Geotechnical and Geological Engineering

, Volume 29, Issue 3, pp 307–317 | Cite as

Seismic Passive Earth Pressure on Walls with Bilinear Backface Using Pseudo-Dynamic Approach

Original paper

Abstract

By using pseudo-dynamic approach, a method has been proposed in this paper to compute the seismic passive earth pressure behind a rigid cantilever retaining wall with bilinear backface. The wall has sudden change in inclination along its depth and a planar failure surface has been considered behind the retaining wall. The effects of a wide range of parameters like soil friction angle, wall inclination, wall friction angle, amplification of vibration, variation of shear modulus and horizontal and vertical seismic accelerations on the passive earth pressure have been explored in the present study. For the sake of illustration, the computations have been exclusively carried out for constant wall friction through out the depth. Unlike the Mononobe-Okabe method, which incorporates pseudo-static analysis, the present analysis predicts a nonlinear variation of passive earth pressure along the wall.

Keywords

Bilinear backface Cantilever retaining wall Earthquakes Passive earth pressure Pseudo-dynamic analysis 

Abbreviations

ah(z, t)

Horizontal acceleration at depth z and time t

av(z, t)

Vertical acceleration at depth z and time t

fa

Amplification factor

G

Shear modulus of the backfill soil

G0

Constant

g

Acceleration due to gravity

H

Height of retaining wall

H1

Height of the upper part of wall backface

Kpe1

Passive thrust coefficient relative to the thrust P pe1(t)

Kpe2

Passive thrust coefficient relative to the thrust P pe2(t)

m(z)

Mass of small shaded part of thickness dz in wedge ABDE

m1(z)

Mass of small shaded part dz in wedge ABC

m21(z)

Mass of small shaded part dz in wedge ABDE for z varying from 0 to H 1

m22(z)

Mass of small shaded part dz in wedge ABDE for z varying from H 1 to H

Ppe1(t)

Passive thrust on the upper part of wall backface

Ppe2(t)

Passive thrust on the lower part of wall backface

ppe(z, t)

Passive earth pressure behind the wall at depth z and time t

ppe1(z, t)

Passive earth pressure on the upper part of wall at depth z and time t

ppe2(z, t)

Passive earth pressure on the lower part of wall at depth z and time t

Qh(t)

Horizontal inertia force in the wedge ABDE due to horizontal seismic acceleration

Qv(t)

Vertical inertia force in the wedge ABDE due to vertical seismic acceleration

Qh1(t)

Horizontal inertia force in the wedge ABC due to horizontal seismic acceleration

Qv1(t)

Vertical inertia force in the wedge ABC due to vertical seismic acceleration

R

Thrust acting on the internal failure plane limiting the thrust wedge

T

Period of lateral shaking

t

Time

Δtp

Time increment for passage of primary wave from the base to a depth z

Δts

Time increment for passage of shear wave from the base to a depth z

Vp

Primary wave velocity

Vpavg

Mean primary wave velocity

Vs

Shear wave velocity

Vsavg

Mean shear wave velocity

W

Weight of the failure wedge ABDE behind the wall

W1

Weight of the failure wedge ABC behind the upper part of wall

z

Depth of a generic point below the wall top

α1

Inclination angle of the failure plane BC limiting the local thrust wedge acting on the upper part of wall backface

α2

Inclination angle of the failure plane DE limiting the thrust wedge behind the wall

αh

Seismic acceleration coefficient in the horizontal direction

αv

Seismic acceleration coefficient in the vertical direction

β

Depth exponent causing shear modulus variation

δ1

Friction angle between soil and wall along the upper part of wall backface

δ2

Friction angle between soil and wall along the lower part of wall backface

ϕ

Friction angle of the backfill

γ

Unit weight of the soil

ν

Poisson’s ratio

θ1

Angle of inclination of the upper part of wall backface

θ2

Angle of inclination of the lower part of wall backface

ρ

Density of the soil

ω

Angular frequency of base shaking

Notes

Acknowledgments

The second author wants to acknowledge the partial financial support provided by the Indian Institute of Technology Kanpur to carry out the present work through a sponsored research project.

References

  1. Choudhary D, Nimbalkar S (2005) Seismic passive resistance by pseudo-dynamic method. Geotechnique 55(9):699–702CrossRefGoogle Scholar
  2. Das BM (1993) Principles of soil dynamics. PWS-KENT Publishing Company, Boston, MAGoogle Scholar
  3. Ghosh P (2007) Seismic passive earth pressure behind nonvertical retaining wall using pseudo-dynamic analysis. Geotech Geol Eng 25:693–703CrossRefGoogle Scholar
  4. Ghosh P (2008) Upper bound solutions of bearing capacity of strip footing by pseudo-dynamic approach. Acta Geotech 3(2):115–123CrossRefGoogle Scholar
  5. Greco VR (2007) Analytical earth thrust on walls with bilinear backface. Geotech Eng 160(Issue GEI):23–29Google Scholar
  6. Kramer SL (1996) Geotechnical earthquake engineering. Prentice Hall, New JerseyGoogle Scholar
  7. Kumar J (2001) Seismic passive earth pressure coefficients for sands. Can Geotech J 38:876–881Google Scholar
  8. Kumar J, Chitikela S (2002) Seismic passive earth pressure coefficients using the method of characteristics. Can Geotech J 39(2):463–471CrossRefGoogle Scholar
  9. Kumar J, Subba Rao KS (1997) Passive pressure determination by method of slices. Int J Numer Anal Meth Geomech 21:337–345CrossRefGoogle Scholar
  10. Lancellotta R (2007) Lower bound approach for seismic passive earth resistance. Geotechnique 57(3):319–321CrossRefGoogle Scholar
  11. Mononobe N, Matsuo H (1929) On the determination of earth pressure during earthquakes. In: Proceedings of the world engineering conference, vol. 9, pp 179–187Google Scholar
  12. Okabe S (1926) General theory of earth pressure. J Japan Soc Civil Eng 12(1):311Google Scholar
  13. Sadrekarimi A, Ghalandarzadeh A, Sadrekarimi J (2008) Static and dynamic behavior of hunchbacked gravity quay walls. Soil Dyn Earthquake Eng 28(2):99–117CrossRefGoogle Scholar
  14. Sokolovski VV (1960) Statics of soil media. Butterworths Scientific Publications, LondonGoogle Scholar
  15. Soubra AH (2000) Static and Seismic passive earth pressure coefficients on rigid retaining structures. Can Geotech J 37(2):463–478Google Scholar
  16. Sreevalsa K, Ghosh P (2009) Seismic active earth pressure with varying shear modulus in backfill—pseudo-dynamic approach. International conference on performance-based design in earthquake geotechnical engineering—from case history to practice (IS-Tokyo 2009), Tokyo, JapanGoogle Scholar
  17. Steedman RS, Zeng X (1990) The influence of phase on the calculation of pseudo-static earth pressure on a retaining wall. Geotechnique 40(1):103–112CrossRefGoogle Scholar
  18. Zhu D, Qian Q (2000) Determination of passive earth pressure coefficients by the method of triangular slices. Can Geotech J 37(2):485–491Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Civil EngineeringIITKanpurIndia
  2. 2.Department of Civil EngineeringIITKanpurIndia
  3. 3.Department of Civil EngineeringIndian Institute of TechnologyKanpurIndia

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