Active Earth Thrust Theory for Horizontal Granular Backfill on a Cantilever Wall with a Short Heel
Publication: International Journal of Geomechanics
Volume 17, Issue 8
Abstract
Cantilever retaining walls are earth-retaining structures commonly used in construction. Conventional methods used to determine the active earth thrust acting on a wall often neglect friction between the soil and wall. This study presents an analytical solution for determining the active earth thrusts acting on a cantilever retaining wall with a short heel and a shear key that supports granular backfill. Three different earth thrusts were considered to be acting on three different parts of the rear face of the wall; the thrusts were derived using the limit equilibrium method. The active earth thrust formulas were also simplified in terms of earth thrust coefficients, unit weight, and wall height. An algorithm was developed to obtain earth thrust coefficients depending on various wall dimensions and internal friction angles and to prepare graphs representing earth thrust coefficients and failure surface angles. The effects of wall dimensions and internal friction angles on the earth thrusts and failure surface angles were determined. Finally, the proposed method of determining earth thrust coefficients was compared with other approaches.
Get full access to this article
View all available purchase options and get full access to this article.
References
Altunbaş, A. (2015). “Influence of dilatancy on slip planes and on localization of strains.” Ph.D. thesis, Boğaziçi Univ., Istanbul, Turkey.
Baker, R., and Klein, Y. (2004a). “An integrated limiting equilibrium approach for design of reinforced soil retaining structures. Part I: formulation.” Geotext. Geomembr., 22(3), 119–150.
Baker, R., and Klein, Y. (2004b). “An integrated limiting equilibrium approach for design of reinforced soil retaining structures. Part III: Optimal design.” Geotext. Geomembr., 22(6), 455–479.
Barghouthi, A. (1990). “Active earth pressure on walls with base projection.” J. Geotech. Eng., 1570–1575.
Benmebarek, S., Khelifa, T., Benmebarek, N., and Kastner, R. (2008). “Numerical evaluation of 3D passive earth pressure coefficients for retaining wall subjected to translation.” Comput. Geotech., 35(1), 47–60.
Benmeddour, D., Mellas, M., Frank, R., and Mabrouki, A. (2012). “Numerical study of passive and active earth pressures of sands.” Comput. Geotech., 40, 34–44.
Bentler, J., and Labuz, J. (2006). “Performance of a cantilever retaining wall.” J. Geotech. Geoenviron. Eng., 1062–1070.
Bowles, J. E. (1992). Engineering properties of soils and their measurement, 4th Ed., McGraw-Hill, New York.
Camp, C., and Akin, A. (2012). “Design of retaining walls using big bang–big crunch optimization.” J. Struct. Eng., 438–448.
Chen, L. (2014). “Active earth pressure of retaining wall considering wall movement.” Eur. J. Environ. Civ. Eng., 18(8), 910–926.
Chen, W. F., and Liu, X. L. (1990). Limit analysis in soil mechanics, Elsevier, Amsterdam, Netherlands.
Cheng, Y., Hu, Y., and Wei, W. (2007). “General axisymmetric active earth pressure by method of characteristics–theory and numerical formulation.” Int. J. Geomech., 1–15.
Chugh, A. K., and Labuz, J. F. (2011). “Numerical simulation of an instrumented cantilever retaining wall.” Can. Geotech. J., 48(9), 1303–1313.
Clayton, C. R. I., Milititsky, J., and Woods, R. I. (1993). Earth pressures and earth-retaining structures, 2nd Ed., Chapman and Hall, London.
Colas, A. S., Morel, J. C., and Garnier, D. (2010). “Full-scale field trials to assess dry-stone retaining wall stability.” Eng. Struct., 32(5), 1215–1222.
Coulomb, C. A. (1776). “Essaisurune application des redles de maximis et minimis a quelques problems de statique, relatives al’architecture.” Memories de Mathematique et de Physique presents a L’Academie Royale des Sciences, 7, 343–383.
Craig, R. F. (2004). Craig’s soil mechanics, Taylor and Francis, London.
Das, B. M. (1984). Principles of foundation engineering, Brooks/Cole Engineering Division, Monterrey, CA.
Duncan, J., and Mokwa, R. (2001). “Passive earth pressures: theory and tests.” J. Geotech. Geoenviron. Eng., 248–257.
Fang, Y., and Ishibashi, I. (1986). “Static earth pressures with various wall movements.” J. Geotech. Engrg., 317–333.
Fenton, G. A., Griffiths, D. V., and Williams, M. B. (2005). “Reliability of traditional retaining wall design.” Géotechnique, 55(1), 55–62.
FLAC [Computer software]. Itasca Consulting Group, Inc., Minneapolis.
Gezgin, A. T., and Çinicioğlu, O. (2014). “Aktif zemin itkisinin genleşim açısına bağlı hesaplanması [Calculation of active earth thrust based on dilatancy angle].” Proc., 15th National Soil Mechanic and Foundation Engineering Congress, Bizim Grup, Ankara, Turkey, 485–494.
Ghazavi, M., and Yeganeh, M. M. (2012). “Mathematical analysis of lateral earth pressure distribution on rigid retaining walls.” J. Eng. Geol., 6(2), 1459–1472.
Goel, S., and Patra, N. (2008). “Effect of arching on active earth pressure for rigid retaining walls considering translation mode.” Int. J. Geomech., 123–133.
Greco, V. R. (1999). “Active earth thrust on cantilever walls in general conditions.” Soils Found., 39(6), 6–78.
Greco, V. R. (2001). “Active earth thrust on cantilever walls with short heel.” Can. Geotech. J., 38(2), 401–409.
Greco, V. R. (2008). “Analytical active earth thrust on cantilever walls with short heel.” Can. Geotech. J., 45(12), 1649–1658.
Habibagahi, K., and Ghahramani, A. (1977). “Zero extension theory of earth pressure.” J. Geotech. Eng. Div., 105(GT7), 881–896.
Hazarika, H., and Matsuzawa, H. (1996). “Wall displacement modes dependent active earth pressure analyses using smeared shear band method with two bands.” Comput. Geotech., 19(3), 193–219.
Horvath, J. (1991). “Effect of footing shape on behavior of cantilever retaining wall.” J. Geotech. Engrg., 973–978.
Huang, Y. P., Huang, C. Y., Chen, S. S., and Lin, W. C. (1999). “The world wide web and the databases for retaining wall design.” Adv. Eng. Software, 30(9–11), 799–808.
Iskander, G. M. (2012). “Simplified analytical solution for point load acting behind a cantilever wall.” Int. J. Numer. Anal. Methods Geomech., 36(3), 344–351.
Kamiloğlu, H. A., and Şadoğlu, E. (2014). “Experimental examination of active and passive wedge in backfill soil of model cantilever retaining wall.” Int. J. Struct. Anal. Des., 1(3), 96–100.
Kaveh, A., and Abadi, A. S. M. (2010). “Harmony search based algorithms for the optimum cost design of reinforced concrete cantilever retaining walls.” Int. J. Civ. Eng., 9(1), 1–8.
Khosravi, M. H., Pipatpongsa, T., and Takemura, J. (2013). “Experimental analysis of earth pressure against rigid retaining walls under translation mode.” Géotechnique, 63(12), 1020–1028.
Lancellotta, R. (2002). “Analytical solution of passive earth pressure.” Géotechnique, 52(8), 617–619.
Leśniewska, D., and Mróz, Z. (2001). “Study of evolution of shear band systems in sand retained by flexible wall.” Int. J. Numer. Anal. Methods Geomech., 25(9), 909–932.
Liu, F. Q., and Wang, J. H. (2008). “A generalized slip line solution to the active earth pressure on circular retaining walls.” Comput. Geomech., 35(2), 155–164.
Liu, F. Q., Wang, J. H., and Zhang, L. L. (2009). “Axi-symmetric active earth pressure obtained by the slip line method with a general tangential stress coefficient.” Comput. Geotech., 36(1–2), 352–358.
MATLAB [Computer software]. MathWorks, Natick, MA.
Mei, G. M. G., Chen, Q. C. Q., and Song, L. S. L. (2009). “Model for predicting displacement dependent lateral earth pressure.” Can. Geotech. J., 46(8), 969–975.
Milligan, G. W. E. (1983). “Soil deformations near anchored sheet-pile walls.” Géotechnique, 33(1), 41–55.
Milligan, G. W. E., and Bransby, P. L. (1976). “Combined active and passive rotational failure of a retaining wall in sand.” Géotechnique, 26(3), 473–494.
Mylonakis, G., Kloukinas, P., and Papantonopoulos, C. (2007). “An alternative to Mononobe-Okabe equations for seismic earth pressures.” Soil Dyn. Earthquake Eng., 27(10), 957–969.
Mythily, M., and Rao, D. B., and Babu, G. L. S. (2000). “Probabilistic design of retaining walls.” GEOSHORE, Int. Conf. on Offshore and Nearshore Geotechnical Engineering, Oxford & IBH, Panvel, India, 383–386.
Niedostatkiewicz, M., Lesniewska, D., and Tejchman, J. (2011). “Experimental analysis of shear zone patterns in cohesionless for earth pressure problems using particle image velocimetry.” Strain, 47(s2), 218–231.
Paik, K. H., and Salgado, R. (2003). “Estimation of active earth pressure against rigid retaining walls considering arching effects.” Géotechnique, 53(7), 643–653.
Pietrzak, M., and Leśniewska, D. (2012). “Failure evolution in granular material retained by rigid wall in active mode.” Stud. Geotech. Mech., 34(4), 1–9.
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.
Rankine, W. J. M. (1857). “On the stability of loose earth.” Philos. Trans. R. Soc. London, Ser. A, 147, 9–27.
Reddy, N. S. C. (2013). “Computation of passive earth pressure coefficients for a horizontal cohesionless backfill using the method of slices.” Int. J. Adv. Civ. Eng. Archit. Res., 2(1), 32–41.
Rowe, P. W., and Peaker, K. (1965). “Passive earth pressure measurements.” Géotechnique, 15(1), 57–78.
Şadoğlu, E., Kamiloglu, H. A., Kuvat, A., and Uzuner, B. A. (2013). “Konsol istinat duvarlarında olusan aktif kamanın deneysel ve analitik incelenmesi [The experimental and analytical examination of active wedge occurring in cantilever walls].” Proc., 5th Geotechnical Symp., Ufuk Ofset Printing, Adana, Turkey.
Santolo, A. S., and Evangelista, A. (2011). “Dynamic active earth pressure on cantilever retaining walls.” Comput. Geotech., 38(8), 1041–1051.
Shahgholi, M., Fakher, A., and Jones, C. J. F. P. (2001). “Horizontal slice method of analysis.” Géotechnique, 51(10), 881–885.
Shields, D. H., and Tolunay, A. Z. (1973). “Passive pressure coefficients by method of slices.” J. Soil Mech. Found. Div., 99(12), 1043–1053.
Sokolovskii, V. V. (1965). Statics of granular media, Pergamon, New York.
Soubra, A. H., and Macuh, B. (2002). “Active and passive earth pressure coefficients by a kinematical approach.” Proc., Institution of Civil Engineers, Geotechnical Engineering, Thomas Telford, London.
Teng, W. C. (1962). Foundation design, Prentice Hall, Englewood Cliffs, NJ.
Whitlow, R. (2001). Basic soil mechanics, Prentice Hall. London.
Yang, X. L. (2007). “Upper bound limit analysis of active earth pressure with different fracture surface and nonlinear yield criterion.” Theor. Appl. Fract. Mech., 47(1), 46–56.
Zhu, D. Y., and Qian, Q. (2000). “Determination of passive earth pressure coefficients by the method of triangular slices.” Can. Geotech. J., 37(2), 485–491.
Zhu, J. F., Xu, R. Q., Li, X. R., and Chen, Y. K. (2011). “Calculation of earth pressure based on disturbed state concept theory.” J. Cent. South Univ. Technol., 18(4), 1240–1247.
Information & Authors
Information
Published In
Copyright
© 2017 American Society of Civil Engineers.
History
Received: May 4, 2016
Accepted: Nov 14, 2016
Published online: Feb 14, 2017
Discussion open until: Jul 14, 2017
Published in print: Aug 1, 2017
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.