Analytical Model to Predict Dynamic Responses of Railway Subgrade due to High-Speed Trains Considering Wheel–Track Interaction
Publication: International Journal of Geomechanics
Volume 16, Issue 2
Abstract
In this paper, a full vehicle–track–ground coupling model is presented to evaluate the dynamic response of the subgrade due to high-speed trains. The vehicle was modeled as a multibody. The track was considered as an Euler beam. The ground soil was regarded as two elastic layers and a poroelastic half-space, taking into account a complete subgrade/subsoil system. The wheel–track interaction was considered by using the linear Hertzian contact theorem. The stiffness matrix method and the Fourier transform were introduced to deal with formulations of the coupling model in a transformed domain, and the time-domain solutions were derived by using the fast Fourier transform algorithm. The wheel–track contact forces and the dynamic responses of the subgrade were studied, and the effects of the rail irregularity and the properties of the subgrade bed were then investigated. It was concluded that the dynamic responses of the subgrade are significant compared with responses induced by the axle load and are influenced greatly by rail irregularity and parameters of the subgrade bed.
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Acknowledgments
The authors gratefully acknowledge the financial support of the National 973 Project of China (No. 2013CB036405) and the Natural Science Foundation of China (Nos. 41472286, 51209201, 51279198, and 41402276).
References
Alves Costa, P., Calçada, R., and Silva Cardoso, A. (2011). “Track-ground vibrations induced by railway traffic: In-situ measurements and validation of a 2.5 D FEM-BEM model.” Soil Dyn. Earthquake Eng., 32(1), 111–128.
Ang, K. K., and Dai, J. (2013). “Response analysis of high-speed rail system accounting for abrupt change of foundation stiffness.” J. Sound Vib., 332(12), 2954–2970.
Apsel, R. J., and Luco, J. E. (1983). “On the Green’s functions for a layered half-space: Part II.” Bull. Seismol. Soc. Am., 73(4), 931–951.
Beskou, N. D., and Theodorakopoulos, D. D. (2011). “Dynamic effects of moving loads on road pavements: A review.” Soil Dyn. Earthquake Eng., 31(4), 547–567.
Biot, M. A. (1956). “Theory of propagation of elastic waves in a fluid-saturated porous solid. I: Low-frequency range. II: Higher frequency range.” J. Acoust. Soc. Am., 28(2), 168–191.
Biot, M. A. (1962). “Mechanics of deformation and acoustic propagation in porous media.” J. Appl. Phys., 33(4), 1482–1498.
Cai, Y., Cao, Z., Sun, H., and Xu, C. (2010). “Effects of the dynamic wheel–rail interaction on the ground vibration generated by a moving train.” Int. J. Solids Struct., 47(17), 2246–2259.
Cai, Y., Sun, H., and Xu, C. (2008a). “Response of railway track system on poroelastic half-space soil medium subjected to a moving train load.” Int. J. Solids Struct., 45(18), 5015–5034.
Cai, Y., Sun, H., and Xu, C. (2008b). “Three-dimensional analyses of dynamic responses of track–ground system subjected to a moving train load.” Comput. Struct., 86(7), 816–824.
Cao, Z., and Boström, A. (2013). “Dynamic response of a poroelastic half-space to accelerating or decelerating trains.” J. Sound Vib., 332(11), 2777–2794.
Çelebi, E., and Kırtel, O. (2013). “Non-linear 2-D FE modeling for prediction of screening performance of thin-walled trench barriers in mitigation of train-induced ground vibrations.” Constr. Build. Mater., 42, 122–131.
Çelebi, E., and Schmid, G. (2005). “Investigation of ground vibrations induced by moving loads.” Eng. Struct., 27(14), 1981–1998.
El Kacimi, A., Woodward, P., Laghrouche, O., and Medero, G. (2012). “Time domain 3D finite element modelling of train-induced vibration at high speed.” Comput. Struct., 118, 66–73.
Esveld, C. (2001). “Noise and vibration.” Modern railway track, MRT-productions, Zaltbommel, Netherlands, 462–464.
FHWA (Federal Highway Administration). (1998). “Analyses relating to pavement material characterizations and their effects on pavement performance.” Rep. FHWA-RD-97-085, Austin, TX.
Ferrara, R., Leonardi, G., and Jourdan, F. (2012). “Numerical modelling of train induced vibrations.” Proc. Soc. Behav. Sci., 53(3), 155–165.
Galvín, P., Romero, A., and Domínguez, J. (2010). “Fully three-dimensional analysis of high-speed train-track-soil-structure dynamic interaction.” J. Sound Vib., 329(24), 5147–5163.
Gomes Correia, A., and Cunha, J. (2014). “Analysis of nonlinear soil modelling in the subgrade and rail track responses under HST.” Transp. Geotech., 1(4),147–156.
Hall, L. (2003). “Simulations and analyses of train-induced ground vibrations in finite element models.” Soil Dyn. Earthquake Eng., 23(5), 403–413.
Haskell, N. A. (1953). “The dispersion of surface waves on multilayered media.” Bull. Seismol. Soc. Am., 43(1), 17–34.
Kargarnovin, M. H., and Younesian, D. (2004). “Dynamics of Timoshenko beams on Pasternak foundation under moving load.” Mech. Res. Commun., 31(6), 713–723.
Karlström, A., and Boström, A. (2006). “An analytical model for train-induced ground vibrations from railways.” J. Sound Vib., 292(1), 221–241.
Kausel, E., and Roësset, J. M. (1981). “Stiffness matrices for layered soils.” Bull. Seismol. Soc. Am., 71(6), 1743–1761.
Kouroussis, G., Gazetas, G., Anastasopoulos, I., Conti, C., and Verlinden, O. (2011a). “Discrete modelling of vertical track–soil coupling for vehicle–track dynamics.” Soil Dyn. Earthquake Eng., 31(12), 1711–1723.
Kouroussis, G., and Verlinden, O. (2013). “Prediction of railway induced ground vibration through multibody and finite element modelling.” Mech. Sci., 4(1), 167–183.
Kouroussis, G., Verlinden, O., and Conti, C. (2011b). “Free field vibrations caused by high-speed lines: Measurement and time domain simulation.” Soil Dyn. Earthquake Eng., 31(4), 692–707.
Lak, M. A., Degrande, G., and Lombaert, G. (2011). “The effect of road unevenness on the dynamic vehicle response and ground-borne vibrations due to road traffic.” Soil Dyn. Earthquake Eng., 31(10), 1357–1377.
Lefeuve-Mesgouez, G., Le Houédec, D., and Peplow, A. (2000). “Ground vibration in the vicinity of a high-speed moving harmonic strip load.” J. Sound Vib., 231(5), 1289–1309.
Lefeuve-Mesgouez, G., and Mesgouez, A. (2012). “Three-dimensional dynamic response of a porous multilayered ground under moving loads of various distributions.” Adv. Eng. Software, 46(1), 75–84.
Lefeuve-Mesgouez, G., Peplow, A., and Le Houédec, D. (2002). “Surface vibration due to a sequence of high speed moving harmonic rectangular loads.” Soil Dyn. Earthquake Eng., 22(6), 459–473.
Liang, B., Zhu, D., and Cai, Y. (2001). “Dynamic analysis of the vehicle–subgrade model of a vertical coupled system.” J. Sound Vib., 245(1), 79–92.
Lombaert, G., and Degrande, G. (2009). “Ground-borne vibration due to static and dynamic axle loads of InterCity and high-speed trains.” J. Sound Vib., 319(3), 1036–1066.
Lu, J.-F., and Hanyga, A. (2004). “Fundamental solution for a layered porous half space subject to a vertical point force or a point fluid source.” Comput. Mech., 35(5), 376–391.
Lu, Z., Yao, H. L., Liu, J., and Hu, Z. (2014). “Dynamic response of a pavement-subgrade-soft ground system subjected to moving traffic load.” J. Vibroeng., 16(1), 195–209.
Luco, J. E., and Apsel, R. J. (1983). “On the Green’s functions for a layered half-space. Part I.” Bull. Seismol. Soc. Am., 73(4), 909–929.
Maheshwari, P., and Khatri, S. (2013). “Response of infinite beams on geosynthetic-reinforced granular bed over soft soil with stone columns under moving loads.” Int. J. Geomech., 10.1061/(ASCE)GM.1943-5622.0000269, 713–728.https://doi.org/10.1061/(ASCE)GM.1943-5622.0000269
Mal, A. (1988). “Wave propagation in layered composite laminates under periodic surface loads.” Wave Motion, 10(3), 257–266.
Mazilu, T. (2009a). “Analysis of infinite structure response due to moving wheel in the presence of irregularities via Green’s functions method.” Proc., Rom. Acad. Ser. A., 10(1), 139–150.
Mazilu, T. (2009b). “On the dynamic effects of wheel running on discretely supported rail.” Proc., Rom. Acad. Ser. A., 10(3), 269–276.
Mazilu, T., Dumitriu, M., Tudorache, C., and Sebeşan, M. (2010). “On vertical analysis of railway track vibration.” Proc., Rom. Acad. Ser. A., 11(2), 156–162.
Mei, C. C., and Foda, M. A. (1981). “Wave-induced responses in a fluid-filled poro-elastic solid with a free surface—A boundary layer theory.” Geophys. J. Int., 66(3), 597–631.
Mesgouez, A., and Lefeuve-Mesgouez, G. (2009). “Transient solution for multilayered poroviscoelastic media obtained by an exact stiffness matrix formulation.” Int. J. Numer. Anal. Methods Geomech., 33(18), 1911–1931.
Ouyang, H. (2011). “Moving-load dynamic problems: A tutorial (with a brief overview).” Mech. Syst. Signal Process., 25(6), 2039–2060.
Pan, G., Okada, H., and Atluri, S. N. (1994). “Nonlinear transient dynamic analysis of soil-pavement interaction under moving load: A coupled BEM-FEM approach.” Eng. Anal. Boundary Elem., 14(1), 99–112.
Patil, V. A., Sawant, V. A., and Deb, K. (2013). “3D finite-element dynamic analysis of rigid pavement using infinite elements.” Int. J. Geomech., 10.1061/(ASCE)GM.1943-5622.0000255, 533–544.https://doi.org/10.1061/(ASCE)GM.1943-5622.0000255
Picoux, B., and Le Houédec, D. (2005). “Diagnosis and prediction of vibration from railway trains.” Soil Dyn. Earthquake Eng., 25(12), 905–921.
Picoux, B., Rotinat, R., Regoin, J., and Le Houédec, D. (2003). “Prediction and measurements of vibrations from a railway track lying on a peaty ground.” J. Sound Vib., 267(3), 575–589.
Senjuntichai, T., and Rajapakse, R. (1995). “Exact stiffness method for quasi-statics of a multi-layered poroelastic medium.” Int. J. Solids Struct., 32(11), 1535–1553.
Sheng, X., Jones, C., and Petyt, M. (1999). “Ground vibration generated by a harmonic load acting on a railway track.” J. Sound Vib., 225(1), 3–28.
Sheng, X., Jones, C. J. C., and Thompson, D. J. (2004a). “A theoretical study on the influence of the track on train-induced ground vibration.” J. Sound Vib., 272(3–5), 909–936.
Sheng, X., Jones, C. J. C., and Thompson, D. J. (2004b). “A theoretical model for ground vibration from trains generated by vertical track irregularities.” J. Sound Vib., 272(3–5), 937–965.
Sneddon, I. N. (1952). “The stress produced by a pulse of pressure moving along the surface of a semi-infinite solid.” Rend. Circ. Mat. Palermo, 1(1), 57–62.
Theodorakopoulos, D. D. (2003). “Dynamic analysis of a poroelastic half-plane soil medium under moving loads.” Soil Dyn. Earthquake Eng., 23(7), 521–533.
Thomson, W. T. (1950). “Transmission of elastic waves through a stratified solid medium.” J. Appl. Phys., 21(2), 89–93.
Xia, H., et al. (2009). “Experimental investigation of railway train-induced vibrations of surrounding ground and a nearby multi-story building.” Earthquake Eng. Eng. Vib., 8(1), 137–148.
Xu, B., Lu, J.-F., and Wang, J. H. (2008). “Dynamic response of a layered water-saturated half space to a moving load.” Comput. Geotech., 35(1), 1–10.
Yang, Y. B., Hung, H. H., and Chang, D. W. (2003). “Train-induced wave propagation in layered soils using finite/infinite element simulation.” Soil Dyn. Earthquake Eng., 23(4), 263–278.
Zhai, W. M., and Cai, Z. (1997). “Dynamic interaction between a lumped mass vehicle and a discretely supported continuous rail track.” Comput. Struct., 63(5), 987–997.
Zhai, W. M., He, Z. X., and Song, X. L. (2010). “Prediction of high-speed train induced ground vibration based on train-track-ground system model.” Earthquake Eng. Eng. Vib., 9(4), 545–554.
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Published In
International Journal of Geomechanics
Volume 16 • Issue 2 • April 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Oct 30, 2014
Accepted: May 7, 2015
Published online: Oct 2, 2015
Discussion open until: Mar 2, 2016
Published in print: Apr 1, 2016
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