Indian Geotechnical Journal

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

Performance Evaluation of Gravity Type Retaining Wall Under Earthquake Load

Original Paper


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.


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

List of Symbols


Corss-sectional area of beam with uniform cross section


Corss-sectional area of retaining wall at base


Corss-sectional area of retaining wall at any height z


Width of retaining wall at base

C1to C4

Intergration constant


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


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


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


Dynamic Shear Modulus of retaining wall material


Acceleration due to gravity


Height of retaining wall


Importance factor


Moment of inertia of retaining wall at base


Moment of inertia of retaining wall at any height z


Stiffness of a system


Stiffness matrix of retaining wall


Equivalent stiffness


Stiffness in bending mode


Stiffness in shear mode


Mass matrix of retaining wall in bending or shear mode


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


SRSS value of seismic Moment


Load vector


Any arbitrary load on a beam


Slenderness ratio @ H/Bb


Response reduction/Ductility factor


Spectral acceleration of retaining wall in ith mode


Any time instant


Natural modal period of a body


Natural modal period of retaining wall in bending mode


Natural modal period of retaining wall in shear mode


Effective natural modal period under combined shear and bending mode


Lateral deflection of the retaining wall


Shear wave velocity


SRSS value of base shear under earthquake force


Base shear at retaining wall–soil interface


Co-ordinate in horizontal direction


Co-ordinate in vertical direction


Zone factor


Dimensionless term z/H


Code factor (=ZI/2R)


Deflection due to bending


Deflection due to shear


Total deflection


Scaling factor for the eigen vectors


Weight density of concrete


Shear correction factor


Modal mass participation in ith mode




Poisson’s ratio of retaining wall material


Mass density of concrete


Natural modal frequency


Effective natural frequency


Natural frequency in bending mode


Natural frequency in shear mode


Dimensionless term


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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