Undrained Limit Analyses for Combined Loading of Strip Footings on Clay
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 124, Issue 3
Abstract
This paper applies numerical limit analyses to evaluate the undrained stability of surface footings on nonhomogeneous and layered clay deposits under the combined effects of vertical, horizontal, and moment (V, H, M) loading. The analyses are able to resolve the true collapse loads to within ±5% by computing rigorous upper and lower bound solutions for these plane strain problems using linear programming methods and finite element discretization. The results focus on the geometry of the three-dimensional failure envelope and illustrate the effects of underbase suction and non-homogeneous undrained strength profiles. The existing empirical bearing capacity factors for inclined, eccentric loading are conservative, often underestimating the exact collapse solutions for footings on homogeneous clay by more than 25%. However, the same correction factors can become completely unreliable when there is a significant undrained strength gradient. The numerically-derived failure envelope for footings on homogeneous clay is described approximately by curve fitting techniques using relatively simple functions that can be used to update the existing bearing capacity factors.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Andersen, K. H., and Lauritzen, R.(1988). “Bearing capacity for foundations with cyclic loads.”J. Geotech. Engrg., ASCE, 114(5), 540–555.
2.
Assadi, A., and Sloan, S. W.(1991). “Undrained stability of shallow square tunnel.”J. Geotech. Engrg., ASCE, 117(8), 1152–1173.
3.
Best, M. J., and Ritter, K. (1985). Linear programming: Active set analysis and computer programs. Prentice-Hall, Englewood Cliffs, N.J.
4.
Bolton, M. D. (1979). A guide to soil mechanics. Macmillan, London.
5.
Bottero, A., Negre, R., Pastor, J., and Turgeman, S.(1980). “Finite element method and limit analysis theory for soil mechanics problems.”Comp. Meth. Appl. Mech. Engrg., 22, 131–149.
6.
Bransby, M. F., and Randolph, M. F. (1997). “Shallow foundations subject to combined loadings.”Proc., ISOPE'97.
7.
Brinch Hansen, J. (1970). “A revised and extended formula for bearing capacity.”DGI Bull. No. 28, Danish Geotech. Inst., 5–11.
8.
Davis, E. H., and Booker, J. R.(1973). “The effect of increasing strength with depth on the bearing capacity of clays.”Géotechnique, 23(4), 551–563.
9.
Dean, E. T. R., James, R. G., Schofield, A. N., Tan, F. S. C., and Tsukamoto, Y. (1992). “The bearing capacity of conical footings on sand.”Predictive soil mechanics. Thomas Telford, London, 230–253.
10.
Det Norske Veritas. (1992). “Foundations.”Classification Notes No. 30.4, Det Norske Veritas, Hovik, Norway.
11.
Drucker, D. C., Greenberg, H. J., and Prager, W.(1952). “Extended limit design theorems for continuous media.”Q. Appl. Math., 9, 381–389.
12.
Gottardi, G., and Butterfield, R.(1993). “On the bearing capacity of surface footings on sand under general planar loads.”Soils and Found., 33(3), 68–79.
13.
Houlsby, G. T., and Martin, C. M. (1992). “Modelling on the behaviour of jack-up units on clay.”Predictive soil mechanics. Thomas Telford, London, 339–358.
14.
Janbu, N.(1985). “Soil models in offshore engineering.”Géotechnique, 35(3), 239–283.
15.
Lauritzen, R., and Schjetne, K. (1976). “Stability calculations for offshore gravity structures.”Proc., 8th Offshore Technol. Conf., Paper No. OTC 2431.
16.
Lysmer, J.(1970). “Limit analysis of plane problems in soil mechanics.”J. Soil Mech. Found. Div., ASCE, 96(4), 1311–1334.
17.
Meyerhof, G. G.(1953). “The bearing capacity of foundation under eccentric and inclined loads.”Proc., 3rd Int. Conf. on Soil Mech. and Found. Engrg., 1, 440–445.
18.
Murff, J. D.(1994). “Limit analysis of multi-footing foundation systems.”Proc., 8th IACMAG, 1, 233–244.
19.
Prandtl, L. (1920). Über die harte plastischer körper. Nachr. K. Ges. Wiss. Gott., Math-Phys. Kl., 74–85.
20.
Salencon, J., and Pecker, A.(1995a). “Ultimate bearing capacity of shallow foundations under inclined and eccentric loads. Part I: Purely cohesive soil.”Eur. J. Mech. A/Solids, 14(3), 349–375.
21.
Salencon, J., and Pecker, A.(1995b). “Ultimate bearing capacity of shallow foundations under inclined and eccentric loads. Part II: Purely cohesive soil without tensile strength.”Eur. J. Mech. A/Solids, 14(3), 377–396.
22.
Sekiguchi, H., and Ohmaki, S.(1992). “Overturning of caissons by storm wave.”Soils and Found., 32(3), 144–155.
23.
Sloan, S. W.(1988a). “Lower bound limit analysis using finite elements and linear programming.”Int. J. Numer. Anal. Methods in Geomech., 12(1), 61–77.
24.
Sloan, S. W.(1988b). “A steepest edge active set algorithm for solving sparse linear programming problems.”Int. J. Numer. Anal. Methods in Geomech., 26(12), 2671–2685.
25.
Sloan, S. W., and Kleeman, P. W.(1995). “Upper bound limit analysis using discontinuous velocity fields.”Comp. Methods in Appl. Mech. and Engrg., 127, 293–314.
26.
Terzaghi, K. (1943). Theoretical soil mechanics. John Wiley & Sons, Inc., New York, N.Y.
27.
Ukritchon, B. (1996). “Evaluation of numerical limit analyses by finite elements and linear programming,” MS thesis, Dept. of Civ. and Envir. Engrg., Massachusetts Inst. of Technol., Cambridge, Mass.
28.
Vesic, A. S. (1975). “Bearing capacity of shallow foundations.”Foundation engineering handbook, H. F. Winterkorn and H. Y. Fang, eds., Van Nostrand Reinhold, New York, N.Y., 121–145.
29.
Zienkiewicz, O. C. (1983). The finite element method. McGraw-Hill Book Co., Inc., New York, N.Y.
Information & Authors
Information
Published In
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Mar 1, 1998
Published in print: Mar 1998
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.