Determination of Tire Contact Stress and Deflection Distributions in a Layered Half-Space Using 3-D Boundary Element Method

Year 2022, Volume: 5 Issue: 3, 1480 - 1493, 12.12.2022

İbrahim Özgür Deneme , Metin Hakan Severcan

https://doi.org/10.47495/okufbed.1036077

Abstract

In this study, the Boundary Element Method (BEM) was employed for the numerical determination of the response of a layered half-space. The material behaviour of the soil was assumed to be isotropic and linear elastic. The BEM was used in the Fourier transform space (FTS). The focus of this paper is to determine the stress and deflection distributions of interior points of a layered half-space. To achieve this aim, in this study, a computer program is developed for three-dimensional elastic or visco-elastic problems. The results of stress and deflection distributions in a layered half-space determined using boundary element formulation are presented in figures.

Keywords

Boundary element method, Elasto-statics, Fourier transform space, Pavement response, Layered half-space

Tabakalı Zeminlerde Tekerlek Temas Gerilmesi ve Deplasman Dağılımlarının Üç Boyutlu Sınır Eleman Yöntemi ile Belirlenmesi

Abstract

Bu çalışmada, tabakalı bir yarım uzayın tepkisinin sayısal olarak belirlenmesi için sınır eleman yöntemi kullanılmıştır. Zeminin malzeme davranışının lineer elastik olduğu varsayılmıştır. Sınır eleman yöntemi, Fourier dönüşüm uzayında kullanıldı. Bu makalenin odak noktası, tabakalı bir yarım uzayın iç noktalarında oluşan gerilme ve deplasman dağılımlarının belirlenmesisdir. Bu amaca ulaşmak için bu çalışmada, üç boyutlu elastik veya visko-elastik problemler için bir bilgisayar programı geliştirilmiştir. Sınır eleman formülasyonu kullanılarak belirlenen tabakalı bir yarım uzaydaki gerilme ve deplasman dağılımları şekillerde sunulmuştur.

Keywords

Sınır elamn yöntemi, Elasto-statik, Fourier dönüşüm uzayı, Üstyapı tepkisi, Tabakalı yarım uzay

References

• References [1] Yoder EJ, Witczak MW. Principles of Pavement Design, Second Edition. 1975.
• [2] Kim SM, Roesset JM. Dynamic response of a beam on a frequency-independent damped elastic foundation to moving load. Canadian Journal of Civil Engineering 2003;30:460–7. doi:10.1139/l02-109.
• [3] Sun L. Analytical dynamic displacement response of rigid pavements to moving concentrated and line loads. International Journal of Solids and Structures 2006;43:4370–83. doi:10.1016/j.ijsolstr.2005.06.105.
• [4] Huang YH. Pavement design and analysis. New Jersey: Pearson Prentice Hall; 2004. [5] Hu X Di, Sun LJ. Measuring tire ground pressure distribution of heavy vehicle. Journal of Tongji University 2005;33:1443–8.
• [6] Hernandez JA, Al-Qadi IL. Tire–pavement interaction modelling: hyperelastic tire and elastic pavement. Road Materials and Pavement Design 2017;18:1067–83. doi:10.1080/14680629.2016.1206485.
• [7] Weissman SL. Influence of tire-pavement contact stress distribution on development of distress mechanisms in pavements. Transportation Research Record 1998:161–7.
• [8] Duncan JM, Monismith CL, Wilson EL. Finite Element Analyses of Pavements. Highway Research Board 1968;38:18–33.
• [9] Mamlouk MS, Davies TG. Elasto-dynamic analysis of pavement deflections. Journal of Transportation Engineering 1984;110:536–550. doi:10.1061/(ASCE)0733-947X(1984)110:6(536).
• [10] Zheng L, Hai-lin Y, Wan-ping W, Ping C. Dynamic stress and deformation of a layered road structure under vehicle traffic loads: Experimental measurements and numerical calculations. Soil Dynamics and Earthquake Engineering 2012;39:100–12. doi:10.1016/j.soildyn.2012.03.002.
• [11] Sousa BJ, Lysmer J, Chen S-S, Monismith CL. Effects of Dynamic Loads on Performance of Asphalt Concrete Pavements. Transportation Research Record 1988;1207:145–68.
• [12] Siddharthan R V., Yao J, Sebaaly PE. Pavement strain from moving dynamic 3D load distribution. Journal of Transportation Engineering 1998;124:557–66.
• [13] Lee JH, Kim JK, Tassoulas JL. Dynamic analysis of a layered half-space subjected to moving line loads. Soil Dynamics and Earthquake Engineering 2013;47:16–31. doi:10.1016/j.soildyn.2012.07.013.
• [14] Yoo PJ, Al-Qadi IL. Effect of transient dynamic loading on flexible pavements. Transportation Research Record 2007:129–40. doi:10.3141/1990-15.
• [15] Al-Qadi IL, Wang H, Yoo PJ, Dessouky SH. Dynamic analysis and in situ validation of perpetual pavement response to vehicular loading. Transportation Research Record 2008;2087:29–39. doi:10.3141/2087-04.
• [16] Khavassefat P, Jelagin D, Birgisson B. A computational framework for viscoelastic analysis of flexible pavements under moving loads. Materials and Structures 2012;45:1655–71. doi:10.1617/s11527-012-9863-9.
• [17] Jiang X, Zeng C, Gao X, Liu Z, Qiu Y. 3D FEM analysis of flexible base asphalt pavement structure under non-uniform tyre contact pressure. International Journal of Pavement Engineering 2017;8436:1–13. doi:10.1080/10298436.2017.1380803.
• [18] Beskou ND, Hatzigeorgiou GD, Theodorakopoulos DD. Dynamic inelastic analysis of 3-D flexible pavements under moving vehicles: A unified FEM treatment. Soil Dynamics and Earthquake Engineering 2016;90:420–31. doi:10.1016/j.soildyn.2016.09.018.
• [19] Castillo D, Gamez A, Al-Qadi I. Homogeneous versus Heterogeneous Response of a Flexible Pavement Structure: Strain and Domain Analyses. Journal of Engineering Mechanics 2019;145:1–11. doi:10.1061/(ASCE)EM.1943-7889.0001639.
• [20] Djellali A, Houam A, Saghafi B, Hamdane A, Benghazi Z. Static Analysis of Flexible Pavements over Expansive Soils. International Journal of Civil Engineering 2017;15:391–400. doi:10.1007/s40999-016-0058-6.
• [21] Vale C. Influence of vertical load models on flexible pavement response - An investigation. International Journal of Pavement Engineering 2008;9:247–55. doi:10.1080/10298430701444977.
• [22] Pan G, Atluri SN. Dynamic response of finite sized elastic runways subjected to moving loads: A coupled BEM/FEM approach. International Journal for Numerical Methods in Engineering 1995;38:3143–66. doi:10.1002/nme.1620381808.
• [23] François S, Pyl L, Masoumi HR, Degrande G. The influence of dynamic soil-structure interaction on traffic induced vibrations in buildings. Soil Dynamics and Earthquake Engineering 2007;27:655–74. doi:10.1016/j.soildyn.2006.11.008.
• [24] Deneme IO, Yerli HR, Severcan MH, Tanrikulu AH, Tanrikulu AK. Use and comparison of different types of boundary elements for 2D soil-structure interaction problems. Advances in Engineering Software 2009;40:847–55. doi:10.1016/j.advengsoft.2009.01.006.
• [25] Yerli HR, Deneme IO. Elastodynamic boundary element formulation employing discontinuous curved elements. Soil Dynamics and Earthquake Engineering 2008;28:480–91. doi:10.1016/j.soildyn.2007.07.007.
• [26] Banerjee PK. The boundary element methods in engineering. London: McGraw-Hill Book Company; 1994.
• [27] Brebbia CA, Dominguez J. Boundary elements an introductory course. Southampton: Computational Mechanics Publications; 1989.
• [28] Partridge PW, Brebbia CA, Wrobel LC. The Dual Reciprocity Boundary Element Method. Southampton: Computational Mechanics Publications; 1992.
• [29] Mengi Y, Tanrikulu AH, Tanrikulu AK. Boundary element method for elastic media: an introduction. Ankara: METU Press; 1994.
• [30] Lombaert G, Degrande G, Clouteau D. Numerical modelling of free field traffic-induced vibrations. Soil Dynamics and Earthquake Engineering 2000;19:473–88. doi:10.1016/S0267-7261(00)00024-5.
• [31] Beskou ND, Theodorakopoulos DD. Dynamic effects of moving loads on road pavements: A review. Soil Dynamics and Earthquake Engineering 2011;31:547–67. doi:10.1016/j.soildyn.2010.11.002.
• [32] Lu YJ, Wang LJ, Yang Q, Ren JY. Analysis of asphalt pavement mechanical behaviour by using a tire-pavement coupling model. International Journal of Simulation Modelling 2018;17:245–56. doi:10.2507/IJSIMM17(2)423.
• [33] Grundmann H, Lieb M, Trommer E. The response of a layered half-space to traffic loads moving along its surface. Archive of Applied Mechanics 1999;69:55–67. doi:10.1007/s004190050204.
• [34] Payton RG. An application of the dynamic Betti-Rayleigh reciprocal theorem to moving-point loads in elastic media. Quarterly of Applied Mathematics 1964;21:299–313. doi:10.1090/qam/155477.
• [35] Rasmussen KM, Nielsen SRK, Kirkegaard PH. Boundary element method solution in the time domain for a moving time-dependent force. Computers and Structures 2001;79:691–701. doi:10.1016/S0045-7949(00)00175-9.
• [36] Andersen L, Nielsen SRK. Boundary element analysis of the steady-state response of an elastic half-space to a moving force on its surface. Engineering Analysis with Boundary Elements 2003;27:23–38. doi:10.1016/S0955-7997(02)00096-6.