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.
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- 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 :
- G :
Shear modulus of backfill soil
- V s :
Shear wave velocity
- P AE :
Seismic active force
- p ae :
Seismic active pressure
- K AE :
- 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 :
- η s :
- 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
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.
Rankine WM (1856) On the stability of loose earth. Proc R Soc Lond 147:185–187
Okabe S (1926) General theory on earth pressure and seismic stability of RWs and dams. J Jpn Soc Civ Eng 12:311
Mononobe N (1929) Earthquake proof construction of masonry dams. In: Proceedings of world engineering congress, international association of earthquake engineering, Tokyo 9:275
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
Das BM, Puri VK (1996) Static and dynamic active earth pressure. Geotech Geol Eng 14:353–366
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
Shukla SK (2013) SAEP from the sloping c-φ soil backfills. Indian Geotech J 43(3):274–279
Steedman RS, Zeng X (1990) The influence of phase on the calculation of pseudo-static earth pressure on RW. Geotechnique 40(1):103–112
Choudhury D, Nimbalkar SS (2006) Pseudo-dynamic approach of SAEP behind RW. Geotech Geol Eng 24(5):1103–1113
Ghosh P (2008) SAEP behind a non-vertical RW using pseudo-dynamic analysis. Can Geotech J 45(1):117–123
Ghosh S, Sharma RP (2012) SAEP on back of battered RW supporting inclined backfill. Int J Geomech 12(1):54–64
Bellezza I (2014) A new pseudo-dynamic approach for seismic active soil thrust. Geotech Geol Eng 32(2):561–576
Kramer SL (1996) Geotechnical earthquake engineering. Prentice- Hall, Upper Saddle River, NJ
Richards R, Elms D (1979) Seismic behavior of gravity RWs. J Geotech Eng Div ASCE 105:449–464
Whitman RV, Liao S (1985) Seismic design of RWs. Miscellaneous Paper GL-85–1, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Mississippi.
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
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
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
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
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.
NCHRP Report 472 (2008) Comprehensive specification for the seismic design of bridges. TRB, National Research Council, Washington, DC
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.
American Association of State Highway and Transportation Officials (2010). AASHTO LRFD bridge construction specifications. AASHTO.
IS 1893 (2016) Indian Standard criteria for earthquake resistant design of structures. Part 1: General provisions and buildings.
IS 1893 (2014) Indian Standard criteria for earthquake resistant design of structures. Part 3: Bridges and RWs
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
Matsuzawa H, Ishibashi I, Kawamura M (1985) Dynamic soil and water pressures on submerged soils. J Geotech Eng, pp 1161–1176.
Westergaard HM (1933) Water pressures on dams during earthquakes. Trans Am Soc Civ Eng 98:418–433
Ahmad SM, Choudhury D (2008) Stability of waterfront RW subjected to pseudo-dynamic earthquake forces. J Waterway Port Coastal Ocean Eng 4:252–260
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
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.
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
Fang YS, Ishibashi I (1986) Static earth pressures with various wall movements. J Geotech Eng 112(3):317–333
Hardy RL (1985) The arch in soil arching. J Geotech Eng 111(3):302–318
Paik KH, Salgado R (2003) Estimation of active earth pressure against rigid retaining walls considering arching effects. Geotechnique 53(7):643–653
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
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
Goh AT (1993) Behavior of cantilever retaining walls. J Geotech Eng 119(11):1751–1770
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
Nakamura S (2006) Reexamination of Mononobe-Okabe theory of gravity retaining walls using centrifuge model tests. Soils Found 46(2):135–146
Qin C, Chian SC (2020) Pseudo-dynamic lateral earth pressures on rigid walls with varying cohesive-frictional backfill. Comput Geotech 119:103289
Chang CS, Chao SJ (1994) Discrete element analysis for active and passive pressure distribution on retaining wall. Comput Geotech 16(4):291–310
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
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Singh, S., Kumar, A. Methodologies Available for the Determination of Seismic Active Thrust Acting on Retaining Walls: A Critical Review. Indian Geotech J (2021). https://doi.org/10.1007/s40098-020-00495-3
- Pseudo-static analysis
- Pseudo-dynamic analysis
- Seismic coefficient
- Damping ratio
- Excess pore pressure ratio