THE BASIS OF MATHEMATICAL DESCRIPTION FOR WAVE MODEL OF STRESSES PROPAGATION IN RAILWAY TRACK

D. M. Kurhan

Abstract


Purpose. Modern scientific research has repeatedly cited practical examples of the dynamic effects of railway track operation that go beyond the static calculation schemes. For the track sections where the train speed is approaching to the velocity of wave propagation in the slab track layers such issues are of particular relevance. An adequate tool for the study of such issues can be the use of the wave theory of stress propagation. The purpose of the article is the creation of a mathematical description of the basic principles of the stress propagation wave model in the railway track, which can be used as a basis for the practical development of the relevant calculation system. Methodology. The model of stress-strain states of the railway track on the basis of the stress wave propagation theory is to bring together the equations of the geometry of the outline of the space systems that is involved in the interaction at a given time, and the dynamic equilibrium equations of deformation. The solution is based on the use of the laws of the theory of elasticity. The wave front is described by an ellipsoid equation. When determining the variation in time of the surface position of the ellipsoid a vector approach is used. Findings. The geometry equations of the wave motion determine the volumes of material layers of the slab track involved in the interaction at a given time. The dynamic equilibrium determination of the deformed condition of the space bounded by the wave front makes it possible to calculate both the stresses and strains, and their changes during the time of the load perception. Thus, mathematical descriptions of the processes that occur in the perception of the load by the elements of railway track at high speeds were obtained. Originality. The simulation tasks of the track and rolling stock interaction, in particular taking into account the dynamic deflection of slab track were further developed. For the first time the article presents the basics of the mathematical description of the wave stress propagation model in the railroad track, which can be used to perform practical calculations. Practical value. The obtained data can be used to justify the track construction or establishing appropriate values of permissible speeds for the introduction of train motion with high speeds.


Keywords


railway track; track and rolling stock interaction; wave model; high-speed movement; theory of elasticity

References


Brandl, Kh., & Paulmichl, A. (2007). Vzaimodeystviye osnovaniy i sooruzheniy vysokoskorostnykh zheleznykh dorog. Razvitiye gorodov i geotekhnicheskoye stroitelsttvo – Urban Development and Geotechnical Construction, 11, 157-164.

Danilenko, E. I. (2010). Zaliznychna koliia. Tom 2. Kyiv: Inpres.

Danilenko, E. I. (2015). Novitni doslidzhennia bichnoi pruzhnosti reikovykh nytok pry spilnii dii vertykalnykh i horyzontalnykh syl. Nauka ta prohres transportu – Science and Transport Progress, 6, 65-77. doi:10.15802/stp2015/57021

Danilenko, E. I., & Rybkin, V. V. (2004). Pravyla rozrakhunkiv zaliznychnoi kolii na mitsnist i stiikist: TsP-0117. Kyiv: Transport Ukrainy.

Kolskiy, G. (1955). Volny napryazheniya v tverdykh telakh. Moscow: Inostrannaya literatura.

Kurhan, D. (2015). Modelirovaniye vzaimodeystviya puti i podvizhnogo sostava s uchetom vremeni progiba podrelsovogo osnovaniya. Proyektirovaniye razvitiya regionalnoy seti zheleznykh dorog, 3, 167-175.

Kurhan, N. B. (2015). Predposylki sozdaniya vysokoskorostnykh magistraley v Ukraine. Ukrainski zaliznytsi – Ukrainian Railways, 5-6, 16-21.

Landau, L. D., & Lifshits, L. D. (1987). Teoreticheskaya fizika. T. VII. Elastic theory. Moscow: Nauka.

Verkhovna Rada Ukrainy . Transportna stratehiia Ukrainy na period do 2020 roku. Verkhovna Rada Ukrainy, Retrieved from http://zakon1.rada.gov.ua/laws/show/2174-2010-%D1%80

Ukraine-EU Association Agreement . Uhoda pro asotsiatsiiu mizh Ukrainoiu, z odniiei storony, ta Yevropeiskym Soiuzom, yevropeiskym spivtovarystvom z atomnoi enerhii i yikhnimy derzhavamy-chlenamy, z inshoi storony. Ukraine-EU Association Agreement, Retrieved from http://www.kmu.gov.ua/kmu/docs/EA/00_Ukraine-EU_Association_Agreement_%28body%29.pdf

Connolly, D. P., & Forde, M. C. (2015). Use of Conventional Site Investigation Parameters to Calculate Critical Velocity of Trains from Rayleigh Waves. Transportation Research Record: Journal of the Transportation Research Board, 2476, 32-36. doi:10.3141/2476-05

Fischer, S. (2015). Investigation of inner shear resistance of geogrids built under granular protection layers and railway ballast. Nauka ta prohres transportu – Science and Transport Progress, 5, 97-106. doi:10.15802/stp2015/53169

Fisher, Sz., (2015). A vasúti zúzottkövek aprózódásvizsgálata egyedi laboratóriumi módszerrel. Sínek Világa, 57(3), 12-19.

Kurhan, D. M. (2015). Features of perception of loading elements of the railway track at high speeds of the movement. Nauka ta prohres transportu – Science and Transport Progress, 2, 136-145. doi:10.15802/stp2015/42172

Mosayebi, S., Zakeri, J., & Esmaeili, M. (2016). Some Aspects of Support Stiffness Effects on Dynamic Ballasted Railway Tracks. Periodica Polytechnica Civil Engineering, 60(3), 427-436. doi:10.3311/PPci.7933

Oliver, T., Wayne, M., & Kwon, J. (2016). Mechanical Stabilization of Unbound Layers to Increase Pavement Performance and Incorporation of Benefits into ME analysis. Procedia Engineering, 143, 896-910. doi:10.1016/j.proeng.2016.-06.153

Petrenko, V., & Sviatko, I. . Simulation of subgrade embankment on weak base. Nauka ta prohres transportu – Science and Transport Progress, 4(4), 198-204. doi:10.15802/stp2015/49286

Krylov, V. V., Dawson, A. R., Heelis, M. E., & Collop, A. C. (2000). Rail movement and ground waves caused by high-speed trains approaching track-soil critical velocities. Proc. of The Institution of Mechanical Engineers. Part F: Journal of Rail and Rapid Transit, 214(2), 107-116. doi:10.1243/0954409001531379

Kouroussis, G., Connolly, D. P., Olivier, B., Laghrouche, O., & Costa, P. A. (2016). Railway cuttings and embankments: Experimental and numerical studies of ground vibration. Science of the Total Environment, 557, 110-122. doi:10.1016/j.scitotenv.2016.03.016

Ruiz, J. F., Costa, P. A., Calçada, R., Rodríguez Luis, E. M., , & Colaço, A. (2016). Study of ground vibrations induced by railway traffic in a 3D FEM model formulated in the time domain: experimental validation. Structure and Infrastructure Engineering, 2016, 1-13. doi:10.1080/15732479.2016.1172649

Woldringh, R. F., & New, B. M. (1999). Embankment design for high speed trains on soft soils. Paper presented at 12th European Conf. on Soil Mechanics and Geotechnical Engineering


GOST Style Citations


  1. Брандль, Х. Взаимодействие оснований и сооружений высокоскоростных железных дорог / Х. Брандль, А. Паульмичл // Развитие городов и геотехн. стр-во. – 2007. – № 11. – С. 157–164.
  2. Даніленко, Е. І. Залізнична колія / Е. І. Да-ніленко : підруч. для ВНЗ. – Київ : Інпрес, 2010. – Т. 2. – 456 с.
  3. Даніленко, Е. І. Новітні дослідження бічної пружності рейкових ниток при спільній дії вертикальних і горизонтальних сил / Е. І. Даніленко // Наука та прогрес транспорту. – 2015. – № 6 (60). – С. 65–77. doi : 10.15802/stp2015/57021.
  4. Даніленко, Е. І. Правила розрахунків заліз-ничної колії на міцність і стійкість : ЦП-0117 / Е. І. Даніленко, В. В. Рибкін. – Киів : Транспорт України, 2004. – 64 с.
  5. Кольский, Г. Волны напряжения в твердых телах / Г. Кольский. – Москва : Иностр. лит., 1955. – 192 с.
  6. Курган, Д. Моделирование взаимодействия пути и подвижного состава с учетом времени прогиба подрельсового основания / Д. Курган // Проектирование развития региональной сети железных дорог : сб. науч. тр. / Дальневост. гос. ун-т путей сообщ. – Хабаровск, 2015. – Вып. 3. – С. 167–175.
  7. Курган, Н. Б. Предпосылки создания высокоскоростных магистралей в Украине / Н. Б. Курган // Укр. залізниці. – 2015. – № 5–6. – С. 16–21.
  8. Ландау, Л. Д. Теоретическая физика. Т. VII. Теория упругости / Л. Д. Ландау, Е. М. Лифшиц. – Москва : Наука, 1987. – 248 с.
  9. Транспортна стратегія України на період до 2020 року [Електронний ресурс] : схвалено розпорядж. Кабінету Міністрів України від 20 жовт. 2010 р. № 2174-р. – Режим доступу: http://zakon1.rada.gov.-ua/laws/show/2174-2010-%D1%80. – Назва з екрана. – Перевірено : 15.09.2016.
  10. Угода про асоціацію між Україною, з однієї сторони, та Європейським Союзом, європейським співтовариством з атомної енергії і їхніми державами-членами, з іншої сторони [Електронний ресурс]. – Режим доступу: http://www.kmu.gov.ua/kmu/docs/EA/00_Uk-raine-EU_Association_Agreement_%28body%29-.pdf. – Назва з екрана. – Перевірено : 15.09.2016.
  11. Connolly, D. P. Use of Conventional Site Investigation Parameters to Calculate Critical Velocity of Trains from Rayleigh Waves / D. P. Connolly, M. C. Forde // Transportation Research Record: J. of the Transportation Research Board. – 2015. – Vol. 2476. – P. 32–36. doi: http://dx.doi.org/10.3141/2476-05.
  12. Fischer, S. Investigation of inner shear resistance of geogrids built under granular protection layers and railway ballast / S. Fischer // Наука та прогрес транспорту. – 2015. – № 5 (59). – С. 97–106. doi:10.15802/stp20-15/53169.
  13. Fisher, Sz. A vasúti zúzottkövek aprózó-dásvizsgálata egyedi laboratóriumi módszerrel / Sz. Fisher // Sínek Világa. – 2015. – № 57 (3). – P. 12–19.
  14. Kurhan, D. M. Features of perception of loading elements of the railway track at high speeds of the movement / D. M. Kurhan // Наука та прогрес транспорту. – 2015. – № 2 (56). – С. 136–145. doi: 10.15802/stp20-15/42172.
  15. Mosayebi, S. Some Aspects of Support Stiffness Effects on Dynamic Ballasted Railway Tracks / S. Mosayebi, J. Zakeri, M. Esmaeili // Periodica  Polytechnica Civil Engineering. – 2016. – Vol. 3 (60). – P. 427–436. doi: 10.3311/PPci.7933.
  16. Oliver, T. Mechanical Stabilization of Unbound Layers to Increase Pavement Performance and Incorporation of Benefits into M-E analysis / T. Oliver, M. Wayne, J. Kwon // Procedia Engineering. – 2016. – Vol. 143. – P. 896–910. doi : 10.1016/j.proeng.2016.-06.153.
  17. Petrenko, V. Simulation of subgrade embankment on weak base / V. Petrenko, I. Sviatko // Наука та прогрес транспорту. – 2015. – № 4 (58). – С. 198–204. doi:10.15802/stp2015/49286.
  18. Rail movement and ground waves caused by high-speed trains approaching track-soil criti-cal velocities / V. V. Krylov, A. R. Dawson, M. E. Heelis, A. C. Collop // Proc. of The Institution of Mechanical Eng. Part F: J. of Rail and Rapid Transit. – 2000. – Vol. 214. – Iss. 2. – P. 107–116. doi: 10.1243/095440-9001531379.
  19. Railway cuttings and embankments: Experimental and numerical studies of ground vibration / G. Kouroussis, D. P. Connolly, B. Olivier [et al.] // Science of the Total Environment. – 2016. – Vol. 557–558. – P. 110–122. http://dx. doi: 10.1016/j.-scitotenv.2016.03.016.
  20. Study of ground vibrations induced by railway traffic in a 3D FEM model formulated in the time domain: experimental validation / J. F. Ruiz, P. A. Costa, R. Calçada [et al.] // Structure and Infrastructure Engineering. – 2016. – P. 1–13. doi: 10.1080/15732479.2016.11-72649.
  21. Woldringh, R. F. Embankment design for high speed trains on soft soils / R. F. Woldringh, B. M. New // Proc. of the 12th Europ. Conf. on Soil Mechanics and Geotechnical Engineering (7.06–10.06.1999). – Amsterdam, The Nether-lands, 1999. – Vol. 3. – P. 1703–1712.


DOI: https://doi.org/10.15802/stp2016/84032

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