Comptes Rendus
no. 9-10
Soils, granular media, civil engineering
Use of the Boussinesq solution in geotechnical and road engineering: influence of plasticity
Marwan Sadek1; Isam Shahrour1 
1 Laboratoire de mécanique de Lille (UMR 8107), Université des sciences et technologies de Lille, 59655 Villeneuve d'Ascq cedex, France
Comptes Rendus. Mécanique, Joseph Boussinesq, a Scientist of bygone days and present times, Volume 335 (2007) no. 9-10, pp. 516-520.

The Boussinesq solution for the distribution of stresses in a half-space resulting from surface loads is largely used in geotechnical and road engineering. It is based on the assumption of a linear–elastic homogeneous isotropic half-space for the soil media. Since the soil exhibits nonlinear and irreversible behavior, it is of major interest to study the validity of this solution for elastoplastic soils. This paper includes an investigation of this issue using finite element modeling. The study is conducted by comparing the elastic stress distribution to that obtained using elastoplastic finite element analyses. Results show that the plasticity reduces the attenuation of the vertical stresses in the soil mass, which means that the Boussinesq solution underestimates the stresses in an area which contributes to the soil settlement.

La solution de Boussinesq pour la distribution des contraintes dans un espace semi infini est utilisée en géotechnique et dans le domaine des chaussées. Cette solution est fondée sur l'hypothèse d'un milieu isotrope, homogène et linéaire–élastique. Puisque le sol a un comportement non-linéaire et irréversible, il est intéressant d'étudier la validité de cette solution pour les sols élastoplastiques. Cet article comporte une analyse de cette question en utilisant une modélisation par éléments finis. L'analyse est réalisée en comparant la solution élastique à celle obtenue par une modélisation élastoplastique par éléments finis. Les résultats montrent que la plasticité réduit l'atténuation des contraintes verticales dans le sol, ce qui signifie que la solution de Boussinesq sous-estime les contraintes dans un domaine qui contribue aux tassements.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2007.08.007
Keywords: Soils, Boussinesq, Plasticity, Finite element, Half-space, Settlement, Stress
Mots-clés : Sols, Boussinesq, Plasticité, Éléments finis, Demi-espace, Élastique, Tassement, Contraintes

Marwan Sadek 1; Isam Shahrour 1

1 Laboratoire de mécanique de Lille (UMR 8107), Université des sciences et technologies de Lille, 59655 Villeneuve d'Ascq cedex, France 
@article{CRMECA_2007__335_9-10_516_0,
     author = {Marwan Sadek and Isam Shahrour},
     title = {Use of the {Boussinesq} solution in geotechnical and road engineering: influence of plasticity},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {516--520},
     publisher = {Elsevier},
     volume = {335},
     number = {9-10},
     year = {2007},
     doi = {10.1016/j.crme.2007.08.007},
     language = {en},
}
TY  - JOUR
AU  - Marwan Sadek
AU  - Isam Shahrour
TI  - Use of the Boussinesq solution in geotechnical and road engineering: influence of plasticity
JO  - Comptes Rendus. Mécanique
PY  - 2007
SP  - 516
EP  - 520
VL  - 335
IS  - 9-10
PB  - Elsevier
DO  - 10.1016/j.crme.2007.08.007
LA  - en
ID  - CRMECA_2007__335_9-10_516_0
ER  - 
%0 Journal Article
%A Marwan Sadek
%A Isam Shahrour
%T Use of the Boussinesq solution in geotechnical and road engineering: influence of plasticity
%J Comptes Rendus. Mécanique
%D 2007
%P 516-520
%V 335
%N 9-10
%I Elsevier
%R 10.1016/j.crme.2007.08.007
%G en
%F CRMECA_2007__335_9-10_516_0
Marwan Sadek; Isam Shahrour. Use of the Boussinesq solution in geotechnical and road engineering: influence of plasticity. Comptes Rendus. Mécanique, Joseph Boussinesq, a Scientist of bygone days and present times, Volume 335 (2007) no. 9-10, pp. 516-520. doi : 10.1016/j.crme.2007.08.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.08.007/

[1] J. Boussinesq Applications des potentiels à l'étude de l'équilibre et mouvement des solides elastiques, Gauthier–Villard, Paris, 1885

[2] D.M. Burmister The general theory of stresses and displacements in layered systems I, J. Appl. Phys., Volume 16 (1943) no. 2, pp. 89-94

[3] D.M. Burmister The general theory of stresses and displacements in layered systems II, J. Appl. Phys., Volume 16 (1943) no. 3, pp. 126-127

[4] R.L. Schiffman General solution of stresses and displacements in layered elastic systems, International Conference on the Structural Design of Asphalt Pavement, Proceedings, University of Michigan, Ann Arbor, Michigan, USA, 1962

[5] R.V. Siddharthan, J. Yao, P. Sebaaly, Field verification of a moving load model for pavement response, Transportation Research Record 1540, TRB, National Research Council, Washington, DC, USA, 1996

[6] R.N. Nilsson, I. Oost, P.C. Hopman, Visco-elastic analysis of full scale pavements: Validation of VEROAD, Transportation Research Record 1539, TRB, National Research Council, Washington, DC, USA, 1996

[7] P. Ullidtz Pavement Analysis, Elsevier Science, Amsterdam, 1987

[8] P. Ullidtz, V. Askegaard, F.O. Sjölin, Normal stresses in a granular material under FWD loading, Transportation Record 1540, TRB, National Research Council, Washington, DC, USA, 1996

[9] W. Zhang, P. Ullidtz, R. Macdonald, Pavement subgrade performance study, part II: Modeling pavement response and prediction pavement performance, Report 87, Danish Road Institute, Roskilde, Denmark, 1998

[10] C. Vrettos The Boussinesq problem for soils with bounded non-homogeneity, International Journal for Numerical and Analytical Methods in Geomechanics, Volume 22 (1998) no. 8, pp. 655-669

[11] L. Prandtl, Über die Härte plastischer Körper, Nachrichten Ges. Wiss. Göttingen, Math.–Physikal. Klasse, 1920, p. 74

[12] J. Schmertmann Stress diffusion experiment in sand, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Volume 131 (2005) no. 1

Cited by Sources:

Comments - Policy