Lower-Bound Limit Analysis of Seismic Passive Earth Pressure on Rigid Walls
Publication: International Journal of Geomechanics
Volume 14, Issue 5
Abstract
Static and seismic passive earth pressure coefficients for the general case of an inclined wall and a sloping cohesionless backfill were computed by using finite-element lower-bound limit analysis based on second-order cone programming (SOCP). The comparison with the best existing upper-bound solution and the widely accepted solution obtained by the method of stress characteristics has shown that the present lower-bound solutions can provide a safe estimate of the passive earth pressures. Therefore, combining present results and upper-bound solutions can bracket the true value of passive earth pressures. In addition, design tables are presented that allow geotechnical engineers to easily use the present results in practice.
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References
ABAQUS 6.5 [Computer software]. Vélizy-Villacoublay, France, Dassault Systèmes.
Caquot, A., and Kérisel, J. (1948). Tables for the calculation of passive pressure, active pressure and bearing capacity of foundations, Gauthier-Villars, Paris.
Chen, W.-F. (1975). Limit analysis and soil plasticity, Elsevier, Amsterdam, Netherlands.
Ciria, H., Peraire, J., and Bonet, J. (2008). “Mesh adaptive computation of upper and lower bounds in limit analysis.” Int. J. Numer. Methods Eng., 75(8), 899–944.
Commission of the European Communities. (1994). “Design provisions for earthquake resistance of structures. Part 5: Foundations, retaining structures and geotechnical aspects.” Eurocode 8, Luxembourg.
Fang, Y.-S., and Chen, T.-J. (1995). “Modification of Mononobe-Okabe theory.” Geotechnique, 45(1), 165–167.
Fardis, M. N., Carvalho, E., Elnashai, A., Faccioli, E., Pinto, P., and Pumier, A. (2005). Designers’ guide to EN 1998-1 and EN 1998-5, Thomas Telford, London.
Ghosh, P., and Kolathayar, S. (2011). “Seismic passive pressure behind non-vertical wall with composite failure mechanism: Pseudo-dynamic approach.” Geotech. Geol. Eng., 29(3), 363–373.
Kérisel, J., and Absi, E. (1990). Tables de poussée et de butée des terres, 3rd Ed., Presses de l’École Nationale des Ponts et Chaussées, Paris.
Kumar, J. (2001). “Seismic passive earth pressure coefficients for sands.” Can. Geotech. J., 38(4), 876–881.
Kumar, J., and Chitikela, S. (2002). “Seismic passive earth pressure coefficients using the method of characteristics.” Can. Geotech. J., 39(2), 463–471.
Lyamin, A. V., and Sloan, S. W. (2002a). “Lower bound limit analysis using non-linear programming.” Int. J. Numer. Methods Eng., 55(5), 573–611.
Lyamin, A. V., and Sloan, S. W. (2002b). “Upper bound limit analysis using linear finite elements and non-linear programming.” Int. J. Numer. Anal. Methods Geomech., 26(2), 181–216.
Lysmer, J. (1970). “Limit analysis of plane problems in soil mechanics.” J. Soil Mech. and Found. Div., 96(4), 1311–1334.
Makrodimopoulos, A., and Martin, C. M. (2006). “Lower bound limit analysis of cohesive-frictional materials using second-order cone programming.” Int. J. Numer. Methods Eng., 66(4), 604–634.
Makrodimopoulos, A., and Martin, C. M. (2007). “Upper bound limit analysis using simplex strain elements and second-order cone programming.” Int. J. Numer. Anal. Methods Geomech., 31(6), 835–865.
MATLAB 7.10.0 [Computer software]. Natick, MA, MathWorks.
Mononobe, N., and Matsuo, H. (1929). “On determination of earth pressure during earthquakes.” Proc., World Engineering Congress, Vol. 9, 177–185, Paper No. 388.
Morrison, E. E., Jr., and Ebeling, R. M. (1995). “Limit equilibrium computation of dynamic passive earth pressure.” Can. Geotech. J., 32(3), 481–487.
MOSEK 7.0 [Computer software]. Copenhagen, Denmark, Mosek.
Okabe, S. (1924). “General theory on earth pressure and seismic stability of retaining walls and dams.” J. Jap. Soc. Civ. Eng., 10(6), 1277–1323.
Potts, D. M., and Fourie, A. B. (1986). “A numerical study of the effects of wall deformation on earth pressures.” Int. J. Numer. Anal. Methods Geomech., 10(4), 383–405.
Richards, R., Jr., and David, E. G. (1979). “Seismic behavior of gravity retaining walls.” J. Geotech. Engrg. Div., 105(4), 449–464.
Seed, H. B., and Whitman, R. V. (1970). “Design of earth retaining structures for dynamic loads.” Proc., ASCE Special Conf. on Lateral Stresses in the Ground and Design of Earth-Retaining Structures, ASCE, New York, 103–147.
Shiau, J. S., Augarde, C. E., Lyamin, A. V., and Sloan, S. W. (2008). “Finite element limit analysis of passive earth resistance in cohesionless soils.” Soils Found., 48(6), 843–850.
Shiau, J. S., Lyamin, A. V., and Sloan, S. W. (2006). “Application of pseudo-static limit analysis in geotechnical earthquake design.” Proc., 6th European Conf. on Numerical Methods in Geotechnical Engineering, H. F. Schweiger, ed., Taylor & Francis, London, 249–255.
Sloan, S. W. (1988). “Lower bound limit analysis using finite elements and linear programming.” Int. J. Numer. Anal. Methods Geomech., 12(1), 61–77.
Sloan, S. W. (1989). “Upper bound limit analysis using finite elements and linear programming.” Int. J. Numer. Anal. Methods Geomech., 13(3), 263–282.
Soubra, A. H. (2000). “Static and seismic passive earth pressure coefficients on rigid retaining structures.” Can. Geotech. J., 37(2), 463–478.
Soubra, A. H., and Macuh, B. (2002). “Active and passive earth pressure coefficients by a kinematical approach.” Proc. Inst. Civil Eng. Geotech. Eng., 155(2), 119–131.
Subba Rao, K., and Choudhury, D. (2005). “Seismic passive earth pressures in soils.” J. Geotech. Geoenviron. Eng., 131–135.
Tang, C., Toh, K., and Phoon, K. (2014). “Axisymmetric lower-bound limit analysis using finite elements and second-order cone programming.” J. Eng. Mech., 268–278.
Terzaghi, K. (1943). Theoretical soil mechanics, Wiley, New York.
Wu, G., and Finn, W. D. L. (1999). “Seismic lateral pressures for design of rigid walls.” Can. Geotech. J., 36(3), 509–522.
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Published In
International Journal of Geomechanics
Volume 14 • Issue 5 • October 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: May 21, 2013
Accepted: Jan 7, 2014
Published online: Jan 9, 2014
Discussion open until: Aug 31, 2014
Published in print: Oct 1, 2014
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