Skip to main content
SpringerLink
Log in

A New Pseudo-dynamic Approach for Seismic Active Soil Thrust

  • Original Paper
  • Published:
Geotechnical and Geological Engineering Aims and scope Submit manuscript

Abstract

A critical review of the existing pseudo-dynamic approach is provided and a new pseudo-dynamic approach is proposed based on a visco-elastic behavior of backfill overlying rigid bedrock subjected to harmonic horizontal acceleration. Considering a planar failure surface, closed form expressions for seismic active soil thrust, soil pressure distribution and overturning moment are obtained. The results of this study indicate that the existing pseudo-dynamic method can strongly underestimate the soil active thrust especially close to the fundamental frequency of the backfill, where the soil response is more sensitive to the damping ratio. The acting point of the total seismic active thrust is always found to be higher than that predicted by the traditional pseudo-dynamic approach. The effect of the shear resistance angle and wall friction angle on the acting point increases as the amplitude of the base acceleration increases, whereas their effect is generally small far from the natural frequencies of the backfill.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Abbreviations

a h (z, t), a v (z, t):

Horizontal and vertical acceleration in the backfill at depth z and time t

A h , B h :

Numerical coefficients for horizontal inertia force

a h0, a v0 :

Amplitude of horizontal and vertical acceleration at the base of the wall

A m , B m :

Numerical coefficients for overturning moment

A pz , B pz :

Numerical coefficients for seismic active pressure

D :

Damping ratio

f a :

Amplification factor

g :

Acceleration due to gravity

G :

Shear modulus of the soil

G* :

Complex shear modulus

H :

Height of the wall

h M , h P :

Distance of the point of application of P AE,M and P AE,max from the base of the wall

K AE :

Active earth pressure coefficient in the pseudo-dynamic approach

k * s  = k s1 + i k s2 :

Complex wave number

M max , M P :

Maximum overturning moment with respect to the base of the wall and overturning moment corresponding to the maximum dynamic thrust

p ae (z, α, t):

Total seismic pressure

P AE (α, t):

Generic value for active thrust in the pseudo-dynamic approach

P AE,M :

Value of P AE (α, t) when the moment is maximum

P AE,max :

Maximum value of P AE

Q h :

Horizontal inertia force of the soil wedge

R :

Resultant of soil force acting on the failure plane

T = 2π/ω :

Period of the harmonic seismic acceleration

t :

Time

u h , u v :

Horizontal and vertical soil displacement

V S , V P :

Velocity of P- and S-waves in the soil

W :

Weight of the soil wedge

y 1 :

k s1 H

y 2 :

k s2 H

z :

Depth from the top of the backfill

z n :

z/H

α :

Inclination of the soil wedge with respect to the horizontal plane

δ :

Friction angle between the backfill and the wall

φ :

Shear resistance angle of the backfill

γ s :

Shear strain

γ :

Unit weight of soil

η s :

Viscosity of the soil

λ :

First Lamé constant

ρ :

Soil density

σ h , σ v , τ :

Horizontal, vertical and shear stress in the soil

ω :

Angular frequency of motion = 2π/T

References

  • Ahmad SM, Choudhury D (2008a) Pseudo-dynamic approach of seismic design for waterfront reinforced soil wall. Geotext Geomembr 26(4):291–301

    Article  Google Scholar 

  • Ahmad SM, Choudhury D (2008b) Stability of waterfront retaining wall subjected to pseudo-dynamic earthquake forces and tsunami. J Earthq Tsunami 2(2):107–131

    Article  Google Scholar 

  • Ahmad SM, Choudhury D (2009) Seismic design factor for sliding of waterfront retaining wall. Proc Inst Civ Eng Geotech Eng 162(5):269–276

    Article  Google Scholar 

  • ASTM D 4015 (2007) Standard method for modulus and damping of soils by resonant-column method. ASTM International, West Conshohocken, PA

    Google Scholar 

  • 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 

  • Choudhury D, Ahmad SM (2008) Stability of waterfront retaining wall subjected to pseudo-dynamic earthquake forces. J Waterw Port Coast Ocean Eng ASCE 134(4):252–262

    Article  Google Scholar 

  • Choudhury D, Nimbalkar SS (2005) Seismic passive resistance by pseudo-dynamic method. Géotechnique 55(9):699–702

    Article  Google Scholar 

  • Choudhury D, Nimbalkar SS (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 SS (2007) Seismic rotational displacement of gravity walls by pseudo-dynamic method: passive case. Soil Dyn Earthq Eng 27(3):242–249

    Article  Google Scholar 

  • Choudhury D, Nimbalkar SS (2008) Seismic rotational displacement of gravity walls by pseudo-dynamic method. Int J Geomech ASCE 8(3):169–175

    Article  Google Scholar 

  • Ebeling RM, Morrison EE (1992) The seismic design of waterfront retaining structures. US Army Corps of Engineers, Washington, DC

    Google Scholar 

  • Ghosh P (2007) Seismic passive earth pressure behind non-vertical retaining wall using pseudo-dynamic analysis. Geotech Geol Eng 25(5):693–703

    Article  Google Scholar 

  • Ghosh S (2010) Pseudo-dynamic active force and pressure behind battered retaining wall supporting inclined backfill. Soil Dyn Earthq Eng 30(11):1226–1232

    Article  Google Scholar 

  • Kramer SL (1996) Geotechnical earthquake engineering. Pearson Education, NJ

    Google Scholar 

  • Mononobe N, Matsuo H (1929) On the determination of earth pressures during earthquakes. In: Proceedings of the world engineering congress, Tokyo, pp 177–185

  • Nimbalkar SS, Choudhury D (2007) Sliding stability and seismic design of retaining wall by pseudo-dynamic method for passive case. Soil Dyn Earthq Eng 27(6):497–505

    Article  Google Scholar 

  • Nimbalkar SS, Choudhury D, Mandal JN (2006) Seismic stability of reinforced-soil wall by pseudo-dynamic method. Geosynth Int 13(3):111–119

    Article  Google Scholar 

  • Okabe S (1926) General theory of earth pressures. J Jpn Soc Civ Eng (JSCE) 12(1):123–134

    Google Scholar 

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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. SIMAU, Università Politecnica delle Marche, Ancona, Italy

    Ivo Bellezza

Authors
  1. Ivo Bellezza
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ivo Bellezza.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bellezza, I. A New Pseudo-dynamic Approach for Seismic Active Soil Thrust. Geotech Geol Eng 32, 561–576 (2014). https://doi.org/10.1007/s10706-014-9734-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10706-014-9734-y

Keywords

Search

Navigation