Skip to main content

A regression-based approach for estimating preliminary dimensioning of reinforced concrete cantilever retaining walls


The reinforced concrete cantilever retaining walls (RCCRWs) are among the most commonly used type of structures to support the soil in civil engineering applications. In the conventional trial and error design of RCCRWs, which are based on engineering experiences and literature reviews, the preliminary dimensions of the wall are selected by considering the wall height only. However, it is known that the properties of backfill soil and surcharge loads also affect the dimensions of the wall. Therefore, in order to take into account the effects of the backfill soil properties and surcharge loads in addition to the height of the wall, a new regression-based approach is developed for predicting the preliminary dimensions of T-shaped RCCRWs. For this aim, a total of 375 optimization analyses are carried out for the optimum design of RCCRWs resting on soil with high bearing capacity by using the artificial bee colony (ABC) algorithm. Based on these calculated optimum solutions, the regression equations are developed for preliminary dimensioning of the T-shaped RCCRWs by using multiple regression analyses. Moreover, a set of 15 random problems are generated to assess prediction ability of the proposed regression equations, and their optimum dimensions are calculated by ABC algorithm and then these calculated dimensions are compared with the preliminary dimensions estimated by the proposed regression equations. From this comparison, it is observed that the maximum difference between the calculated and the estimated wall dimensions is only 6.2%. This means that the proposed preliminary dimensioning regression equations are capable of predicting dimensions that are close enough to the optimum dimensions. Therefore, for the most economical design of the T-shaped RCCRWs resting on soil with high bearing capacity, the predicted dimensions, which are supplied by the proposed regression equations, can be used as a good starting point when an optimization technique or a conventional trial and error method is employed.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7


  • Ahmadi-Nedushan B, Varaee H (2009) Optimal design of reinforced concrete retaining walls using a swarm intelligence technique. In: The first international conference on soft computing technology in civil, structural and environmental engineering, pp 1–12

  • Akay B, Karaboga D (2012) A modified artificial bee colony algorithm for real-parameter optimization. Inf Sci 192:120–142

    Google Scholar 

  • American Concrete Institute (2005) Building code requirements for structural concrete and commentary (ACI 318M-05). American Concrete Institute

  • Aydoğdu I, Akin A, Saka MP (2016) Design optimization of real world steel space frames using artificial bee colony algorithm with levy flight distribution. Adv Eng Softw 92:1–14

    Google Scholar 

  • Boddula S, Eldho T (2018) Groundwater management using a new coupled model of meshless local Petrov-Galerkin method and modified artificial bee colony algorithm. Comput Geosci 22(3):657–675

    MathSciNet  MATH  Google Scholar 

  • Bolaji AL, Khader AT, Al-Betar MA, Awadallah MA (2013) Artificial bee colony algorithm, its variants and applications: a survey. J Theor Appl Inform Technol 47(2):434–459

    Google Scholar 

  • Bowles J (1997) Foundation analysis and design. Civil engineering series. McGraw-Hill, New York

    Google Scholar 

  • Budhu M (2008) Foundations and earth retaining structures

  • Camp CV, Akin A (2011) Design of retaining walls using big bang–big crunch optimization. J Struct Eng 138(3):438–448

    Google Scholar 

  • Chakraborty A, Goswami D (2017) Prediction of slope stability using multiple linear regression (mlr) and artificial neural network (ann). Arab J Geosci 10(17):385

    Google Scholar 

  • Dağdeviren U, Kaymak B (2018) Investigation of parameters affecting optimum cost design of reinforced concrete retaining walls using artificial bee colony algorithm. J Faculty Eng Archit Gazi Univ 33(1):239–253

    Google Scholar 

  • Das BM (2016) Principles of foundation engineering, Eighth Ed

  • Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2-4):311– 338

    MATH  Google Scholar 

  • Gandomi AH, Kashani AR, Roke DA, Mousavi M (2017) Optimization of retaining wall design using evolutionary algorithms. Struct Multidiscip Optim 55:809–825

    Google Scholar 

  • Greco A, Pluchino A, Cannizzaro F (2019) An improved ant colony optimization algorithm and its applications to limit analysis of frame structures. Eng Optim 51(11):1867–1883

    Google Scholar 

  • Ghazavi M, Bonab S (2011) Optimization of reinforced concrete retaining walls using ant colony method. 3rd International Symposium on Geotechnical Safety and Risk (1996): 297– 305

  • Ghazavi M, Salavati V (2011) Sensitivity analysis and design of reinforced concrete cantilever retaining walls using bacterial foraging optimization algorithm. In: 3rd international symposium on geotechnical safety and risk, pp 307–314

  • Jafrasteh B, Fathianpour N (2017) Optimal location of additional exploratory drillholes using afuzzy-artificial bee colony algorithm. Arab J Geosci 10:213

    Google Scholar 

  • Karaboga D (2005) An idea based on honey bee swarm form numerical optimization. Technical Report TR06, Erciyes University, Turkey

  • Karaboga D, Akay B (2011) A modified artificial bee colony (ABC) algorithm for constrained optimization problems. Appl Soft Comput 11(3):3021–3031

    Google Scholar 

  • Karaboga D, Basturk B (2007) Artificial bee colony (ABC) optimization algorithm for solving constrained optimization. Lnai 4529:789–798

    MATH  Google Scholar 

  • Karaboga D, Basturk B (2008) On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput 8(1):687–697

    Google Scholar 

  • Kaveh A, Abadi ASM (2011) Harmony search based algorithms for the optimum cost design of reinforced concrete cantilever retaining walls. Int J Civil Eng 9(1):1–8

    Google Scholar 

  • Kaveh A, Behnam AF (2013) Charged system search algorithm for the optimum cost design of reinforced concrete cantilever retaining walls. Arab J Sci Eng 38:563–570

    Google Scholar 

  • Kaymak B (2019) Parameter analysis of bacterial foraging optimization algorithm for least weight design of truss structures. Süleyman Demirel University Journal of Natural and Applied Sciences 23(2):24–38

    MathSciNet  Google Scholar 

  • Ma C, Yu T, Van Lich L, Quoc Bui T (2017) An effective computational approach based on XFEM and a novel three-step detection algorithm for multiple complex flaw clusters. Comput Struct 193:207–225

    Google Scholar 

  • Pei Y, Xia Y (2012) Design of reinforced cantilever retaining walls using heuristic optimization algorithms. Procedia Earth and Planetary Science

  • Sarıbaş A, Erbatur F (2003) Optimization and sensitivity of retaining structures. J Geotech Eng 122 (8):649–656

    Google Scholar 

  • Sharma LK, Singh TN (2018) Regression-based models for the prediction of unconfined compressive strength of artificially structured soil. Engineering with Computers

  • Sheikholeslami R, Khalili BG, Sadollah A, Kim J (2016) Optimization of reinforced concrete retaining walls via hybrid firefly algorithm with upper bound strategy. KSCE J Civ Eng 20(6):2428– 2438

    Google Scholar 

  • Song X, Gu H, Tang L, Zhao S, Zhang X, Li L, Huang J (2015) Application of artificial bee colony algorithm on surface wave data. Comput Geosci

  • Sonmez M (2018) Performance comparison of metaheuristic algorithms for the optimal design of space trusses. Arab J Sci Eng 43(10):5265–5281

    Google Scholar 

  • Sun SH, Yu TT, Nguyen TT, Atroshchenko E, Bui TQ (2018) Structural shape optimization by IGABEM and particle swarm optimization algorithm. Engineering Analysis with Boundary Elements 88:26–40

    MathSciNet  MATH  Google Scholar 

  • Vargas DEC, Lemonge ACC, Barbosa HJC, Bernardino HS (2019) Differential evolution with the adaptive penalty method for structural multi-objective optimization. Optim Eng 20(1):65–88

    MATH  Google Scholar 

  • Venkatramaiah C (2016) Geotechnical engineering. Third Edition, New Age International Publishers

  • Wang C, Yu T, Curiel-Sosa JL, Xie N, Bui TQ (2019a) Adaptive chaotic particle swarm algorithm for isogeometric multi-objective size optimization of FG plates. Struct Multidiscip Optim 60(2):757–778

  • Wang C, Yu T, Shao G, Nguyen TT, Bui TQ (2019b) Shape optimization of structures with cutouts by an efficient approach based on XIGA and chaotic particle swarm optimization. European Journal of Mechanics, A/Solids 74:176–187

  • Yılmaz N, Temel Gencer C (2019) Integration of sensor vision capabilities on UAV flight route optimization: a linear model and a heuristic algorithm proposal. J Fac Eng Archit Gazi Univ 34:1917–1928

    Google Scholar 

  • Yoon GL, Kim BT, Jeon SS (2005) Empirical correlations of compression index for marine clay from regression analysis. Canadian Geotechnical Journal

  • Zhang Y, Gong C, Fang H, Su H, Li C, Da Ronch A (2019) An efficient space division–based width optimization method for RBF network using fuzzy clustering algorithms. Struct Multidiscip Optim 60(2):461–480

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Ugur Dagdeviren.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Replication of results

The optimization algorithm and the design details of RCCRWs used the study are given in Sections 23, and 4. The data set used in the developed regression models for estimation of preliminary dimensions of the RCCRWs is obtained from a total of 375 optimization problem results using the artificial bee colony algorithm, and the data set is given in the Supplementary Table 1. Also, 15 different data set used to test and verify the proposed regression models are given in the Supplementary Table 2.

Additional information

Responsible Editor: Mehmet Polat Saka

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

(XLSX 36.6 KB)

(XLSX 12.4 KB)

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dagdeviren, U., Kaymak, B. A regression-based approach for estimating preliminary dimensioning of reinforced concrete cantilever retaining walls. Struct Multidisc Optim 61, 1657–1675 (2020).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: