[Utilisation de la solution de Boussinesq en géotechnique et dans le domaine des chaussées : influence de la plasticité]
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.
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.
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Publié le :
Mots-clés : Sols, Boussinesq, Plasticité, Éléments finis, Demi-espace, Élastique, Tassement, Contraintes
Marwan Sadek 1 ; Isam Shahrour 1
@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 -
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] Applications des potentiels à l'étude de l'équilibre et mouvement des solides elastiques, Gauthier–Villard, Paris, 1885
[2] The general theory of stresses and displacements in layered systems I, J. Appl. Phys., Volume 16 (1943) no. 2, pp. 89-94
[3] The general theory of stresses and displacements in layered systems II, J. Appl. Phys., Volume 16 (1943) no. 3, pp. 126-127
[4] 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] 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] 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] Stress diffusion experiment in sand, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Volume 131 (2005) no. 1
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