Summary
It is known that an isotropic, incompressible, elastic half-space with a rigidity modulus which increases linearly with depth from zero at the surface, responds to vertical surface loading exactly like a uniform array of springs (Winkler's medium). The validity of this result is examined here for a cross-anisotropic medium.
Résumé
On sait qu'un semi-espace de terrain isotrope, élastique et incompressible—dont le module de cisaillement accroît linéairement avec la profondeur, partant de zéro à la surface—réagit à la charge superficielle exactement selon les hypothèses faites par Winkler dans sa théorie de la réaction du niveau de fondation. On examine ici jusqu' à quel point la validité de ce résultat s'applique à un milieu anisotrope, élastique et incompressible.
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References
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E. Winkler,Die Lehre von Elastizität und Festigkeit, p. 182 (Prague 1867).
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D. J. Pickering,Anisotropic Elastic Parameters for Soil, Géotechnique20, 271 (1970).
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Gibson, R.E., Kalsi, G.S. The surface settlement of a linearly inhomogeneous cross-anisotropic elastic half-space. Journal of Applied Mathematics and Physics (ZAMP) 25, 843–847 (1974). https://doi.org/10.1007/BF01590269
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DOI: https://doi.org/10.1007/BF01590269