- Forrest, J. A. and Hunt, H. E. M., (2006), A three-dimensional tunnel model for calculation of train- induced ground vibration, Journal of Sound and Vibration, 294, 4, pp. 678-705.
- Forrest, J. A. and Hunt, H. E. M., (2006), Ground vibration generated by trains in underground tunnels, Journal of Sound and Vibration, 294, 4, pp. 706-736.
- Bayındır, C., Kesten, A. S. and Etminan, E., (2018), A Theoretical Method for the Investigation of the Effects of Soil Improvement on Train Induced Ground-Borne Vibrations, 13th International
- Conference on Advances in Civil Engineering, Izmir, Turkey. Sheng, X., Jones, C. J. C. and Petyt, M., (1999), Ground vibration generated by a harmonic load acting on a railway track, Journal of Sound and Vibration, 225, 1, pp. 3-28.
- Sheng, X., Jones, C. J. C. and Petyt, M., (1999), Ground vibration generated by a load moving along a railway track, Journal of Sound and Vibration, 228, 1, pp. 129-156.
- Jones, C. J. C., Sheng, X. and Petyt, M., (2000), Simulations of ground vibration from a moving harmonic load on a railway track, Journal of Sound and Vibration, 231, 3, pp. 739-751.
- Bayındır, C., (2018), Efficient Sensing of Ground-Borne Vibrations Induced by Pile Driving using
- Compressive Sampling, Researchgate Preprint 10.13140/RG.2.2.16837.09444.
- Persson, N., (2016), Predicting Railway-Induced Ground Vibrations, M.S. Thesis, Lund University.
- Sheng, X., Jones, C. J. C. and Thompson, D. J., (2003), A comparison of a theoretical model for quasi-statically and dynamically induced environmental vibration from trains with measurements
- Journal of Sound and Vibration, 267, 3, pp. 621-635. Sheng, X., Jones, C. J. C. and Thompson, D. J., (2004), A theoretical study on the influence of the track on train-induced ground vibration, Journal of Sound and Vibration, 272, 3, pp. 909-936.
- Sheng, X., Jones, C. J. C. and Thompson, D. J., (2004), A theoretical model for ground vibration from trains generated by vertical track irregularities, Journal of Sound and Vibration, 272, 3, pp. 965.
- Bayındır, C., (2009), Implementation of a Computational Model for Random Directional Seas and Underwater Acoustics, M.S. Thesis. University of Delaware.
- Canuto, C., (2006), Spectral Methods: Fundamentals in Single Domains. Springer-Verlag, Berlin.
- Demiray, H. and Bayındır, C., (2015), A note on the cylindrical solitary waves in an electron-acoustic plasma with vortex electron distribution, Physics of Plasmas, 22, 092105.
- Karjadi, E. A., Badiey, M., Kirby, J. T. and Bayındır, C., (2012), The effects of surface gravity waves on high-frequency acoustic propagation in shallow water, IEEE Journal of Oceanic Engineering, 37, pp. 112-121.
- Bayındır, C., (2015), Compressive split step Fourier method, Journal of Applied and Engineering Mathematics, 5, 2, pp. 298-306.
- Bayındır, C., (2016), Compressive spectral method for the simulation of the nonlinear gravity waves, Scientific Reports, 22100.
- Bayındır, C., (2016), Rogue waves of the Kundu-Eckhaus equation in a chaotic wave field, Physical Review E, 93, 032201.
- Santamarina, J. C., Klein, K. A. and Fam, M. A., (2001), Soils and Waves: Particulate Materials Behavior, Wiley.
- Bayındır, C., (2016), Rogue wave spectra of the Kundu-Eckhaus equation, Physical Review E, 93
- Newland, D. E., (1993), An Introduction to Random Vibrations, Spectral & Wavelet Analysis. Long- man, London.
- Trefethen, L. N., (2000), Spectral Methods in MATLAB. SIAM, Philadelphia.
- Bayındır, C., (2016), Early detection of rogue waves by the wavelet transforms, Physics Letters A, , 1, pp. 156-161.
- Jiang, J., Toward, M. G. R., Dijckmans, A. and Thompson, D. J., (2014), The influence of soil conditions on railway induced ground-borne vibration and relevant mitigation measures, The 21st
- International Congress on Sound and Vibration, pp. 2895-2904.
- Thompson, D. J., Jiang, J., Toward, M. G. R., Hussein, M. F. M., Dijckmans, A., Coulier, P., De- grande, G. and Loambert, G., (2015), The mitigation of railway-induced vibration by using subgrade stiffening, Soil Dynamics and Earthquake Engineering, 79, pp. 89-103.
- Schevenels, M., Degrande, G. and Lombaert, G., (2004), The influence of the depth of the ground water table on free field road traffic-induced vibrations, International Journal for Numerical and Analytical
- Methods in Geomechanics, 28, pp. 395-419. Jones, S. and Hunt, H., (2011), Effect of inclined soil layers on surface vibration from underground railways using the thin-layer method, Journal of engineering mechanics, 137, 12, pp. 887-900.
- Erdem, S. N., (1988), Tezkiret’¨ul B¨unyan, Binbirdirek Yayınları. ˙Istanbul. (In Turkish)
- Frederich, F., (1984), Die Gleislage -aus fahrzeugtechnischer Sicht, Zeitschrift f¨ur Eisenbahnwesen und
- Vekehrstechnik-Glasers Annalen, 108, pp. 355-362. (In German) Bowles, E. J., (2001), Foundation Analysis and Design. McGraw Hill, London.
- Coduto, D. P., (2000), Foundation Design. Prentice Hall, New Jersey.
- Cihan Bayındır for the photography and short autobiography, see TWMS J. App. Eng. Math., V.5, N.2.

Passage of the train wheels induces ground-borne vibrations at the railwheel interface, where the main contribution is due to the axle loads moving on irregular track and wheel interface. These vibrations can cause problems such as the compaction and settlement of the foundation soil of the structures nearby, liquefaction of the soil or discomfort of people, just to name a few. Therefore predicting and controlling such phenomena is critically important for the design and operation of the railways. These vibrations are modeled using many dierent methods existing in the literature. In this paper we analyze the eects of groundwater depth and ground inclination angle on those vibrations using a random vibration model, where the elastic rail-soil system is modeled as a Winkler foundation. We examine the eects of changing fully saturated groundwater levels and changing ground inclination angles on such vibrations. We relate the groundwater depth and ground inclination angle parameters with the stiness of the Winkler model using Terzaghi's, Vesic's and Bowles's bearing capacity formulas. The common 5-axle and the 6-axle tram load congurations and dierent train speeds of 30 km/hr, 40 km/hr, 50 km/hr are used in our implemented model. It is shown that the decrease in groundwater depth and/or higher ground inclination angle can signicantly change the peak and rms vibration velocity and acceleration levels, both for the 5-axle and 6-axle congurations and all three dierent train speeds. We present exponential and exponential-trigonometric t curves to the results of the implemented random vibration model, which can be used to model the approximate changes in the ground-borne vibration velocity and acceleration levels due to dierent groundwater depth and diferent ground inclination angles. We also discuss our results and their applicability.

Train induced vibrations, Winkler foundation, Random vibrations, Groundwater table, Ground inclination angle.

- Forrest, J. A. and Hunt, H. E. M., (2006), A three-dimensional tunnel model for calculation of train- induced ground vibration, Journal of Sound and Vibration, 294, 4, pp. 678-705.
- Forrest, J. A. and Hunt, H. E. M., (2006), Ground vibration generated by trains in underground tunnels, Journal of Sound and Vibration, 294, 4, pp. 706-736.
- Bayındır, C., Kesten, A. S. and Etminan, E., (2018), A Theoretical Method for the Investigation of the Effects of Soil Improvement on Train Induced Ground-Borne Vibrations, 13th International
- Conference on Advances in Civil Engineering, Izmir, Turkey. Sheng, X., Jones, C. J. C. and Petyt, M., (1999), Ground vibration generated by a harmonic load acting on a railway track, Journal of Sound and Vibration, 225, 1, pp. 3-28.
- Sheng, X., Jones, C. J. C. and Petyt, M., (1999), Ground vibration generated by a load moving along a railway track, Journal of Sound and Vibration, 228, 1, pp. 129-156.
- Jones, C. J. C., Sheng, X. and Petyt, M., (2000), Simulations of ground vibration from a moving harmonic load on a railway track, Journal of Sound and Vibration, 231, 3, pp. 739-751.
- Bayındır, C., (2018), Efficient Sensing of Ground-Borne Vibrations Induced by Pile Driving using
- Compressive Sampling, Researchgate Preprint 10.13140/RG.2.2.16837.09444.
- Persson, N., (2016), Predicting Railway-Induced Ground Vibrations, M.S. Thesis, Lund University.
- Sheng, X., Jones, C. J. C. and Thompson, D. J., (2003), A comparison of a theoretical model for quasi-statically and dynamically induced environmental vibration from trains with measurements
- Journal of Sound and Vibration, 267, 3, pp. 621-635. Sheng, X., Jones, C. J. C. and Thompson, D. J., (2004), A theoretical study on the influence of the track on train-induced ground vibration, Journal of Sound and Vibration, 272, 3, pp. 909-936.
- Sheng, X., Jones, C. J. C. and Thompson, D. J., (2004), A theoretical model for ground vibration from trains generated by vertical track irregularities, Journal of Sound and Vibration, 272, 3, pp. 965.
- Bayındır, C., (2009), Implementation of a Computational Model for Random Directional Seas and Underwater Acoustics, M.S. Thesis. University of Delaware.
- Canuto, C., (2006), Spectral Methods: Fundamentals in Single Domains. Springer-Verlag, Berlin.
- Demiray, H. and Bayındır, C., (2015), A note on the cylindrical solitary waves in an electron-acoustic plasma with vortex electron distribution, Physics of Plasmas, 22, 092105.
- Karjadi, E. A., Badiey, M., Kirby, J. T. and Bayındır, C., (2012), The effects of surface gravity waves on high-frequency acoustic propagation in shallow water, IEEE Journal of Oceanic Engineering, 37, pp. 112-121.
- Bayındır, C., (2015), Compressive split step Fourier method, Journal of Applied and Engineering Mathematics, 5, 2, pp. 298-306.
- Bayındır, C., (2016), Compressive spectral method for the simulation of the nonlinear gravity waves, Scientific Reports, 22100.
- Bayındır, C., (2016), Rogue waves of the Kundu-Eckhaus equation in a chaotic wave field, Physical Review E, 93, 032201.
- Santamarina, J. C., Klein, K. A. and Fam, M. A., (2001), Soils and Waves: Particulate Materials Behavior, Wiley.
- Bayındır, C., (2016), Rogue wave spectra of the Kundu-Eckhaus equation, Physical Review E, 93
- Newland, D. E., (1993), An Introduction to Random Vibrations, Spectral & Wavelet Analysis. Long- man, London.
- Trefethen, L. N., (2000), Spectral Methods in MATLAB. SIAM, Philadelphia.
- Bayındır, C., (2016), Early detection of rogue waves by the wavelet transforms, Physics Letters A, , 1, pp. 156-161.
- Jiang, J., Toward, M. G. R., Dijckmans, A. and Thompson, D. J., (2014), The influence of soil conditions on railway induced ground-borne vibration and relevant mitigation measures, The 21st
- International Congress on Sound and Vibration, pp. 2895-2904.
- Thompson, D. J., Jiang, J., Toward, M. G. R., Hussein, M. F. M., Dijckmans, A., Coulier, P., De- grande, G. and Loambert, G., (2015), The mitigation of railway-induced vibration by using subgrade stiffening, Soil Dynamics and Earthquake Engineering, 79, pp. 89-103.
- Schevenels, M., Degrande, G. and Lombaert, G., (2004), The influence of the depth of the ground water table on free field road traffic-induced vibrations, International Journal for Numerical and Analytical
- Methods in Geomechanics, 28, pp. 395-419. Jones, S. and Hunt, H., (2011), Effect of inclined soil layers on surface vibration from underground railways using the thin-layer method, Journal of engineering mechanics, 137, 12, pp. 887-900.
- Erdem, S. N., (1988), Tezkiret’¨ul B¨unyan, Binbirdirek Yayınları. ˙Istanbul. (In Turkish)
- Frederich, F., (1984), Die Gleislage -aus fahrzeugtechnischer Sicht, Zeitschrift f¨ur Eisenbahnwesen und
- Vekehrstechnik-Glasers Annalen, 108, pp. 355-362. (In German) Bowles, E. J., (2001), Foundation Analysis and Design. McGraw Hill, London.
- Coduto, D. P., (2000), Foundation Design. Prentice Hall, New Jersey.
- Cihan Bayındır for the photography and short autobiography, see TWMS J. App. Eng. Math., V.5, N.2.

Primary Language | English |
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Journal Section | Research Article |

Authors | |

Publication Date | December 1, 2019 |

Published in Issue | Year 2019 Volume: 9 Issue: 4 |