Numerical Solutions for Biot's Consolidation of Layered Soil
Publication: Journal of Engineering Mechanics
Volume 109, Issue 3
Abstract
In this paper, Biot's consolidation of layered soil is solved by the finite layer (strip) method based on quasi‐variational as well as least square approaches. The two‐ (three‐) dimensional medium is idealized by as many strips (layers) as is necessary to achieve the required accuracy, and the formulation of the relevant matrices requires only simple mathematics involving polynomials and Fourier series, and therefore is much simpler to compare with other techniques using intergral transforms. Examples are computed and the results compare favorably with known solutions.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Biot, M. A., “General Theory of Three‐Dimensional Consolidation,” Journal of Applied Physics, Vol. 12, 1941, pp. 155–164.
2.
Booker, I. R., and Small, J. C., “Finite Layer Analysis of Consolidation, Part I,” Research Report No. 357, University of Sydney, Sydney, Australia, 1979(b).
3.
Booker, J. R., and Small, J. C., “An Investigation of the Stability of Numerical Solutions of Biot's Equations of Consolidation,” International Journal of Solid Structures, Vol. 2, 1975, pp. 907–917.
4.
Booker, J. R., and Small, J. C., “Finite Layer Analysis of Consolidation, Part II,” Research Report No. 358, University of Sydney, Sydney, Australia, 1979(c).
5.
Cheung, Y. K., and Fan, S. C., “Analysis of Pavements and Layered Foundations by Finite Layer Method,” Third International Conference on Numerical Methods in Geomechanics, Aachen, Vol. 3, 1979, pp. 1129–1135.
6.
Christian, J. T., and Boehmer, J. W., “Plane Strain Consolidation by Finite Elements,” Journal of Soil Mechanics and Foundation Engineering Division, ASCE, Vol. 96, No.SM4, 1970, pp. 1435–1457.
7.
Herrmann, L. R., “Elasticity Equations for Incompressible and Nearly Incompressible Materials by a Variational Theorem,” AIAA Journal, Vol. 3, 1965, pp. 1896–1900.
8.
Hwang, C. T., Morgenstern, N. R., and Murray, D. T., “On Solution of Plane Strain Consolidation Problems by Finite Element Methods,” Canadian Geotechnical Journal, Vol. 8, No. 1, 1971, pp. 109–118.
9.
Rendulic, L., “Porenziffer und Poven Wasserdruck in Tonen,” Buingenieur, Vol. 17, 1936, pp. 559–564.
10.
Sandhu, R. S., and Wilson, E. L., “Finite Element Analysis of Seepage in Elastic Media,” Journal of Engineering Mechanics Division, ASCE, Vol. 95, No. EM3, 1969, pp. 641–652.
11.
Sandhu, R. S., “Variational Principles for Finite Element Analysis of Consolidation,” Numerical Methods in Geomechanics, Desai, C. S., ed., ASCE 2nd International Conference on Numerical Methods in Geomechanics held at Virginia Polytechnic, Blacksburg, Va., 1976, pp. 20–40.
12.
Small, J. C., and Booker, J. R., “Analysis of the Consolidation of Layered Soils using the Methods of Lines,” Third International Conference on Numerical Methods in Geomechanics, Aachen, Vol. 1, 1979(a), pp. 201–211.
13.
Sneddon, I. N., The Use of Integral Transform, Tata McGraw Hill Publishing Co. Ltd., New Delhi, India, 1979.
14.
Terzaghi, K., Theoretical Soil Mechanics, John Wiley & Sons, Inc., New York, N.Y., 1943.
15.
Verruijt, A., “Elastic Storage of Aquifers,” Flow Through Porous Media, DeWiest, R. J. M., ed., Academic Press, New York, N.Y., 1969, pp. 331–376.
16.
Yokoo, Y., Yamagata, K., and Nagaoka, H., “Finite Element Method Applied to Biot Consolidation Theory,” Soils and Foundations, Vol. 11, No. 1, 1971, pp. 29–46.
17.
Yokoo, Y., Yamagata, K., and Nagaoka, H., “Variational Principles for Consolidation,” Soils and Foundations, Vol. 11, No. 4, 1971, pp. 25–35.
18.
Yokoo, Y., Yamagata, K., and Nagaoka, H., “Finite Element Analysis of Consolidation Following Undrained Deformation,” Soils and Foundations, Vol. 11, No. 4, 1971, pp. 37–58.
19.
Zienkiewicz, O. C., Humpheson, C., and Lewis, R. W., “A Unified Approach to Soil Mechanics Problems including Plasticity and Viscoplasticity,” Finite Element in Geomechanics, Gudehus, G., ed., John Wiley & Sons, Inc., New York, N.Y., 1975, pp. 179–190.
20.
Zienkiewicz, O. C., The Finite Element Method, Third Edition, McGraw Hill Book Co., Ltd., London, England, 1976.
Information & Authors
Information
Published In
Copyright
Copyright © 1983 ASCE.
History
Published online: Aug 1, 1983
Published in print: Aug 1983
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.