Advertisement

Acta Geotechnica

, Volume 14, Issue 2, pp 579–594 | Cite as

Estimation of static earth pressures for a sloping cohesive backfill using extended Rankine theory with a composite log-spiral failure surface

  • Shi-Yu XuEmail author
  • Abiodun Ismail Lawal
  • Anoosh Shamsabadi
  • Ertugrul Taciroglu
Research Paper
  • 215 Downloads

Abstract

The Rankine earth pressure theory is extended herein to an inclined cϕ backfill. An analytical approach is then proposed to compute the static passive and active lateral earth pressures for a sloping cohesive backfill retained by a vertical wall, with the presence of wall–soil interface adhesion. The proposed method is based on a limit equilibrium analysis coupled with the method of slices wherein the assumed profile of the backfill failure surface is a composite of log-spiral and linear segments. The geometry of the failure surface is determined using the stress states of the soil at the two boundaries of the mobilized soil mass. The resultant lateral earth thrust, the point of application, and the induced moment on the wall are computed considering global and local equilibrium of forces and moments. Results of the proposed approach are compared with those predicted by a number of analytical models currently adopted in the design practice for various combinations of soil’s frictional angles, wall–soil interface frictional angles, inclined angles of backfill and soil cohesions. The predicted results are also verified against those obtained from finite element analyses for several scenarios under the passive condition. It is found that the magnitude of earth thrust increases with the backfill inclination angle under both the passive and active conditions.

Keywords

Limit equilibrium Log-spiral Rankine Method of slices Retaining wall Sloping ground Stress state 

Notes

Acknowledgement

The work presented in this paper was funded by City University of Hong Kong (CityU), HKSAR (Project No.: 7004375 (ACE) and 7200440 (ACE)) and by the California Department of Transportation (Grant No. 65A0582). The authors gratefully acknowledge the financial and technical support from these sources. Any opinions, findings and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of CityU or Caltrans.

References

  1. 1.
    AASHTO (2012) AASHTO LRFD bridge design specifications, 6th edn. American Association of State Highway and Transportation Officials, WashingtonGoogle Scholar
  2. 2.
    ABAQUS (2007) ABAQUS documentation, version 6.7Google Scholar
  3. 3.
    Alejano LR, Antonio B (2012) Drucker–Prager criterion. Rock Mech Rock Eng 45(6):995–999CrossRefGoogle Scholar
  4. 4.
    Atkinson JH (1981) Foundations and slopes: an introduction to applications of critical state soil mechanics. McGraw-Hill, LondonGoogle Scholar
  5. 5.
    Caltrans (2012) Caltrans reference manual for the design of earth retaining structures. California Department of Transportation, SacramentoGoogle Scholar
  6. 6.
    Caquot A, Kerisel J (1948) Tables for the calculation of passive pressure, active pressure and bearing capacity of foundations. Gauthier-Villars, ParisGoogle Scholar
  7. 7.
    Chen WF, Liu XL (1990) Limit analysis in soil mechanics. Elsevier, Amsterdam, pp 1–477Google Scholar
  8. 8.
    Chen WF, Rosenfarb JL (1973) Limit analysis solutions of earth pressure problems. Soils Found 13(4):45–60CrossRefGoogle Scholar
  9. 9.
    Cheng YM (2016) Rankines earth pressure coefficients for inclined ground reconsidered by slip lime method. MOJ Civil Eng 1(1):1–7MathSciNetGoogle Scholar
  10. 10.
    Colmenares L, Zoback M (2002) A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks. Int J Rock Mech Min Sci 39(6):695–729CrossRefGoogle Scholar
  11. 11.
    Coulomb C (1776) Essai sur une application de maximis et minimis à quelques problèmes de statique, relatifs à l’Architecture, pubblicato tra i “.Mèmoires de Mathématique et de Physique présentés à l’Académie Royale des Sciences, par divers Savans, et lûs dans les Assemblées, 7, Paris, pp 143–167Google Scholar
  12. 12.
    Davis RO, Selvadurai APS (2002) Plasticity and geomechanics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  13. 13.
    Drucker DC, Prager W (1952) Soil mechanics and plastic analysis for limit design. Q Appl Math 10(2):157–165MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Fang Y, Ho Y, Chen T (2002) Passive earth pressure with critical state concept. J Geotech Geoenviron Eng 128(8):651–659CrossRefGoogle Scholar
  15. 15.
    Fang Y, Chen J, Chen C (1997) Earth pressures with sloping backfill. J Geotech Geoenviron Eng 123(3):250–259CrossRefGoogle Scholar
  16. 16.
    GEOGUIDE (2000) Guide to retaining wall design. Geotechnical Engineering Office, Hong Kong, pp 1–259Google Scholar
  17. 17.
    Helwany S (2007) Applied soil mechanics with Abaqus applications. Wiley, New York, p 265CrossRefzbMATHGoogle Scholar
  18. 18.
    Iskander M, Omidvar M, Elsherif O (2013) Conjugate stress approach for Rankine seismic active earth pressure in cohesionless soils. J Geotech Geoenviron Eng 139(7):1205–1210CrossRefGoogle Scholar
  19. 19.
    James RG, Bransby PL (1970) Experimental and theoretical investigations of a passive earth pressure problem. Geotechnique 20:17–37CrossRefGoogle Scholar
  20. 20.
    Kumar J, Subba Rao KS (1997) Passive pressure coefficients, critical failure surface and its kinematic admissibility. Géotechnique 47(1):185–192CrossRefGoogle Scholar
  21. 21.
    Kumar J, Chitikela S (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 CrossRefGoogle Scholar
  22. 22.
    Lin YL, Yang X, Yang GL, Li Y, Zhao LH (2017) A closed-form solution for seismic passive earth pressure behind a retaining wall supporting cohesive–frictional backfill. Acta Geotech 12(2):453–461CrossRefGoogle Scholar
  23. 23.
    Mazindrani ZH, Ganjali MH (1997) Lateral earth pressure problem of cohesive backfill with inclined surface. J Geotech Geoenviron Eng 123(2):110–112CrossRefGoogle Scholar
  24. 24.
    Milligan GWE, Bransby PL (1976) Combined active and passive rotational failure of a retaining wall in sand. Geotechnique 26:473–494CrossRefGoogle Scholar
  25. 25.
    Mueller-Breslau H (1906) Erddruck auf stuetzmauern. Kroener, StuttgartGoogle Scholar
  26. 26.
    Mylonakis G, Kloukinas P, Papantonopoulos C (2007) An alternative to the Mononobe–Okabe equations for seismic earth pressures. Soil Dyn Earthq Eng 27:957–969CrossRefGoogle Scholar
  27. 27.
    Patki MA, Mandal NJ, Dewaikar DM (2015) Computation of passive earth pressure coefficients for a vertical retaining wall with inclined cohesionless backfill. Int J Geo-eng 6(4):1–17Google Scholar
  28. 28.
    Rankine W (1857) On the stability of loose earth. Phil Trans R Soc 147:185–187Google Scholar
  29. 29.
    Rowe PW, Peaker K (1965) Passive earth pressure measurements. Géotechnique 15(1):57–78CrossRefGoogle Scholar
  30. 30.
    Shamsabadi A, Ashour M, Norris G (2005) Bridge abutment nonlinear force-displacement-capacity prediction for seismic design. J Geotech Geoenviron Eng 131(2):151–161CrossRefGoogle Scholar
  31. 31.
    Shamsabadi A, Rollins KM, Kapuskar M (2007) Nonlinear soil-abutment-bridge structure interaction for seismic performance-based design. J Geotech Geoenviron Eng 133(6):707–720CrossRefGoogle Scholar
  32. 32.
    Shamsabadi A, Khalili-Tehrani P, Stewart JP, Taciroglu E (2010) Validated simulation models for lateral response of bridge abutments with typical backfills. J Bridge Eng 15(3):302–311CrossRefGoogle Scholar
  33. 33.
    Shamsabadi A, Xu S-Y, Taciroglu E (2013) A generalized log-spiral-Rankine limit equilibrium model for seismic earth pressure analysis. Soil Dyn Earthq Eng 49:197–209CrossRefGoogle Scholar
  34. 34.
    Sitar N, Mikola R, Candia G (2012) Seismically induced lateral earth pressure on retaining structures and basement walls. In: Proceedings of GSP No. 226. ASCE, pp 335–358Google Scholar
  35. 35.
    Sokolovski VV (1965) Statics of granular media. Pergamon Press, New YorkGoogle Scholar
  36. 36.
    Song EX (1990) Elasto-plastic consolidation under steady and cyclic loads. Ph.D. thesis, Delft University of Technology, The NetherlandsGoogle Scholar
  37. 37.
    Soubra AH (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 CrossRefGoogle Scholar
  38. 38.
    Soubra AH, Macuh B (2002) Active and passive earth pressure coefficients by a kinematical approach. Proc ICE Geotech Eng 155(2):119–131CrossRefGoogle Scholar
  39. 39.
    Stewart JP, Taciroglu E, Wallace JW, Ahlberg ER, Lemnitzer A, Rha CS, Khalili-Tehrani P, Keowen S, Nigbor RL, Salamanca A (2007) Full scale cyclic testing of foundation support systems for highway bridges. Part II: Abutment backwalls, Report No. UCLA-SGEL 2007/02, Structural and Geotechnical Engineering Laboratory, University of California, Los AngelesGoogle Scholar
  40. 40.
    Sun YJ, Song EX (2016) Active earth pressure analysis based on normal stress distribution function along failure surface in soil obeying nonlinear failure criterion. Acta Geotech 11(2):255–268CrossRefGoogle Scholar
  41. 41.
    Tang C, Phoon KK, Toh KC (2014) Lower-bound limit analysis of seismic passive earth pressure on rigid walls. Int J Geomech.  https://doi.org/10.1061/(ASCE)GM.1943-5622.0000385 Google Scholar
  42. 42.
    Terzaghi K (1943) Theoretical soil mechanics. Wiley, New YorkCrossRefGoogle Scholar
  43. 43.
    Xu S-Y, Shamsabadi A, Taciroglu E (2015) Evaluation of active and passive seismic earth pressures considering internal friction and cohesion. Soil Dyn Earthq Eng 70:30–47CrossRefGoogle Scholar
  44. 44.
    Zhu D (2000) The least upper bound solutions for bearing capacity factor ”. Soils Found 40(1):123–129CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018
corrected publication May 2018

Authors and Affiliations

  1. 1.Architecture and Civil Engineering DepartmentCity University of Hong KongKowloonHong Kong SAR
  2. 2.Caltrans, Office of Earthquake EngineeringSacramentoUSA
  3. 3.Civil and Environmental Engineering DepartmentUniversity of CaliforniaLos AngelesUSA

Personalised recommendations