Analysis of Concrete Pavement Slab resting on Non-uniform Elastic Foundation using the Finite Element Method


  • Le Vinh An University of Transport and Communications, Vietnam
  • Nguyen Trong Hiep University of Transport and Communications, Hanoi, Vietnam
  • Dao Ngoc Tien Hanoi Architectural University, Vietnam
Volume: 13 | Issue: 4 | Pages: 11242-11247 | August 2023 |


During the rigid pavement design, the concrete slab working on the base/subbase and subgrade is usually modeled as the slab on the elastic foundation. However, the non-uniform distribution of materials in the base or subgrade layers naturally exists in real conditions and should be considered. In this paper, a finite element method for calculating concrete pavement slabs on an elastic foundation with non-uniform stiffness distribution is developed. This study applies 4-node finite elements and Mindlin plate theory to formulate the finite element equations. The results predicted by the proposed approach are verified analytically. Calculation examples are conducted with the practical settings to investigate the influence of slab and foundation stiffness parameters on the slab displacement.


pavement slabs, non-uniform foundation, FEM


Download data is not yet available.


D. Froio, E. Rizzi, F. M. F. Simoes, and A. Pinto Da Costa, "Dynamics of a beam on a bilinear elastic foundation under harmonic moving load," Acta Mechanica, vol. 229, no. 10, pp. 4141–4165, Oct. 2018.

S. Lenci, "Propagation of periodic waves in beams on a bilinear foundation," International Journal of Mechanical Sciences, vol. 207, Oct. 2021, Art. no. 106656.

F. W. Beaufait and P. W. Hoadley, "Analysis of elastic beams on nonlinear foundations," Computers & Structures, vol. 12, no. 5, pp. 669–676, Nov. 1980.

G. C. Tsiatas, "Nonlinear analysis of non-uniform beams on nonlinear elastic foundation," Acta Mechanica, vol. 209, no. 1, pp. 141–152, Jan. 2010.

D. Xuan Quy and N. Thị, "Static analysis of beam resting on elastic foundation by anisotropic beam-foundation element taking into account non-contact between beam and foundation," Transport and Communications Science Journal, vol. 72, no. 5, pp. 552–564, Jun. 2021.

O. Khalaj, S. N. M. Tafreshi, B. Masek, and A. Dawson, "Improvement of pavement foundation response with multi-layers of geocell reinforcement: cyclic plate load test," Geomechanics and Engineering, vol. 9, no. 3, pp. 373–395, Sep. 2015.

T. D. Hien, N. D. Hung, N. T. Kien, and H. C. Noh, "The variability of dynamic responses of beams resting on elastic foundation subjected to vehicle with random system parameters," Applied Mathematical Modelling, vol. 67, pp. 676–687, Mar. 2019.

S. Mohammadzadeh, M. Esmaeili, and M. Mehrali, "Dynamic response of double beam rested on stochastic foundation under harmonic moving load," International Journal for Numerical and Analytical Methods in Geomechanics, vol. 38, no. 6, pp. 572–592, 2014.

S. Mohammadzadeh and M. Mehrali, "Dynamic response of ladder track rested on stochastic foundation under oscillating moving load," Journal of Theoretical and Applied Mechanics, vol. 55, no. 1, pp. 281–291, 2017.

A. S. Brand and J. R. Roesler, "Finite element analysis of a concrete slab under various non-uniform support conditions," International Journal of Pavement Engineering, vol. 15, no. 5, pp. 460–470, May 2014.

L. X. Quy, N. M. Lan, N. Q. Tuan, and H. Pierre, "Longitudinal strain analysis in asphalt pavement under full-scale moving loads," Transport and Communications Science Journal, vol. 72, no. 4, pp. 359–370, 2022.

D. H. Duc, D. V. Thom, and P. M. Phuc, "Buckling analysis of variable thickness cracked nanoplates considerting the flexoelectric effect," Transport and Communications Science Journal, vol. 73, no. 5, pp. 470–485, 2022.

D. T. Thuy, L. N. Ngoc, D. N. Tien, and H. V. Thanh, "An Analytical Solution for the Dynamics of a Functionally Graded Plate resting on Viscoelastic Foundation," Engineering, Technology & Applied Science Research, vol. 13, no. 1, pp. 9926–9931, Feb. 2023.

T. D. Hien, N. D. Hung, N. T. Hiep, G. V. Tan, and N. V. Thuan, "Finite Element Analysis of a Continuous Sandwich Beam resting on Elastic Support and Subjected to Two Degree of Freedom Sprung Vehicles," Engineering, Technology & Applied Science Research, vol. 13, no. 2, pp. 10310–10315, Apr. 2023.

T. C. Yu, G. J. Nie, Z. Zhong, F. Y. Chu, and X. J. Cao, "Analytical Solution of the Bending Problem for Rectangular Orthotropic Plates with a Variable in-Plane Stiffness," Mechanics of Composite Materials, vol. 57, no. 1, pp. 115–124, Mar. 2021.

K. Huang, D. G. Zollinger, X. Shi, and P. Sun, "A developed method of analyzing temperature and moisture profiles in rigid pavement slabs," Construction and Building Materials, vol. 151, pp. 782–788, Oct. 2017.

P. M. Phuc, "Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness," Transport and Communications Science Journal, vol. 71, no. 7, pp. 853–867, 2020.

A. Zokaei-Ashtiani, C. Carrasco, and S. Nazarian, "Finite element modeling of slab–foundation interaction on rigid pavement applications," Computers and Geotechnics, vol. 62, pp. 118–127, Oct. 2014.

B. M. Luccioni and M. Luege, "Concrete pavement slab under blast loads," International Journal of Impact Engineering, vol. 32, no. 8, pp. 1248–1266, Aug. 2006.

P.-C. Nguyen, Q. H. Pham, T. T. Tran, and T. Nguyen-Thoi, "Effects of partially supported elastic foundation on free vibration of FGP plates using ES-MITC3 elements," Ain Shams Engineering Journal, vol. 13, no. 3, May 2022, Art. no. 101615.

C. Liu et al., "Numerical Analysis on the Mechanical Properties of the Concrete Precast Pavement of Runways under the Wheel Load," Applied Sciences, vol. 12, no. 19, Jan. 2022, Art. no. 9826.

Y. Tyukalov, "Arbitrary quadrangular finite element for plates with shear deformations," Magazine of Civil Engineering, vol. 107, no. 7, 2021, Art. no. 10707.

B. Bouderba and B. Hamza Madjid, "Bending analysis of P-FGM plates resting on nonuniform elastic foundations and subjected to thermo-mechanical loading," Cogent Engineering, vol. 9, no. 1, Dec. 2022, Art. no. 2108576.

T. D. Hien and B. T. Quang, "Analysis of isotropic rectangular plate resting on non-uniform elastic foundation using Ritz approach," Materials Today: Proceedings, vol. 19, pp. 158–160, Jan. 2019.

E. Bahmyari and A. Rahbar-Ranji, "Free vibration analysis of orthotropic plates with variable thickness resting on non-uniform elastic foundation by element free Galerkin method," Journal of Mechanical Science and Technology, vol. 26, no. 9, pp. 2685–2694, Sep. 2012.

N. T. Hiep, D. S. Dan, N. D. Diem, and D. N. Tien, "NURBS-based Isogeometric Analysis and Refined Plate Theory Application on a Functionally Graded Plate Subjected to Random Loads," Engineering, Technology & Applied Science Research, vol. 13, no. 2, pp. 10243–10248, Apr. 2023.

A. J. M. Ferreira, MATLAB Codes for Finite Element Analysis: Solids and Structures. Dordrecht, Netherlands: Springer, 2009.

J. Reddy, An Introduction to the Finite Element Method, 3rd ed. New York, NY, USA: McGraw-Hill Education, 2005.


How to Cite

L. V. An, N. T. Hiep, and D. N. Tien, “Analysis of Concrete Pavement Slab resting on Non-uniform Elastic Foundation using the Finite Element Method”, Eng. Technol. Appl. Sci. Res., vol. 13, no. 4, pp. 11242–11247, Aug. 2023.


Abstract Views: 539
PDF Downloads: 339

Metrics Information

Most read articles by the same author(s)