Abstract
This paper presents an approach to shakedown of slab track substructures subjected to train loads. The train load is converted into a distributed moving load on the substructure surface using a simplified track analysis. Based on the lower-bound dynamic shakedown theorem, shakedown solutions for the slab track substructures are obtained over a range of train speeds between zero and the critical speed of the track. It is found the shakedown limit is largely influenced by the ratio of layer elastic moduli and the ratio of train speed to critical speed rather than their absolute values. An attenuation factor, as a function of the critical speed and the friction angle of subsoil, is proposed to effectively obtain the shakedown limit of the slab track substructure at any train speed. In light of the shakedown solutions, improvements to the existing design and analysis approaches are also suggested.
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References
Aboustit, B.L., Reddy, D.V.: Finite element linear programming approach to foundation shakedown. In: Proceedings of the International Symposium on Soils under Cyclic and Transient Loading, vol. 2, pp. 727–738. Swansea (1980)
Biot M (1937) Bending of an infinite beam on an elastic foundation. J Appl Mech Trans Am Soc Mech Eng 59: cA1–7
Ceradini, G.: Dynamic shakedown in elastic-plastic bodies. J. Eng. Mech. 106(3), 481-499 (1980)
Collins, I.F., Cliffe, P.F.: Shakedown in frictional materials under moving surface loads. Int. J. Numer. Anal. Methods Geomech. 11(4), 409–420 (1987)
Costa, P.A., Lopes, P., Cardoso, A.S.: Soil shakedown analysis of slab railway tracks: numerical approach and parametric study. Transp. Geotech. 16, 85–96 (2018)
Eason, G.: The stresses produced in a semi-infinite solid by a moving surface force. Int. J. Eng. Sci. 2(6), 581-609 (1965)
Gobel, C., Lieberenz, K., Richter, F.: Railway Foundation Engineering (Chinese). Translated by 2nd Railway Survey and Design Institute and PEC+S Group. Railway Publishing House, Beijing, China (2007)
Haldar, A.K., Reddy, D.V., Arockiasamy, M.: Foundation shakedown of offshore platforms. Comput. Geotech. 10(3), 231–245 (1990)
Heelis, M.E., Collop, A.C., Dawson, A.R., et al.: Predicting and measuring vertical track displacements on soft subgrades. In: Railway Engineering. London (99 May 1999)
Hu, Y.F., Li, N.F.: Subgrade Design Principle of the High-speed Railway of Unballasted Track (Chinese). Railway Publishing House, Beijing, China (2010)
Liu, S., Wang, J., Yu, H.S., Wanatowski, D.: Shakedown solutions for pavements with materials following associated and non-associated plastic flow rules. Comput. Geotech. 78, 218–266 (2016)
Liu, S., Wang, J., Yu, H.S., Wanatowski, D.: Shakedown for slab track substructures with stiffness variation. Geotech. Res. 5(1), 31–38 (2018)
Liu, S., Wang, J.: Application of shakedown theory in track substructure design. Proc. Inst. Civi. Eng. Ground Improv. 172(2), 116–123 (2019)
Melan, E.: Der spannungsgudstand eines Henky-Mises Schen Kontinuums Bei Verlandicher Belastung. Sitzungberichte der Ak Wissenschaften Wie 47(73) (1938)
Nguyen, A.D., Hachemi, A., Weichert, D.: Application of the interior-point method to shakedown analysis of pavements. Int. J. Numer. Methods Eng. 75, 414–439 (2008)
Ponter, A.R.S., Hearle, A.D., Johnson, K.L.: Application of the kinematical shakedown theorem to rolling and sliding point contacts. J. Mech. Phys. Solids 33, 339–362 (1985)
Raad. L., Weichert, D., Najm, W.: Stability of multilayer systems under repeated loads. Transp. Res. Rec. 1207, 181–186 (1988)
Sadrekarimi, J., Akbarzad, M.: Comparative study of methods of determination of coefficient of subgrade reaction. Electron. J. Geotech. Eng. 14(s1–6), 211–216 (2009)
Sharp, R.W., Booker, J.R.: Shakedown of pavements under moving surface loads. J. Transp. Eng. 110(1), 1-14 (1984)
Vesic, A.B.: Bending of beams resting on isotropic elastic solid. J. Eng. Mech. 87(2), 35–54 (1961)
Wang, J., Liu, S., Yang, W.: Dynamics shakedown analysis of slab track substructures with reference to critical speed. Soil Dyn. Earthq. Eng. 106, 1–13 (2018)
Wang, J., Yu, H.S.: Shakedown analysis for design of flexible pavements under movingloads. Road. Mater. Pavement Des. 14, 703–722 (2013)
Wang, J., Yu, H.S.: Shakedown and residual stresses in cohesive-frictional half-space under moving surface loads. Geomech. Geoeng. Int. J. 8, 1–14 (2013)
Wang, J., Yu, H.S.: Three-dimensional shakedown solutions for anisotropic cohesivefrictional materials under moving surface loads. Int. J. Numer. Anal. Methods Geomech. 38, 331–348 (2014)
Yu, H.S., Wang, J.: Three-dimensional shakedown solutions for cohesive-frictional materials under moving surface loads. Int. J. Solids Struct. 49, 3797–3807 (2012)
Yu, H.S.: 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 (2005)
Yu, H.S., Hossain M.Z.: Lower bound shakedown analysis of layered pavements using discontinuous stress fields. Comput Methods Appl. Mech. Eng. 167, 209–222 (1998)
Zhuang, Y., Wang, K.Y.: Three-dimensional shakedown analysis of ballasted railway structures under moving surface loads with different load distributions. Soil. Dyn. Earthq. Eng. 100, 296–300 (2017)
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Financial support from National Natural Science Foundation of China (Grant No. 51408326) and Ningbo Natural Science Foundation (Grant No. 2018A61035) is gratefully acknowledged.
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Wang, J., Yu, HS., Liu, S. (2021). Shakedown Limits of Slab Track Substructures and Their Implications for Design. In: Pisano, A., Spiliopoulos, K., Weichert, D. (eds) Direct Methods. Lecture Notes in Applied and Computational Mechanics, vol 95. Springer, Cham. https://doi.org/10.1007/978-3-030-48834-5_11
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