Arabian Journal for Science and Engineering

, Volume 38, Issue 3, pp 563–570 | Cite as

Charged System Search Algorithm for the Optimum Cost Design of Reinforced Concrete Cantilever Retaining Walls

Research Article - Civil Engineering


In this paper, optimal design of reinforced concrete cantilever retaining walls is performed under static loads utilizing the charged system search (CSS) method. This design is based on ACI 318-05, and optimization is on the basis of cost function of materials used in retaining walls and their constructions. This function is minimized while satisfying the design constraints. Performance of the CSS algorithm is compared to that of the improved harmony search algorithm. Four examples are optimized and their convergence curves are compared.


Optimization Reinforced concrete Cantilever retaining walls Charged system search Improved harmony search 

List of Symbols


Top stem thickness


Bottom stem and key thickness


Top stem height


Bottom stem height


Toe length


Heel length


Total length of the base of the footing


Footing thickness


Density of the fill


Internal friction angle of the fill


Backfill slope


Base friction coefficient


Density of the concrete


Weight of the top stem


Weight of the bottom stem


Weight of the fill on the heel


Surcharge weight


Key depth


Soil over toe


Cost of the concrete


Cost of the steel


Cost of the concreting


Cost of the erecting reinforcement

F1, F2

Type of the back fills

T1, …, T7

The selected variables


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dembicki E., Chi T.: System analysis in calculation of cantilever retaining wall.Int. J. Numer. Anal. Method Geomech. 13, 599–610 (1989)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Keskar, A.V.; Adidam, S.R.: Minimum cost design of a cantilever retaining wall. Indian Concrete J. Bombay, India, 401–405 (1989)Google Scholar
  3. 3.
    Saribas A., Erbatur F.: Optimization and sensitivity of retaining structures. J. Geotech. Eng. 8, 649–656 (1996)CrossRefGoogle Scholar
  4. 4.
    Rhomberg E.J., Street W.M.: Optimal design of retaining walls. J. Struct. Div. ASCE 107, 992–1002 (1981)Google Scholar
  5. 5.
    Basudhar, P.K.; Lakshman, B.: Optimal cost design of cantilever retaining walls. IGC 2006. Chennai, India. 14–16 December 2006Google Scholar
  6. 6.
    Sivakumar V., Munwar B.: Optimum design of cantilever retaining walls using target reliability approach.Int. J. Geomech. 8, 240–252 (2008)CrossRefGoogle Scholar
  7. 7.
    Yepes V., Alcala J., Perea C., Gonzalez-Vidosa F.: A parametric study of optimum earth-retaining walls by simulated annealing. Eng. Struct. 30, 821–830 (2008)CrossRefGoogle Scholar
  8. 8.
    Kaveh A., Talatahari S.: A novel heuristic optimization method: charged system search. Acta Mech. 213(3–4), 267–286 (2010)MATHCrossRefGoogle Scholar
  9. 9.
    Kaveh A., Talatahari S.: Optimal design of truss structures via the charged system search algorithm. Struct. Multidisp. Optim. 37(6), 893–911 (2010)CrossRefGoogle Scholar
  10. 10.
    ACI Committee 318: Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (318R-05). American Concrete Institute, Farmington Hills (2005)Google Scholar
  11. 11.
    Geem Z.W.: Harmony Search Algorithms for Structural Design. Springer, Berlin (2009)CrossRefGoogle Scholar
  12. 12.
    Mahdavi M., Fesanghary M., Damangir E.: An improved harmony search algorithm for solving optimization problems. Appl. Math. Comput. 188, 1567–1579 (2007)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Kaveh A., Talatahari S.: Particle swarm optimizer, ant colony strategy and harmony search scheme hybridized for optimization of truss structures. Comput. Struct. 87, 267–283 (2009)CrossRefGoogle Scholar
  14. 14.
    Kaveh A., Shakouri Mahmud Abadi A.: Harmony search based algorithm for the optimum cost design of reinforced concrete cantilever retaining walls. Int. J. Civ. Eng. 9(1), 1–18 (2011)Google Scholar
  15. 15.
    Das, B.M.: Principles of Foundation Engineering, 5th edn. Brooks/Cole. a Division of Thomson Learning Inc., Belmont (2004)Google Scholar

Copyright information

© King Fahd University of Petroleum and Minerals 2012

Authors and Affiliations

  1. 1.Department of Civil Engineering, Centre of Excellence for Fundamental Studies in Structural EngineeringIran University of Science and TechnologyTehran-16Iran
  2. 2.Building and Housing Research CentreTehran-14Iran

Personalised recommendations