Geomechanics and Engineering

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Rao-3 algorithm for the weight optimization of reinforced concrete cantilever retaining wall

  • Kalemci, Elif N. (Department of Civil Engineering, Karadeniz Technical University) ;
  • ?kizler, S. Banu (Department of Civil Engineering, Karadeniz Technical University)
  • Received : 2020.01.04
  • Accepted : 2020.02.17
  • Published : 2020.03.25
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Abstract

The paper represents an optimization algorithm for reinforced concrete retaining wall design. The proposed method, called Rao-3 optimization algorithm, is a recently developed algorithm. The total weight of the steel and concrete, which are used for constructing the retaining wall, were chosen as the objective function. Building Code Requirements for Structural Concrete (ACI 318-05) and Rankine's theory for lateral earth pressure were considered for structural and geotechnical design, respectively. Number of the design variables are 12. Eight of those express the geometrical dimensions of the wall and four of those express the steel reinforcement of the wall. The safety against overturning, sliding and bearing capacity failure were regarded as the geotechnical constraints. The safety against bending and shear failure, minimum and maximum areas of reinforcement, development lengths of steel reinforcement were regarded as structural constraints. The performance of proposed algorithm was evaluated with two design examples.

Keywords

References

  1. ACI 318-05, (2015), Building code requirements for structural concrete and commentary, American Concrete Institute, Detroit, U.S.A.
  2. Artar M., Catar R. and Daloglu A.T. (2017), "Optimum design of steel bridges including corrosion effect using TLBO", Struct. Eng. Mech., 63(5), 607-615. https://doi.org/10.12989/sem.2017.63.5.607.
  3. Aydin Z. and Cakir E. (2015), "Cost minimization of prestressed steel trusses considering shape and size variables", Steel Compos. Struct., 19(1), 43-58. https://doi.org/10.12989/scs.2015.19.1.043.
  4. Bellman, R.E. (1978), An Introduction to Artificial Intelligence: Can Computers Think?, Boyd & Fraser Publishing Company, San Francisco, California, U.S.A.
  5. Camp, C.V. and Akin, A. (2012), "Design of retaining walls using big bang-big crunch optimization", J. Struct. Eng., 138(3), 438-448. https://doi.org/10.1061/(Asce)St.1943-541x.0000461.
  6. Dagdeviren, U. and Kaymak, B. (2015), "Optimum design of reinforced concrete retaining walls using artificial bee colony algorithm", Proceedings of the International Conference on Civil and Environmental Engineering, Nevsehir, Turkey, May.
  7. Deng, D., Li, L. and Zhao, L. (2019), "Stability analysis of slopes under groundwater seepage and application of charts for optimization of drainage design", Geomech. Eng., 17(2), 181-194. https://doi.org/10.12989/gae.2019.17.2.181.
  8. Epitropakis, M., Tasoulis, D., Pavlidis, N., Plagianakos, V. and Vrahatis, M. (2011), "Enhancing differential evolution utilizing proximity-based mutation operators", IEEE T. Evol. Comput., 15(1), 99-119. https://doi.org/10.1109/TEVC.2010.2083670.
  9. Feoktistov, V. (2006), Differential Evolution: In Search of Solutions, Springer Optimization and Its Applications, Springer, New York, U.S.A.
  10. Gholizadeh, S., Davoudi, H. and Fattahi, F. (2017), "Design of steel frames by an enhanced moth-flame optimization algorithm", Steel Compos. Struct., 24(1), 129-140. https://doi.org/10.12989/scs.2017.24.1.129.
  11. Gandomi, A.H., Kashani, A.R., Mousavi, M. and Roke, D.A. (2015), "Optimization of retaining wall design using recent swarm intelligence techniques", Eng. Struct., 103, 72-84. https://doi.org/10.1016/j.engstruct.2015.08.034.
  12. Gandomi, A.H., Kashani, A.R. and Zeighami, F. (2017a), "Retaining wall optimization using interior search algorithm with different bound constraint handling", Int. J. Numer. Anal. Meth. Geomech., 41(11), 1304-1331. https://doi.org/10.1002/nag.2678.
  13. Gandomi A.H., Kashani A.R., Roke D.A. and Mousavi M. (2017b), "Optimization of retaining wall design using evolutionary algorithms", Struct. Multidisciplin. Optimiz., 55(3), 809. https://doi.org/10.1007/s00158-016-1521-3.
  14. Ghazavi, M. and Bonab, B.S. (2011) "Optimization of reinforced concrete retaining walls using ant colony method", Proceedings of the 3rd International Symposium on Geotechnical Safety and Risk (ISGSR), Munich, Germany, June.
  15. Grzywinski, M. and Dede, T. (2020), "New optimization algorithms and their application for 2d truss structures", Zeszyty Naukowe Politechniki Czestochowskiej. Budownictwo, 175, 50-54. https://doi.org/10.17512/znb.2020.1.07.
  16. GuhaRay A. and Baidya, D.K. (2014), "Partial safety factors for retaining walls and slopes: A reliability based approach", Geomech. Eng., 6(2), 99-115. https://doi.org/10.12989/gae.2014.6.2.099.
  17. Goldberg, D.E, (1989), Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Publishing Company, Inc., Boston, Massachusetts, U.S.A.
  18. Jasim, N.A. and Al-Yaqoobi, A.M. (2016), "Optimum design of tied back retaining wall", Open J. Civ. Eng., 6(2), 139-155. http://dx.doi.org/10.4236/ojce.2016.62013.
  19. Kaveh, A. and Shakouri Mahmud Abadi, A. (2011), "Harmony search based algorithm for the optimum cost design of reinforced concrete cantilever retaining walls", Int. J. Civ. Eng., 1(9), 1-10.
  20. Kaveh, A and Behnam, A.F. (2013), "Charged system search algorithm for the optimum cost design of reinforced concrete cantilever retaining walls", Arab. J. Sci. Eng., 38, 563-570. https://doi.org/10.1007/s13369-012-0332-0.
  21. Kaveh, A., Kalateh-Ahani, M. and Fahimi-Farzam, M. (2013), "Constructability optimal design of reinforced concrete retaining walls using a multi-objective genetic algorithm", Struct. Eng. Mech., 47(2), 227-245. https://doi.org/10.12989/sem.2013.47.2.227.
  22. Kaveh, A. and Khayatazad, M. (2014), "Optimal design of cantilever retaining walls using ray optimization method", Iran. J. Sci. Technol., 38(C1+), 261-274.
  23. Kaveh, A. and Soleimani, N. (2015), "CBO and DPSO for optimum design of reinforced concrete cantilever retaining walls", Asian J. Civ. Eng., 16(6), 751-774.
  24. Kaveh, A. and Laien, D.J. (2017), "Optimal design of reinforced concrete cantilever retaining walls using CBO, ECBO and VPS algorithms", Asian J. Civ. Eng., 18(4), 657-671.
  25. Kayabekir, A.E., Bekdas, G., Nigdeli, S.M. and Temur, R. (2017), "Statik ve dinamik yukler altinda istinat duvarlarinin optimum tasarimi", Eng. Sci., 12(1), 46-56. https://doi.org/10.12739/NWSA.2017.12.1.1A0372/
  26. Kayhan, A.H. and Demir, A. (2018), "Optimum design of RC cantilever retaining walls subjected to static and dynamic loadings by differential evolution algorithm", Pamukkale Univ. Muh Bilim Derg., 24(3), 403-412. https://doi.org/10.5505/pajes.2017.04834.
  27. Khajehzadeh, M., Taha, M.R., El-Shafie, A. and Eslami, M. (2011), "Modified particle swarm optimization for optimum design of spread footing and retaining wall", J. Zhejiang Univ. Sci. A, 12(6), 415-427. https://doi.org/10.1631/jzus.A1000252
  28. Khajehzadeh, M., Taha, M., El-Shafie, A. and Eslami, M. (2012), "Optimization of shallow foundation using gravitational search algorithm", Res. J. Appl. Sci. Eng. Technol., 4(9), 1124-1130. https://doi.org/10.1631/jzus.A1000252.
  29. Khalkhali, A., Sarmadi, A., Khakshournia S. and Jafari N. (2016), "Probabilistic multi-objective optimization of a corrugated-core sandwich structure", Geomech. Eng., 10(6), 709-726. https://doi.org/10.12989/gae.2016.10.6.709.
  30. Kim H., Lee K., Jamin, J.C. and Mission, J.L.C. (2014), "Stochastic cost optimization of ground improvement with prefabricated vertical drains and surcharge preloading", Geomech. Eng., 7(5), 525-537. https://doi.org/10.12989/gae.2014.7.5.525.
  31. Kumar, V.N. and Suribabu, C.R. (2017), "Optimal design of cantilever retaining wall using differential evolution algorithm", Int. J. Optim. Civ. Eng., 7(3), 433-449.
  32. Lopez, R.H. (2017), "Optimum project of cantilever retaining wall using search group algorithm and backtracking search algorithm", Revista Internacional de Metodos Numericos para Calculo y Diseno en Ingenieria.
  33. Man, K.F., Tang, K.S. and Kwong, S., (1999), Genetic Algorithms: Concepts and Designs, Springer Publishing, Heidelberg, Germany.
  34. Mirjalili, S. (2015), "Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm", Knowledge-Based Syst., 89, 228-249. https://doi.org/10.1016/j.knosys.2015.07.006.
  35. Mirzaei, Z., Akbarpour, A., Khatibinia, M. and Siuki A.K. (2015), "Optimal design of homogenous earth dams by particle swarm optimization incorporating support vector machine approach", Geomech. Eng., 9(6), 709-727. https://doi.org/10.12989/gae.2015.9.6.709.
  36. Nigdeli, S., Bekdas, G. and Yang, X.S. (2018), "Metaheuristic optimization of reinforced concrete footings", KSCE J. Civ. Eng., 22(11), 4555-4563. https://doi.org/10.1007/s12205-018-2010-6.
  37. Osman, I. (1995), An Introduction to Metaheuristics, University of Kent, Canterbury, U.K.
  38. Perea, C., Alcala, J., Yepes, V., Gonzalez-Vidosa, F. and Hospitaler, A. (2008), "Design of reinforced concrete bridge frames by heuristic optimization", Adv. Eng. Softw., 39, 676-688. https://doi.org/10.1016/j.advengsoft.2007.07.007.
  39. Parkinson, A.R., Balling, R.J. and Hedengren, J.D. (2013), Optimization Methods for Engineering Design: Applications and Theory (5th Ed.), Brigham Young University, Provo, Utah, U.S.A.
  40. Rao, R.V. (2020), "Rao algorithms: Three metaphor-less simple algorithms for solving optimization problems", Int. J. Industr. Eng. Comput., 11(1), 107-130. https://doi.org/10.5267/j.ijiec.2019.6.002.
  41. Rao, R.V. and Pawar, R.B. (2020), "Constrained design optimization of selected mechanical system components using Rao algorithms", Appl. Soft Comput. J., 89, 106141. https://doi.org/10.1016/j.asoc.2020.106141.
  42. Russell, S.J., Norvig, P. and Davis, E. (2010), Artificial Intelligence: A Modern Approach (3rd Ed.), Prentice Hall, Upper Saddle River, New Jersey, U.S.A.
  43. Saribas, A. and Erbatur, F. (1996), "Optimization and sensitivity of retaining structures", J. Geotech. Eng., 122(8), 649-656. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:8(649).
  44. Sheikholeslami, R., Gholipour Khalili, B. and Zahrai, S.M. (2014), "Optimum cost design of reinforced concrete retaining walls using hybrid firefly algorithm", IACSIT Int. J. Eng. Technol., 6(6), 465-470. https://doi.org/10.7763/IJET.2014.V6.746.
  45. Storn, R. and Price, K. (1997), "Differential evolution: A simple and efficient adaptive scheme for global optimization over continuous spaces", J. Global Optim., 11(4), 341-359. https://doi.org/10.1023/A:1008202821328
  46. Sadoglu, E. (2014), "Design optimization for symmetrical gravity retaining walls", Acta Geotechnica Slovenica, 11(2), 71-79.
  47. Talatahari, S. and Sheikholeslami, R. (2014), "Optimum design of gravity and reinforced retaining walls using enhanced charged system search algorithm", KSCE J. Civ. Eng., 18(5), 1464. https://doi.org/10.1007/s12205-014-0406-5.
  48. Temur, R. and Bekdas, G. (2016), "Teaching learning-based optimization for design of cantilever retaining walls", Struct. Eng. Mech., 57(4), 763-783. https://doi.org/10.12989/sem.2016.57.4.763.
  49. Yepes, V., Alcala, J., Perea, C. and Gonzalez-Vidosa, F. (2008) "A parametric study of optimum earth-retaining walls by simulated annealing", Eng. Struct., 30(3), 821-830. https://doi.org/10.1016/j.engstruct.2007.05.023.
  50. Yepes, V., Gonzalez-Vidosa, F., Alcala, J. and Villalba, P. (2012), "CO2-optimization design of reinforced concrete retaining walls based on a VNS-threshold acceptance strategy", J. Comput. Civ. Eng., 26(3), 378-386. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000140.
  51. Yepes, V., Albinana, M. and Garcia-Segura, T. (2017), "Design optimization of precast-prestressed concrete road bridges with steel fiber-reinforcement by a hybrid evolutionary algorithm", Int. J. Comput. Meth. Exper. Measurement., 5(2), 179-189. https://doi.org/10.2495/CMEM-V5-N2-179-189.
  52. Wang, C.X., Li, C.H., Dong, H. and Zhang, F. (2013), "An efficient differential evolution algorithm for function optimization", Inform. Technol. J., 12(3), 444-448. https://doi.org/10.3923/itj.2013.444.448.
  53. Wang, L., Wang, Z., Liang, H. and Huang, C. (2019), "Parameter estimation of photovoltaic cell model with Rao-1 algorithm", Optik, 163846. https://doi.org/10.1016/j.ijleo.2019.163846.
  54. Zahrai, S.M., Khalili, B.G. and Sheikholeslami, R. (2014), "Optimum cost design of reinforced concrete retaining walls using hybrid firefly algorithm", Int. J. Eng. Technol., 6(6), 465-470. https://doi.org/10.7763/IJET.2014.V6.742.
  55. Zakian, P and Kaveh, A. (2020), "Topology optimization of shear wall structures under seismic loading", Earthq. Eng. Eng. Vib., 19(1), 105. https://doi.org/10.1007/s11803-020-0550-5.

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