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A Strain Dependent Approach for Seismic Stability Assessment of Rigid Retaining Wall

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Abstract

A new method is proposed to evaluate the seismic stability of a rigid retaining wall undergoing translation or rotational failure. In the present method, strain-dependent dynamic properties are used to assess the seismic stability of rigid retaining walls against sliding and overturning failure conditions. The effect of foundation soil properties on the stability of retaining walls is also considered. From the parametric study, it is observed that the foundation soil properties have a significant effect on both sliding and rotational stability of rigid retaining walls. This can be attributed to the use of strain-dependent dynamic properties and the consideration of foundation soil properties. The predictions of the proposed method are compared and verified against the results from other methods proposed in the past. The percentage increase in the results compared to the existing literature is a maximum of 10 and 28% for rigid (bedrock) and flexible (sand deposit) foundation, respectively.

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Abbreviations

ah, ahf, ahw :

Horizontal seismic acceleration in the backfill, foundation and wall, respectively

b :

b w /H

b w :

Top width of the retaining wall

CI, CIE(t):

Static and seismic wall inertia factors

CR, CRD(t):

Static and seismic wall rotational factors

Db, Df, Dw :

Damping Ratio of the backfill soil, foundation soil and wall material respectively

Fb, Nb :

Horizontal and vertical components of reaction on the base of the wall

FT, FI, FR :

Soil active thrust, wall inertia and wall rotational factor, respectively

FWS, FWR :

Combined dynamic factor against sliding and rotational failures, respectively

g :

Acceleration due to gravity

H, Hf :

Height of the retaining wall and foundation depth, respectively

Ka, Kae (t):

Static and seismic active earth pressure coefficients

\(k^{*} , k_{f}^{*}\) :

Complex wave number of the backfill material and foundation soil, respectively

k h :

Horizontal seismic acceleration coefficient at the bedrock

ms (z), mw (z):

Elemental mass of the soil wedge and wall, respectively

Pae (t):

Total active earth thrust

Qhb (t), Qhw (t):

Horizontal inertia forces acting in the failure wedge and wall, respectively

r c :

Radial distance between the centroid of the wall and rotation centre E

t :

Time

T :

Period of lateral shaking

u hb :

Displacement in the bedrock

uh, uhf :

Horizontal displacement in the backfill and foundation soil, respectively

Vs, Vsf, Vsw :

Shear wave velocity of the backfill, foundation soil and wall material, respectively

W w :

Weight of the wall

Wws, static, Wwr, static :

Weight of the wall required for equilibrium against sliding and rotational failure under static conditions, respectively

Wws (t), Wwr (t):

Weight of the wall required for equilibrium against sliding and rotational failure under seismic conditions, respectively

W s :

Weight of the failure wedge

z, zf :

Depth from the top of the wall or backfill and foundation layer, respectively

α :

Angle of the failure plane with respect to horizontal

γs, γsf :

Shear strain in the backfill and foundation soil, respectively

γb, γf, γw :

Unit weight of the backfill, foundation soil and wall material, respectively

ρb, ρf :

Mass density of the backfill and foundation soil, respectively

δ :

Wall friction angle

\(\eta_{0}\) :

Angle of inclination of radial distance between centroid and rotation centre, E with horizontal

θ :

Wall inclination angle

ϕ :

Soil friction angle

ϕ b :

Wall base friction angle

ω :

Angular frequency of motion = 2π/T

λ :

Impedance ratio

References

  • Basha BM, Babu GS (2010) Optimum design of bridge abutments under high seismic loading using modified pseudo-static method. J Earthq Eng 14(6):874–897

    Article  Google Scholar 

  • Baziar MH, Shahnazari H, Rabeti Moghadam M (2013) Sliding stability analysis of gravity retaining walls using the pseudo-dynamic method. Proc Inst Civil Eng Geotech Eng 166(4):389–398

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Bellezza I (2015) Seismic active soil thrust on walls using a new pseudo-dynamic approach. Geotech Geol Eng 33(4):795–812

    Article  Google Scholar 

  • Cai Y, Chen Q, Zhou Y, Nimbalkar S, Yu J (2016) Estimation of passive earth pressure against rigid retaining wall considering arching effect in cohesive-frictional backfill under translation mode. Int J Geomech 17(4):04016093. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000786

    Article  Google Scholar 

  • Caltabiano S, Cascone E, Maugeri M (2000) Seismic stability of retaining walls with surcharge. Soil Dyn Earthq Eng 20(5–8):469–476

    Article  Google Scholar 

  • Choudhury D, Nimbalkar S (2006) Pseudo-dynamic approach of seismic active earth pressure behind retaining wall. Geotech Geol Eng 24(5):1103–1113

    Article  Google Scholar 

  • Choudhury D, Nimbalkar S (2008) Seismic rotational displacement of gravity walls by pseudodynamic method. Int J Geomech 8(3):169–175

    Article  Google Scholar 

  • Conti R, Viggiani GMB, Cavallo S (2013) A two-rigid block model for sliding gravity retaining walls. Soil Dyn Earthq Eng 55:33–43

    Article  Google Scholar 

  • Ghanbari A, Ahmadabadi M (2010) Pseudo-dynamic active earth pressure analysis of inclined retaining walls using horizontal slices method. Sci Iran Trasc A Civil Eng 17(2):118–130

    Google Scholar 

  • Ghosh S, Sharma RP (2012) Seismic active earth pressure on the back of battered retaining wall supporting inclined backfill. Int J Geomech 12(1):54–63

    Article  Google Scholar 

  • Giri D (2011) Pseudo-dynamic approach of seismic earth pressure behind cantilever retaining wall with inclined backfill surface. Geomech Eng 3(4):255–266

    Article  Google Scholar 

  • Handy RL (1985) The arch in soil arching. Journal of Geotechnical Engineering 111(3):302–318

    Article  Google Scholar 

  • Huang CC, Wu SH, Wu HJ (2009) Seismic displacement criterion for soil retaining walls based on soil shear strength mobilization. J Geotech Geoenviron Eng 135(1):74–83

    Article  Google Scholar 

  • Jo SB, Ha JG, Lee JS, Kim DS (2017) Evaluation of the seismic earth pressure for inverted T-shape stiff retaining wall in cohesionless soils via dynamic centrifuge. Soil Dyn Earthq Eng 92:345–357

    Article  Google Scholar 

  • Jung C, Bobet A, Fernández G (2010) Analytical solution for the response of a flexible retaining structure with an elastic backfill. Int J Numer Anal Methods Geomech 34(13):1387–1408

    Article  Google Scholar 

  • Kolathayar S, Ghosh P (2009) Seismic active earth pressure on walls with bilinear backface using pseudo-dynamic approach. Comput Geotech 36(7):1229–1236

    Article  Google Scholar 

  • Kramer SL (1996) Geotechnical earthquake engineering. Dorling Kindersley Pvt. Ltd., Noida

    Google Scholar 

  • Lin YL, Leng WM, Yang GL, Zhao LH, Li L, Yang JS (2015) Seismic active earth pressure of cohesive-frictional soil on retaining wall based on a slice analysis method. Soil Dyn Earthq Eng 70:133–147

    Article  Google Scholar 

  • Mylonakis G, Kloukinas P, Papantonopoulos C (2007) An alternative to the Mononobe-Okabe equations for seismic earth pressures. Soil Dyn Earthq Eng 27(10):957–969

    Article  Google Scholar 

  • 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 

  • Nimbalkar S, Annapareddy VSR, Pain A (2018) A simplified approach to assess seismic stability of tailings dams. J Rock Mech and Geotech Eng 10(6):1082–1090

    Article  Google Scholar 

  • Pain A, Choudhury D, Bhattacharyya SK (2015) Seismic stability of retaining wall-soil sliding interaction using modified pseudo-dynamic method. Geotechnique Letters 5(1):56–61

    Article  Google Scholar 

  • Pain A, Choudhury D, Bhattacharyya SK (2016) Computation of rotational displacements of gravity retaining walls by pseudo-dynamic method. In: proceedings of the 4th geo-china international conference: sustainable civil infrastructures: innovative technologies for severe weathers and climate changes shandong, China, pp 124–132

  • Pain A, Chen QS, Nimbalkar S, Zhou Y (2017a) Evaluation of seismic passive earth pressure of inclined rigid retaining wall considering soil arching effect. Soil Dyn Earthq Eng 100:286–295

    Article  Google Scholar 

  • Pain A, Choudhury D, Bhattacharyya SK (2017b) Seismic rotational stability of gravity retaining walls by modified pseudo-dynamic method. Soil Dyn Earthq Eng 94:244–253

    Article  Google Scholar 

  • Pain A, Annapareddy VSR, Nimbalkar S (2018) Seismic active earth thrust on rigid retaining wall using strain dependent dynamic properties. Int J Geomech 18(12):06018034

    Article  Google Scholar 

  • Psarropoulos PN, Klonaris G, Gazetas G (2005) Seismic earth pressures on rigid and flexible retaining wall. Soil Dyn Earthq Eng 25(7–10):795–809

    Article  Google Scholar 

  • Rao P, Chen Q, Zhou Y, Nimbalkar S, Chiaro G (2015) Determination of active earth pressure on rigid retaining wall considering arching effect in cohesive backfill soil. Int J Geomech. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000589

    Article  Google Scholar 

  • Richards R, Elms DG (1979) Seismic behaviour of gravity retaining walls. J Geotech Eng Div 105(4):449–464

    Google Scholar 

  • Seed HB, Idriss IM (1970) Soil moduli and damping factors for dynamic response analysis, Report EERC 70-10. University of California, Earthquake Engineering Research Centre, Berkeley

    Google Scholar 

  • Shukla SK, Bathurst RJ (2012) An analytical expression for the dynamic active thrust from c–ϕ soil backfill on retaining walls with wall friction and adhesion. Geomech Eng 4(3):209–218

    Article  Google Scholar 

  • Steedman RS, Zeng X (1990) The influence of phase on the calculation of pseudo-static earth pressure on a retaining wall. Géotechnique 40(1):103–112

    Article  Google Scholar 

  • Whitman RV, Liao S (1985) Seismic design of gravity retaining walls. In: Proceedings of 8th world conference on earthquake engineering, San Francisco 3, pp 533–540

  • Zeng X, Steedman RS (2000) Rotating block method for seismic displacement of gravity walls. J Geotech Geo-environ Eng 126(8):709–717

    Article  Google Scholar 

  • Zhou YT, Chen QS, Chen FQ, Xue XH, Basack S (2018) Active earth pressure on translating rigid retaining structures considering soil arching effect. Eur J Environ Civil Eng 22(8):910–926. https://doi.org/10.1080/19648189.2016.1229225

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Civil and Environmental Engineering, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, NSW, 2007, Australia

    Sanjay Nimbalkar

  2. Geotechnical Engineering Group, CSIR-Central Building Research Institute, Roorkee, 247667, India

    Anindya Pain & V. S. Ramakrishna Annapareddy

Authors
  1. Sanjay Nimbalkar
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  2. Anindya Pain
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  3. V. S. Ramakrishna Annapareddy
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Correspondence to Anindya Pain.

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Nimbalkar, S., Pain, A. & Annapareddy, V.S.R. A Strain Dependent Approach for Seismic Stability Assessment of Rigid Retaining Wall. Geotech Geol Eng 38, 6041–6055 (2020). https://doi.org/10.1007/s10706-020-01412-4

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