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Generalized Framework for Three-Dimensional Upper Bound Limit Analysis in a Tresca Material

[+] Author and Article Information
A. M. Puzrin

School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332

M. F. Randolph

Center for Offshore Foundation Systems, The University of Western Australia, Nedlands, WA 6907, Australia

J. Appl. Mech 70(1), 91-100 (Jan 23, 2003) (10 pages) doi:10.1115/1.1507764 History: Received July 20, 2001; Revised March 15, 2002; Online January 23, 2003
Copyright © 2003 by ASME
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References

Murff,  J. D., and Hamilton,  J., 1993, “P-Ultimate for Undrained Analysis of Laterally Loaded Piles,” J. Geotech. Eng., 119, pp. 91–107.
Shield,  R. T., and Drucker,  D. C., 1953, “The Application of Limit Analysis to Punch Indentation Problems,” ASME J. Appl. Mech., 20, pp. 453–460.
Levin,  A., 1955, “Indentation Pressure of a Smooth Circular Punch,” Quart. Appl. Math., , 13, pp. 381–389.
Bransby,  M. F., and Randolph,  M. F., 1998, “Combined Loading on Skirted Foundations,” Geotechnique, 48, pp. 637–655.
Puzrin,  A. M., 2001, “On the Superposition of Work Dissipation in Coulomb’s Soil,” Int. J. Solids Struct., in press.
Puzrin,  A. M., and Randolph,  M. F., 2001, “On the Superposition of Plastically Dissipated Work in Upper Bound Limit Analysis,” Proc. R. Soc. London, Ser. A, 457, pp. 567–586.
Drucker,  D. C., Greenberg,  H. J., and Prager,  W., 1951, “The Safety Factor of an Elastic-Plastic Body in Plane Strain,” ASME J. Appl. Mech., 73, pp. 371–378.
Boresi, A. P., and Chong, K. P., 2000, Elasticity in Engineering Mechanics, John Wiley and Sons, New York.
Abramovitz, M., and Stegun, I. A., eds., 1973, Handbook of Mathematical Functions, Dover, New York.
Randolph,  M. F., and Houlsby,  G. T., 1984, “The Limiting Pressure on a Circular Pile Loaded Laterally in Cohesive Soil,” Geotechnique, 34, pp. 613–623.
Randolph,  M. F., Martin,  C. M., and Hu,  Y., 2000, “Limiting Resistance of a Spherical Penetrometer in Cohesive Material,” Geotechnique, 50, pp. 573–582.
Paolucci,  R., and Pecker,  A., 1997, “Soil Inertia Effects on the Bearing Capacity of Rectangular Foundations on Cohesive Soils,” Eng. Struct., 19(8), pp. 637–643.
Kusakabe,  O., Suzuki,  H., and Nakase,  A., 1986, “An Upper-Bound Calculation on Bearing Capacity of a Circular Footing on a Non-homogeneous Clay,” Soils Found., 26, pp. 143–148.

Figures

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Schematic layout of the bearing capacity problem
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Failure mechanisms: (a) d≥b; (b) 0<d<b
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Examples of hyperbolic velocity fields: (a) discontinuity surfaces bounding the passive shear zone for various values of d; (b) hyperbolic streamlines for d=0.4
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Comparison of different velocity fields in the passive zone
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Rotation of a smooth square footing
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Coordinate transformations and velocity boundary conditions: (a) in the plane of rotation; (b) perpendicular to the plane of rotation
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Rotation of a rough circular footing
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Coordinate transformations and velocity boundary condition
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Bearing capacity coefficient

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