Indian Geotechnical Journal

, Volume 44, Issue 2, pp 156–166 | Cite as

Performance Evaluation of Gravity Type Retaining Wall Under Earthquake Load

Original Paper

Abstract

Gravity retaining walls, especially with improvement of RCC structures though have become more or less obsolete in terms of construction (replaced by RCC cantilever and counter fort type retaining walls), yet in India, there exists a number of them that has been built in the past in many strategically important places (both post and pre independence). Evaluating their health in terms of a future strong motion earthquake remains an important exercise—now that our understanding of this fury of mother nature is far more profound. Unfortunately tools available to assess its behavior as realistically as possible under seismic force even today is quite limited, marred by idealization, that are unrealistic and may not reflect correctly the actual behavior in reality, and this needs a serious evaluation. In Indian context, the only tool available to assess a gravity type retaining wall’s performance is by Mononobe and Okabe Method (M–O method), that continue to dominate IS code, notwithstanding the fact that many countries including US has now abandoned the method, as it has now been proved beyond any dispute that M–O method gives a lower bound solution than reality. Present paper tries to address some of these shortcomings as proposed above and come up with a mathematical model that is more realistic, and which may be used for performance evaluation of such gravity retaining walls under future earthquakes. Finally, the paper suggests some practical strengthening measure that may be undertaken to enhance these walls performance—where to the author’s perception if re-evaluated, many of them would be found unsafe in context to present earthquake code.

Keywords

Gravity wall Cohesion less soil Shape functions Galerkin’s techinque Shear deformation Modal analysis 

List of Symbols

A

Corss-sectional area of beam with uniform cross section

Ab

Corss-sectional area of retaining wall at base

Az

Corss-sectional area of retaining wall at any height z

Bb

Width of retaining wall at base

C1to C4

Intergration constant

CTFi

Time period factor in bending mode of retaining wall in ith mode

CTSi

Time period factor in shear mode of retaining wall in ith mode

E

Youngs modulus of retaining wall material

\( f_{i}^{b} \)

Shape function of beam, bending mode in mode i

\( f_{i}^{s} \)

Shape function of beam, shear mode in mode i

G

Dynamic Shear Modulus of retaining wall material

g

Acceleration due to gravity

H

Height of retaining wall

I

Importance factor

Ib

Moment of inertia of retaining wall at base

Iz

Moment of inertia of retaining wall at any height z

K

Stiffness of a system

[K]ij

Stiffness matrix of retaining wall

Ke

Equivalent stiffness

Kb

Stiffness in bending mode

Ks

Stiffness in shear mode

[M]ij

Mass matrix of retaining wall in bending or shear mode

Mzi

Bending moment along retaining wall height at point z for any mode i

MSRSS

SRSS value of seismic Moment

P

Load vector

q

Any arbitrary load on a beam

rs

Slenderness ratio @ H/Bb

R

Response reduction/Ductility factor

Sai

Spectral acceleration of retaining wall in ith mode

t

Any time instant

T

Natural modal period of a body

Tb

Natural modal period of retaining wall in bending mode

Ts

Natural modal period of retaining wall in shear mode

Te

Effective natural modal period under combined shear and bending mode

u

Lateral deflection of the retaining wall

Vs

Shear wave velocity

VSRSS

SRSS value of base shear under earthquake force

Vz

Base shear at retaining wall–soil interface

x

Co-ordinate in horizontal direction

z

Co-ordinate in vertical direction

Z

Zone factor

ξ

Dimensionless term z/H

β

Code factor (=ZI/2R)

δb

Deflection due to bending

δs

Deflection due to shear

δt

Total deflection

ϕ

Scaling factor for the eigen vectors

γc

Weight density of concrete

η

Shear correction factor

κi

Modal mass participation in ith mode

λ

Εigenvalues

ν

Poisson’s ratio of retaining wall material

ρ

Mass density of concrete

ω

Natural modal frequency

ωe

Effective natural frequency

ωb

Natural frequency in bending mode

ωs

Natural frequency in shear mode

ψb

Dimensionless term

Ω

Dimensionless term

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Copyright information

© Indian Geotechnical Society 2013

Authors and Affiliations

  1. 1.Department of Civil and Structural EngineeringPetrofac International LtdSharjahUnited Arab Emirates

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