Evaluation of Passive Earth Resistance Using an Improved Limit Equilibrium Method of Slices
Publication: International Journal of Geomechanics
Volume 21, Issue 11
Abstract
The present study proposes a new approach to solve passive earth pressure problems using the method of slices, coupled with the limit equilibrium (LE) technique. Unlike existing LE studies that adopted failure surfaces of predetermined shapes, here, the backfill was discretized into thin vertical slices, and the Mohr–Coulomb failure criterion was enforced at each slice. The failure surface was then derived by joining the failure plane of the slices starting from the wall base. Consequently, the failure planes became the base of the respective slices. The outline of the failure surface is governed by the soil, wall, and interslice friction angles. The variation of the interslice friction angle was assumed to follow a power function, and the exponents were achieved by satisfying the static equilibrium of the slices and a boundary condition. The proposed results were verified with the available numerical and experimental results, and they show excellent agreement. Also, the results illustrate that the shape of the failure surface is majorly governed by the wall roughness and interslice friction function. For rough walls, failure surfaces are composite curved planar, and the degree of curvature increases with increasing wall roughness.
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References
Antão, A. N., T. G. Santana, M. Vicente da Silva, and N. M. da Costa Guerra. 2011. “Passive earth-pressure coefficients by upper-bound numerical limit analysis.” Can. Geotech. J. 48 (5): 767–780. https://doi.org/10.1139/t10-103.
Ashour, M., G. Norris, and P. Pilling. 1998. “Lateral loading of a pile in layered soil using the strain wedge model.” J. Geotech. Geoenviron. Eng. 124 (4): 303–315. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:4(303).
Benmeddour, D., M. Mellas, R. Frank, and A. Mabrouki. 2012. “Numerical study of passive and active earth pressures of sands.” Comput. Geotech. 40: 34–44. https://doi.org/10.1016/j.compgeo.2011.10.002.
Caquot, A., and J. Kerisel. 1948. Tables for the calculation of passive pressure, active pressure and bearing capacity of foundations. Paris: Gauthier-Villars.
Chen, W. F. 1975. Limit analysis and soil plasticity. London: Elsevier.
Ching, R. K. H., and D. G. Fredlund. 1983. “Some difficulties associated with the limit equilibrium method of slices.” Can. Geotech. J. 20 (4): 661–672. https://doi.org/10.1139/t83-074.
Coulomb, C. A. 1776. Essai sur une application des regles de maximis et minimis a quelques problemes de statique relatifs a l’architecturea. Paris: Mémoires de l’Académie Des Sciences.
Fan, K. 1983. “Evaluation of the interslice side forces for lateral earth force and slope stability problems.” M.Sc. thesis, Univ. of stockholm.
Fang, Y. S., J. M. Chen, and C. Y. Chen. 1997. “Earth pressures with sloping backfill.” J. Geotech. Geoenviron. Eng. 123 (3): 250–259. https://doi.org/10.1061/(ASCE)1090-0241(1997)123:3(250).
Fang, Y.-S., T.-J. Chen, and B.-F. Wu. 1994. “Passive earth pressures with various wall movements.” J. Geotech. Eng. 120 (8): 1307–1323. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:8(1307).
Fang, Y. S., Y. C. Ho, and T. J. Chen. 2002. “Passive earth pressure with critical state concept.” J. Geotech. Geoenviron. Eng. 128 (8): 651–659. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:8(651).
James, R. G., and P. Bransby. 1970. “Experimental and theoretical investigations of a passive earth pressure problem.” Géotechnique 20 (1): 17–37. https://doi.org/10.1680/geot.1970.20.1.17.
Janbu, N. 1957. “Earth pressure and bearing capacity calculations by generalized method of slices.” In Vol. 2 of Proc., 4th Int. Conf. on Soil Mechanics and Foundation Engineering, 207–213.
Kerisel, J., and E. Absi. 1990. Active and passive earth pressure tables. Rotterdam, Netherlands: A.A. Balkema.
Kumar, J. 2001. “Seismic passive earth pressure coefficients for sands.” Can. Geotech. J. 38 (4): 876–881. https://doi.org/10.1139/t01-004.
Kumar, J., and S. Chitikela. 2002. “Seismic passive earth pressure coefficients using the method of characteristics.” Can. Geotech. J. 39 (2): 463–471. https://doi.org/10.1139/t01-103.
Kumar, J., and K. S. Subba Rao. 1997a. “Passive pressure coefficients, critical failure surface and its kinematic admissibility.” Géotechnique 47 (1): 185–192. https://doi.org/10.1680/geot.1997.47.1.185.
Kumar, J., and K. S. Subba Rao. 1997b. “Passive pressure determination by method of slices.” Int. J. Numer. Anal. Methods Geomech. 21 (5): 337–345. https://doi.org/<337::AID-NAG873>3.0.CO;2-P.
Liu, S., Y. Xia, and L. Liang. 2018. “A modified logarithmic spiral method for determining passive earth pressure.” J. Rock Mech. Geotech. Eng. 10 (6): 1171–1182. https://doi.org/10.1016/j.jrmge.2018.03.011.
Maciejewski, J., and A. Jarze¸bowski. 2004. “Application of kinematically admissible solutions to passive earth pressure problems.” Int. J. Geomech. 4 (2): 127–136. https://doi.org/10.1061/(ASCE)1532-3641(2004)4:2(127).
Morrison, E. E., Jr., and R. M. Ebeling. 1995. “Limit equilibrium computation of dynamic passive earth pressure.” Can. Geotech. J. 32 (3): 481–487. https://doi.org/10.1139/t95-050.
Patki, M. A., D. M. Dewaikar, and J. N. Mandal. 2017. “Numerical study on passive earth pressures using Kötter’s equation.” Int. J. Geomech. 17 (2): 06016015. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000708.
Patki, M. A., J. N. Mandal, and D. M. Dewaikar. 2015. “Determination of passive earth pressure coefficients using limit equilibrium approach coupled with the Kötter equation.” Can. Geotech. J. 52 (9): 1241–1254. https://doi.org/10.1139/cgj-2014-0351.
Qian, Z. H., J. F. Zou, Q. J. Pan, G. H. Chen, and S. X. Liu. 2020a. “Discretization-based kinematical analysis of three-dimensional seismic active earth pressures under nonlinear failure criterion.” Comput. Geotech. 126: 103739. https://doi.org/10.1016/j.compgeo.2020.103739.
Qian, Z. H., J. F. Zou, J. Tian, and Q. J. Pan. 2020b. “Estimations of active and passive earth thrusts of non-homogeneous frictional soils using a discretisation technique.” Comput. Geotech. 119: 103366. https://doi.org/10.1016/j.compgeo.2019.103366.
Qin, C., and S. C. Chian. 2020. “Pseudo-dynamic lateral earth pressures on rigid walls with varying cohesive-frictional backfill.” Comput. Geotech. 119: 103289. https://doi.org/10.1016/j.compgeo.2019.103289.
Rahardjo, H., and D. G. Fredlund. 1984. “General limit equilibrium method for lateral earth force.” Can. Geotech. J. 21 (1): 166–175. https://doi.org/10.1139/t84-013.
Rankine, W. J. M. 1857. “On the stability of loose earth.” Philos. Trans. R. Soc. 147: 185–187.
Shamsabadi, A., M. Ashour, and G. Norris. 2005. “Bridge abutment nonlinear force–displacement–capacity prediction for seismic design.” J. Geotech. Geoenviron. Eng. 131 (2): 151–161. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:2(151).
Shamsabadi, A., K. M. Rollins, and M. Kapuskar. 2007. “Nonlinear soil–abutment–bridge structure interaction for seismic performance-based design.” J. Geotech. Geoenviron. Eng. 133 (6): 707–720. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:6(707).
Shamsabadi, A., S.-Y. Xu, and E. Taciroglu. 2013. “A generalized log-spiral-Rankine limit equilibrium model for seismic earth pressure analysis.” Soil Dyn. Earthquake Eng. 49: 197–209. https://doi.org/10.1016/j.soildyn.2013.02.020.
Shiau, J. S., C. E. Augarde, A. V. Lyamin, and S. W. Sloan. 2008. “Finite element limit analysis of passive earth resistance in cohesionless soils.” Soils Found. 48 (6): 843–850. https://doi.org/10.3208/sandf.48.843.
Shields, D. H., and A. Z. Tolunay. 1973. “Passive pressure coefficients by method of slices.” J. Soil Mech. Found. Div. 99 (12): 1043–1053. https://doi.org/10.1061/JSFEAQ.0001968.
Škrabl, S., and B. Macuh. 2005. “Upper-bound solutions of three-dimensional passive earth pressures.” Can. Geotech. J. 42 (5): 1449–1460. https://doi.org/10.1139/t05-067.
Soubra, A. H. 2000. “Static and seismic passive earth pressure coefficients on rigid retaining structures.” Can. Geotech. J. 37 (2): 463–478. https://doi.org/10.1139/t99-117.
Soubra, A. H., and B. Macuh. 2002. “Active and passive earth pressure coefficients by a kinematical approach.” Geotech. Eng. 155 (2): 119–131. https://doi.org/10.1680/geng.155.2.119.38657.
Subba Rao, K. S., and D. Choudhury. 2005. “Seismic passive earth pressures in soils.” J. Geotech. Geoenviron. Eng. 131 (1): 131–135. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:1(131).
Tang, C., K. K. Phoon, and K. C. Toh. 2014. “Lower-bound limit analysis of seismic passive earth pressure on rigid walls.” Int. J. Geomech. 14 (5): 04014022. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000385.
Terzaghi, K. 1943. Theoretical soil mechanics. New York: John.
Xu, S. Y., K. P. M. Kannangara, and E. Taciroglu. 2018. “Analysis of the stress distribution across a retaining wall backfill.” Comput. Geotech. 103: 13–25. https://doi.org/10.1016/j.compgeo.2018.07.001.
Xu, S. Y., A. I. Lawal, A. Shamsabadi, and E. Taciroglu. 2019. “Estimation of static earth pressures for a sloping cohesive backfill using extended Rankine theory with a composite log-spiral failure surface.” Acta Geotech. 14 (2): 579–594. https://doi.org/10.1007/s11440-018-0673-2.
Zakerzadeh, N., D. G. Fredlund, and D. E. Pufahl. 1999. “Interslice force functions for computing active and passive earth force.” Can. Geotech. J. 36 (6): 1015–1029. https://doi.org/10.1139/t99-065.
Zhu, D. Y., Q. H. Qian, and C. F. Lee. 2001. “Active and passive critical slip fields for cohesionless soils and calculation of lateral earth pressures.” Géotechnique 51 (5): 407–423. https://doi.org/10.1680/geot.2001.51.5.407.
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Published In
International Journal of Geomechanics
Volume 21 • Issue 11 • November 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Dec 7, 2020
Accepted: Jun 29, 2021
Published online: Aug 26, 2021
Published in print: Nov 1, 2021
Discussion open until: Jan 26, 2022
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