Methodologies Available for the Determination of Seismic Active Thrust Acting on Retaining Walls: A Critical Review


Design of retaining walls (RWs) in earthquake (EQ)-prone areas requires the knowledge of the distribution of lateral earth pressure behind it. The lateral earth pressure acting on RW in case of dynamic/ seismic loading comprises of two components: (a) earth pressure due to static loading and (b) dynamic incremental pressure due to seismic forces. Pseudo-static and pseudo-dynamic methods are mostly preferred methods used to estimate the seismic earth pressure acting on the RW. Analysis based on pseudo-static approach (PSA) assumes seismic forces as equivalent constant inertial force acting on the wall, whereas pseudo-dynamic approach (PDA) includes the effect of phase change and dynamic amplification of seismic waves. This state-of-the-art paper presents a systematic review on the methodologies available for the determination of seismic active thrust, which are based on PSA and PDA. In addition, several other methods, e.g. methods involving numerical techniques, methods based on arching effect, etc., are also reviewed in this paper. While doing so, various limitations of above-stated approaches are pointed out. Further, it is found that there is scarcity of any rational method for the determination of seismic coefficients used in the analysis based on PSA. In addition, the effect of damping characteristics and excess pore pressure ratio, on seismic active thrust, is attempted in very limited studies.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17


K h :

Horizontal acceleration coefficient

K v :

Vertical acceleration coefficient


Shear wave velocity

V p :

Primary wave velocity


Angular frequency of base shaking

T :

Time period of shaking

D :

Damping ratio

G :

Shear modulus of backfill soil

V s :

Shear wave velocity

P AE :

Seismic active force

p ae :

Seismic active pressure

K AE :

SAEP coefficient

P wd :

Hydrodynamic water pressure force

ϒ d :

Dry unit weight of soil

ϒ sat :

Saturated unit weight of soil

R s :

Excess pore pressure ratio

ϒ s :

Shear strain

η s :

Soil viscosity

W :

Weight of failure wedge

Φ :

Angle of internal friction for soil

δ :

Wall friction angle

i :

Backfill slope angle

β :

Wall inclination angle

K :

Coefficient of permeability

α :

Angle made by failure wedge with vertical

α′ :

Angle made by failure wedge with horizontal

a h :

Acceleration of seismic waves at the top of RW

a ho :

Acceleration of seismic waves at the base of RW

θ :

Back-face inclination angle


  1. 1.

    Coulomb CA (1776) Essai sur une application des regles de maximis et minimis a quelques problemes de statique relatifs a l'architecture. Memoires de I’Academie Royale pres Divers Savants, 7.

  2. 2.

    Rankine WM (1856) On the stability of loose earth. Proc R Soc Lond 147:185–187

    Google Scholar 

  3. 3.

    Okabe S (1926) General theory on earth pressure and seismic stability of RWs and dams. J Jpn Soc Civ Eng 12:311

    Google Scholar 

  4. 4.

    Mononobe N (1929) Earthquake proof construction of masonry dams. In: Proceedings of world engineering congress, international association of earthquake engineering, Tokyo 9:275

  5. 5.

    Prakash S, Saran S (1966) Static and dynamic earth pressures behind RWs. In: Proceedings of the third symposium on earthquake engineering, University of Roorkee, India vol 1, pp 277–88

  6. 6.

    Das BM, Puri VK (1996) Static and dynamic active earth pressure. Geotech Geol Eng 14:353–366

    Article  Google Scholar 

  7. 7.

    Shukla SK, Gupta SK, Sivakugan N (2009) Active earth pressure on RW for c-φ soil backfill under seismic loading condition. J Geotech Geoenviron Eng 135(5):690–696

    Article  Google Scholar 

  8. 8.

    Shukla SK (2013) SAEP from the sloping c-φ soil backfills. Indian Geotech J 43(3):274–279

    Article  Google Scholar 

  9. 9.

    Steedman RS, Zeng X (1990) The influence of phase on the calculation of pseudo-static earth pressure on RW. Geotechnique 40(1):103–112

    Article  Google Scholar 

  10. 10.

    Choudhury D, Nimbalkar SS (2006) Pseudo-dynamic approach of SAEP behind RW. Geotech Geol Eng 24(5):1103–1113

    Article  Google Scholar 

  11. 11.

    Ghosh P (2008) SAEP behind a non-vertical RW using pseudo-dynamic analysis. Can Geotech J 45(1):117–123

    Article  Google Scholar 

  12. 12.

    Ghosh S, Sharma RP (2012) SAEP on back of battered RW supporting inclined backfill. Int J Geomech 12(1):54–64

    Article  Google Scholar 

  13. 13.

    Bellezza I (2014) A new pseudo-dynamic approach for seismic active soil thrust. Geotech Geol Eng 32(2):561–576

    Article  Google Scholar 

  14. 14.

    Kramer SL (1996) Geotechnical earthquake engineering. Prentice- Hall, Upper Saddle River, NJ

    Google Scholar 

  15. 15.

    Richards R, Elms D (1979) Seismic behavior of gravity RWs. J Geotech Eng Div ASCE 105:449–464

    Article  Google Scholar 

  16. 16.

    Whitman RV, Liao S (1985) Seismic design of RWs. Miscellaneous Paper GL-85–1, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Mississippi.

  17. 17.

    Bellezza I, D’Alberto D, Fentini R (2012) Pseudo-dynamic approach for active thrust of submerged soils. Proc Inst Civ Eng Geotech Eng 165(5):321–333

    Article  Google Scholar 

  18. 18.

    Pain A, Choudhury D, Bhattacharyya SK (2015) Seismic stability of RW-soil sliding interaction using modified pseudo-dynamic method. Geotech Lett 5(1):56–61

    Article  Google Scholar 

  19. 19.

    Rajesh BG, Choudhury D (2017) Generalized seismic active thrust on a RW with submerged backfill using a modified pseudo-dynamic method. Int J Geomech 17(3):06016023

    Article  Google Scholar 

  20. 20.

    Seed HB, Whitman RV (1970) Design of earth retaining structures for dynamic loads. Lateral stresses in the ground and design of earth retaining structures. ASCE, New York, pp 103–107

    Google Scholar 

  21. 21.

    CEN (European Committee for Standardization) (2004) EN1998-5: Eurocode8: Design of structures for earthquake resistance, part 5: Foundations, Retaining Structures and Geotechnical Aspects, Brussels, Belgium.

  22. 22.

    NCHRP Report 472 (2008) Comprehensive specification for the seismic design of bridges. TRB, National Research Council, Washington, DC

  23. 23.

    Law H, Shamsabadi A, Wilson P (2014) Site-specific seismic coefficients for RW and slope design. In: Proceedings of the 10th national conference in earthquake engineering, earthquake engineering research institute, Anchorage, AK.

  24. 24.

    American Association of State Highway and Transportation Officials (2010). AASHTO LRFD bridge construction specifications. AASHTO.

  25. 25.

    IS 1893 (2016) Indian Standard criteria for earthquake resistant design of structures. Part 1: General provisions and buildings.

  26. 26.

    IS 1893 (2014) Indian Standard criteria for earthquake resistant design of structures. Part 3: Bridges and RWs

  27. 27.

    Choudhury D, Katdare AD, Shukla SK, Basha BM, Ghosh P (2014) Seismic behaviour of retaining structures, design issues and requalification techniques. Indian Geotech J 44(2):167–182

    Article  Google Scholar 

  28. 28.

    Matsuzawa H, Ishibashi I, Kawamura M (1985) Dynamic soil and water pressures on submerged soils. J Geotech Eng, pp 1161–1176.

  29. 29.

    Westergaard HM (1933) Water pressures on dams during earthquakes. Trans Am Soc Civ Eng 98:418–433

    Article  Google Scholar 

  30. 30.

    Ahmad SM, Choudhury D (2008) Stability of waterfront RW subjected to pseudo-dynamic earthquake forces. J Waterway Port Coastal Ocean Eng 4:252–260

    Google Scholar 

  31. 31.

    Taiebat M, Shahir H, Pak A (2007) Study of pore pressure variation during liquefaction using two constitutive models for sand. Soil Dyn Earthquake Eng 27(10):60–72

    Article  Google Scholar 

  32. 32.

    Nabili S, Jafarian Y, Baziar MH (2008) Seismic pore water pressure generation models: Numerical evaluation and comparison. In:The 14th world conference on earthquake engineering, Beijing, China.

  33. 33.

    Tsagareli ZV (1965) Experimental investigation of the pressure of a loose medium on retaining walls with a vertical back face and horizontal backfill surface. Soil Mech Found Eng 2(4):197–200

    Article  Google Scholar 

  34. 34.

    Fang YS, Ishibashi I (1986) Static earth pressures with various wall movements. J Geotech Eng 112(3):317–333

    Article  Google Scholar 

  35. 35.

    Hardy RL (1985) The arch in soil arching. J Geotech Eng 111(3):302–318

    Article  Google Scholar 

  36. 36.

    Paik KH, Salgado R (2003) Estimation of active earth pressure against rigid retaining walls considering arching effects. Geotechnique 53(7):643–653

    Article  Google Scholar 

  37. 37.

    Li JP, Wang M (2014) Simplified method for calculating active earth pressure on rigid retaining walls considering the arching effect under translational mode. Int J Geomech 14(2):282–290

    Article  Google Scholar 

  38. 38.

    Zhou QY, Zhou YT, Wang XM, Yang PZ (2018) Estimation of active earth pressure on a translating rigid retaining wall considering soil arching effect. Indian Geotech J 48(3):541–548

    Article  Google Scholar 

  39. 39.

    Goh AT (1993) Behavior of cantilever retaining walls. J Geotech Eng 119(11):1751–1770

    Article  Google Scholar 

  40. 40.

    Athanasopoulos-Zekkos A, Vlachakis VS, Athanasopoulos GA (2013) Phasing issues in the seismic response of yielding, gravity-type earth retaining walls–Overview and results from a FEM study. Soil Dyn Earthquake Eng 55:59–70

    Article  Google Scholar 

  41. 41.

    Nakamura S (2006) Reexamination of Mononobe-Okabe theory of gravity retaining walls using centrifuge model tests. Soils Found 46(2):135–146

    Article  Google Scholar 

  42. 42.

    Qin C, Chian SC (2020) Pseudo-dynamic lateral earth pressures on rigid walls with varying cohesive-frictional backfill. Comput Geotech 119:103289

    Article  Google Scholar 

  43. 43.

    Chang CS, Chao SJ (1994) Discrete element analysis for active and passive pressure distribution on retaining wall. Comput Geotech 16(4):291–310

    Article  Google Scholar 

  44. 44.

    Yang M, Deng B (2019) Simplified method for calculating the active earth pressure on retaining walls of narrow backfill width based on DEM analysis. Adv Civ Eng

Download references

Author information



Corresponding author

Correspondence to Abhishek Kumar.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Singh, S., Kumar, A. Methodologies Available for the Determination of Seismic Active Thrust Acting on Retaining Walls: A Critical Review. Indian Geotech J (2021).

Download citation


  • Pseudo-static analysis
  • Pseudo-dynamic analysis
  • Seismic coefficient
  • Damping ratio
  • Excess pore pressure ratio