308, Australia

    George Kouretzis & Scott William Sloan

Authors
  1. Kangyu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yan Zhuang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. George Kouretzis
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Scott William Sloan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yan Zhuang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, K., Zhuang, Y., Kouretzis, G. et al. Shakedown analysis of ballasted track structure using three-dimensional finite element techniques. Acta Geotech. 15, 1231–1241 (2020). https://doi.org/10.1007/s11440-019-00818-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-019-00818-6

Keywords

Search

Navigation