TECHNICAL PAPERS
Mar 31, 2011

Approximate Boundaries for Finite-Element Models of Static Soil–Foundation Interaction Problems

Publication: Journal of Engineering Mechanics
Volume 137, Issue 10

Abstract

In this paper, we examine the use of boundary springs as approximate external boundary conditions for the typical soil islands encountered in finite-element (FE) models of soil–foundation interaction problems. We present a set of simple uniformly distributed boundary springs and a set of variable boundary springs that account for the lateral distribution of contact forces between the foundation and the soil. We evaluate the accuracy of the approach for shallow foundations resting on soil islands of different dimensions. It is shown that significantly smaller errors can be achieved with these boundary springs than those obtained when fixed-fixed or fixed-free external boundary conditions are used. We present an iterative approach to determine the boundary springs for cases in which extremely small soil islands are required. Although the approach suggested to determine the boundary springs is best suited to shallow foundations, good results are also obtained for pile foundations. The approach presented applies to a uniform elastic half-space, but extensions to layered media are possible.

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Acknowledgments

The work described here was initiated while Carlos M. Mozos was at the University of California, San Diego, on leave from the University of Castilla-La Mancha. The writers acknowledge the support from the Spanish Junta de Comunidades de Castilla-La Mancha, under a postdoctoral stay grant, and from the Spanish Ministry of Education, under the research project UNSPECIFIEDBIA2006-15471-C02-02.

References

Beer, G. (1983). “Finite element, boundary element and coupled analysis of unbounded problems in elastostatics.” Int. J. Numer. Methods Eng., 567–580.
Beer, G., and Meek, L. (1981). “Infinite domain elements.” Int. J. Numer. Methods Eng., 17, 42–52.
Bettes, P. (1977). “Infinite elements.” Int. J. Numer. Methods Eng., 2, 53–64.
Boussinesq, J. (1885). Application des potentiels à l’étude de l’équilibre et du mouvement des solides élastiques, Gauthier-Villars, France (in French).
Brady, B., and Wassyng, A. (1981). “A coupled finite element-boundary element method of stress analysis.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 475–485.
Brebbia, C., Telles, J., and Wrobel, L. (1984). Boundary element techniques, Vol. 1, 1st Ed., Springer-Verlag, Berlin.
Cerruti, V. (1882). “Ricerche intorno all'equilibrio dei corpi elastici isotropi.” Atti accad. Lincei, Mem. Classe sci. fis. mat. et nat., Rome.
Gorbunov-Posadov, M. I., and Serebrjanyi, R. V. (1961). “Design of the structures on elastic foundation.” Proc., 5th Int. Conf. on Soil Mechanics and Foundations Engineering, 643–646.
Hambly, E. C. (1991). Bridge deck behaviour, 2nd Ed., Taylor & Francis Group, London.
Hu, C., and Hartley, G. A. (1994). “Analysis of a thin plate on an elastic half-space.” Comput. Struct., 52(2), 227–235.
Luco, J. E. (2004). “Approximate external boundaries for truncated models of unbounded media.” Proc., 3rd UJNR Workshop on Soil-Structure Interaction, United States-Japan Natural Resources (UJNR) Program, Menlo Park, CA.
Luco, J. E., and Apsel, R. J. (1983). “On the Green’s functions for a layered half-space: Part I.” Bull. Seismol. Soc. Am., 73, 909–929.
Medina, F. (1981). “An axisymetric infinite element.” Int. J. Numer. Methods Eng., 17, 1177–1185.
Medina, F., and Taylor, R. L. (1983). “Finite element techniques for problems of unbounded domains.” Int. J. Numer. Methods Eng., 19, 1209–1226.
Mindlin, R. D. (1936). “Force at a point in the interior of a semi-infinite solid.” J. Appl. Phys., 7(5), 195–202.
Rajapakse, R. K. N. D., and Selvadurai, A. P. S. (1986). “On the performance of Mindlin plate elements in modelling plate-elastic medium: a comparative study.” Int. J. Numer. Methods Eng., 23, 1229–1244.
Thomson, W. (Lord Kelvin). (1848). “A note on the integration of equations of equilibrium of an elastic solid.” Cambridge and Dublin Math. J., reprinted in Mathematical and Physical Papers, (1882), Vol. 1, Cambridge, U.K.

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Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 137Issue 10October 2011
Pages: 648 - 659

History

Received: Sep 6, 2009
Accepted: Mar 29, 2011
Published online: Mar 31, 2011
Published in print: Oct 1, 2011

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Authors

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Dept. of Civil Engineering, Univ. of Castilla-La Mancha, Ciudad Real, Spain (corresponding author). E-mail: carlosmanuel.mozosuclm.es
J. Enrique Luco
Dept. of Structural Engineering, Univ. of California, San Diego, La Jolla, CA.

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