Technical Papers
Mar 24, 2014

Effect of the Flow Rule on the Bearing Capacity of Strip Foundations on Sand by the Upper-Bound Limit Analysis and Slip Lines

Publication: International Journal of Geomechanics
Volume 14, Issue 3

Abstract

The influence of the flow rule on the bearing capacity of strip foundations placed on sand was investigated using a new kinematic approach of upper-bound limit analysis. The method of stress characteristics was first used to find the mechanism of the failure and to compute the stress field by using the Mohr-Coulomb yield criterion. Once the failure mechanism had been established, the kinematics of the plastic deformation was established, based on the requirements of the upper-bound limit theorem. Both associated and nonassociated plastic flows were considered, and the bearing capacity was obtained by equating the rate of external plastic work to the rate of the internal energy dissipation for both smooth and rough base foundations. The results obtained from the analysis were compared with those available from the literature.

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References

Anvar, S. A., and Ghahramani, A. (1997). “Equilibrium equations on zero extension lines and its application to soil engineering.” Iran. J. Sci. Technol., 21(1), 11–34.
Bolton, M. D. (1986). “The strength and dilatancy of sands.” Géotechnique, 36(1), 65–78.
Bolton, M. D., and Lau, C. K. (1993). “Vertical bearing capacity factors for circular and strip footings on Mohr-Coulomb soil.” Can. Geotech. J., 30(6), 1024–1033.
Casagrande, A. (1936). “Characteristics of cohesionless soils affecting the stability of slopes and earth fills.” J. Boston Soc. Civ. Eng., 23(1), 13–32.
Chen, W.-F. (1975). Limit analysis and soil plasticity, Elsevier, Amsterdam, Netherlands.
Chen, W.-F., and Liu, X. L. (1990). Limit analysis in soil mechanics, Elsevier, Amsterdam, Netherlands.
Choudhury, D., and Subba Rao, K. S. (2006). “Seismic bearing capacity of shallow strip footings embedded in slope.” Int. J. Geomech., 176–184.
Cox, A. D. (1962). “Axially-symmetric plastic deformation in soils—II. Indentation of ponderable soils.” Int. J. Mech. Sci., 4(5), 371–380.
Cox, A. D. (1963). “The use of non-associated flow rules in soil plasticity.” Rep. B 2/63, Royal Armament Research and Development Establishment, U.K.
Davis, E. H. (1968). “Theories of plasticity and the failure of soil masses.” Soil mechanics: Selected topics, I. K. Lee, ed., Butterworths, London, 341–380.
Davis, E. H., and Booker, J. R. (1973). “Some adaptations of classical plasticity theory for soil stability problems.” Proc., Symp. on the Role of Plasticity in Soil Mechanics, Transport and Road Research Laboratory, Transportation Research Board, Berkshire, U.K., 24–41.
Davis, R. O., and Selvadurai, A. P. S. (2002). Plasticity and geomechanics, Cambridge University Press, Cambridge, U.K.
De Borst, R., and Vermeer, P. A. (1984). “Possibilities and limitations of finite elements for limit analysis.” Géotechnique, 34(2), 199–210.
DiMaggio, F. L., and Sandler, I. S. (1971). “Material model for granular soils.” J. Engrg. Mech. Div., 97(3), 935–950.
Drescher, A., and Detournay, E. (1993). “Limit load in translational failure mechanisms for associative and non-associative materials.” Géotechnique, 43(3), 443–456.
Drucker, D. C., and Prager, W. (1952). “Soil mechanics and plastic analysis on limit design.” Q. Appl. Math., 10(2), 157–165.
Drucker, D. C., Prager, W., and Greenberg, H. J. (1952). “Extended limit design theorems for continuous media.” Q. Appl. Math., 9(4), 381–389.
Eid, H. (2013). “Bearing capacity and settlement of skirted shallow foundations on sand.” Int. J. Geomech., 645–652.
Frydman, S., and Burd, H. J. (1997). “Numerical studies of bearing-capacity factor Nγ.” J. Geotech. Geoenviron. Eng., 20–29.
Ghazavi, M., and Eghbali, A. (2013). “New geometric average method for calculation of ultimate bearing capacity of shallow foundations on stratified sands.” Int. J. Geomech., 101–108.
Gourvenec, S., Randolph, M. F., and Kingsnorth, O. (2006). “Undrained bearing capacity of square and rectangular footings.” Int. J. Geomech., 147–157.
Harr, M. E. (1966). Foundations of theoretical soil mechanics, McGraw Hill, New York.
Hill, R. (1950). The mathematical theory of plasticity, Oxford University Press, New York.
Hjiaj, M., Lyamin, A. V., and Sloan, S. W. (2005). “Numerical limit analysis solutions for the bearing capacity factor Nγ.” Int. J. Solids Struct., 42(5–6), 1681–1704.
Houlsby, G. T. (1991). “How the dilatancy of soils affects their behavior.” Rep. No. OUEL 1888/91, Dept. of Engineering Science, Univ. of Oxford, Oxford, U.K.
Houlsby, G. T., and Wroth, C. P. (1982). “Direct solution of plasticity problems in soils by the method of characteristics.” Proc., 4th Int. Conf. on Numerical Methods in Geomechanics, Soil Mechanics Rep. No. SM021/BRE/82, Dept. of Engineering Science, Univ. of Oxford, Oxford, U.K.
Jahanandish, M., Habibagahi, G., and Veiskarami, M. (2010a). “Bearing capacity factor, Nγ, for unsaturated soils by ZEL method.” Acta Geotech., 5(3), 177–188.
Jahanandish, M., Veiskarami, M., and Ghahramani, A. (2010b). “Effect of stress level on the bearing capacity factor, Nγ, by the ZEL method.” KSCE J. Civ. Eng., 14(5), 709–723.
Kachanov, L. M. (1974). Fundamentals of the theory of plasticity, Mir Publishers, Moscow.
Kötter, F. (1903). “Die bestimmung des druckesangekrümmtengleitflächen, eineaufgabeaus der lehrevomerddruck.” Sitzungsberichte der Akademie der Wissenschaften, Berlin, 229–233 (in German).
Kumar, J. (2003). “Nγ for rough strip footing using the method of characteristics.” Can. Geotech. J., 40(3), 669–674.
Kumar, J. (2009). “The variation of Nγ with footing roughness using the method of characteristics.” Int. J. Numer. Anal. Methods Geomech., 33(2), 275–284.
Kumar, J., and Ghosh, P. (2005). “Bearing capacity factor Nγ for ring footings using the method of characteristics.” Can. Geotech. J., 42(5), 1474–1484.
Kumar, J., and Kouzer, K. M. (2007). “Effect of footing roughness on bearing capacity factor Nγ.” J. Geotech. Geoenviron. Eng., 502–511.
Lade, P. V., and Duncan, J. M. (1975). “Elasto-plastic stress-strain theory for cohesionless soil.” J. Geotech. Engrg. Div., 101, 1037–1053.
Lyamin, A. V., and Sloan, S. W. (2002). “Upper bound limit analysis using linear finite elements and non-linear programming.” Int. J. Numer. Anal. Methods Geomech., 26(2), 181–216.
Martin, C. M. (2005). “Exact bearing capacity calculations using the method of characteristics.” Proc., 11th Int. Conf. of International Association for Computer Methods and Advances in Geomechanics (IACMAG), Vol. 4, Polytechnic Univ. of Turin and Italian Geotechnical Society, 441–450.
Martin, C. M., and Houlsby, G. T. (2001). “Combined loading of spudcan foundations on clay: Numerical modeling.” Géotechnique, 51(8), 687–699.
Meyerhof, G. G. (1951). “The ultimate bearing capacity of foundations.” Géotechnique, 2(4), 301–332.
Meyerhof, G. G. (1963). “Some recent research on the bearing capacity of foundations.” Can. Geotech. J., 1(1), 16–26.
Michalowski, R. L. (1997). “An estimate of the influence of soil weight on the bearing capacity using limit analysis.” Soils Found., 37(4), 57–64.
Prandtl, L. (1920). “Über die härteplastischerkörper.” Nachr. Ges. Wissensch, Math.-Phys. Klasse, Göttingen, 74–85 (in German).
Randolph, M. F., and Houlsby, G. T. (1984). “The limiting pressure on a circular pile loaded laterally in cohesive soil.” Géotechnique, 34(4), 613–623.
Reissner, H. (1924). “Zumerddruck problem” (“Concerning the earth pressure problem”). Proc., 1st Int. Congress of Applied Mechanics, C. B. Biezeno and J. M. Burgers, eds., J. Waltman Jr., Delft, Netherlands, 295–311.
Roscoe, K. H. (1970). “The influence of strains in soil mechanics.” Géotechnique, 20(2), 129–170.
Rowe, P. W. (1962). “The stress-dilatancy relation for static equilibrium of an assembly of particles in contact.” Proc. R. Soc. Lond. A, 269(1339), 500–527.
Rowe, P. W. (1969). “The relation between the shear strength of sands in triaxial compression, plane strain and direct shear.” Géotechnique, 19(1), 75–86.
Sabzevari, A., and Ghahramani, A. (1972). “The limit equilibrium analysis of bearing capacity and earth pressure problems in nonhomogeneous soils.” Soils Found., 12(3), 33–48.
Sloan, S. W. (1989). “Upper bound limit analysis using finite elements and linear programming.” Int. J. Numer. Anal. Methods Geomech., 13(3), 263–282.
Sloan, S. W., and Kleeman, P. W. (1995). “Upper bound limit analysis using discontinuous velocity fields.” Comput. Meth. Appl. Mech. Eng., 127(1–4), 293–314.
Sokolovskii, V. V. (1960). Statics of soil media. Trans. D. H. Jones and A. N. Schofield, Butterworths, London.
Taylor, D. W. (1948). Fundamentals of soil mechanics, Wiley, New York.
Terzaghi, K. (1943). Theoretical soil mechanics, Wiley, New York.
Veiskarami, M., Eslami, A., and Kumar, J. (2011). “End bearing capacity of driven piles in sand using the stress characteristics method: Analysis and implementation.” Can. Geotech. J., 48(10), 1570–1586.
Veiskarami, M., and Kumar, J. (2012). “Bearing capacity of foundations subjected to groundwater flow.” Geomech. Geoeng., 7(4), 293–301.
Vesić, A. S. (1973). “Analysis of ultimate loads of shallow foundations.” J. Soil Mech. and Found. Div., 99(1), 45–73.
Wroth, C. P. (1958). “The behaviour of soils and other granular media when subjected to shear.” Ph.D. dissertation, Univ. of Cambridge, Cambridge, U.K.
Yu, H.-S. (2006). Plasticity and geotechnics, Springer, New York.
Yu, H.-S., and Houlsby, G. T. (1991). “Finite cavity expansion in dilatant soils: Loading analysis.” Géotechnique, 41(2), 173–184.
Yu, H.-S., Salgado, R., Sloan, S. W., and Kim, J. M. (1998). “Limit analysis versus limit equilibrium for slope stability.” J. Geotech. Geoenviron. Eng., 124(1), 1–11.
Zienkiewicz, O. C., Humpheson, C., and Lewis, R. W. (1975). “Associated and non-associated visco-plasticity and plasticity in soil mechanics.” Géotechnique, 25(4), 671–689.

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Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 14Issue 3June 2014

History

Received: Dec 21, 2012
Accepted: Jun 3, 2013
Published online: Mar 24, 2014
Published in print: Jun 1, 2014
Discussion open until: Aug 24, 2014

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Mehdi Veiskarami [email protected]
Assistant Professor, Dept. of Civil Engineering, Faculty of Engineering, Univ. of Guilan, 3756 Rasht, Iran (corresponding author). E-mail: [email protected]; [email protected]
Jyant Kumar [email protected]
Professor, Civil Engineering Dept., Indian Institute of Science, Bangalore 560012, India. E-mail: [email protected]
Fatemeh Valikhah [email protected]
M.Sc. Student, Dept. of Civil Engineering, Faculty of Engineering, Univ. of Guilan, 3756 Rasht, Iran. E-mail: [email protected]

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