Abstract
This paper proposes a new approach for the formulation of compressive strength of carbon fiber reinforced plastic (CFRP) confined concrete cylinders using a promising variant of genetic programming (GP) namely, linear genetic programming (LGP). The LGP-based models are constructed using two different sets of input data. The first set of inputs comprises diameter of concrete cylinder, unconfined concrete strength, tensile strength of CFRP laminate and total thickness of utilized CFRP layers. The second set includes unconfined concrete strength and ultimate confinement pressure which are the most widely used parameters in the CFRP confinement existing models. The models are developed based on experimental results collected from the available literature. The results demonstrate that the LGP-based formulas are able to predict the ultimate compressive strength of concrete cylinders with an acceptable level of accuracy. The LGP results are also compared with several CFRP confinement models presented in the literature and found to be more accurate in nearly all of the cases. Moreover, the formulas evolved by LGP are quite short and simple and seem to be practical for use. A subsequent parametric study is also carried out and the trends of the results have been confirmed via some previous laboratory studies.
Similar content being viewed by others
References
Lorenzis LA (2001) Comparative study of models on confinement of concrete cylinders with FRP composites. PhD thesis, Division for Building Technology, Chalmers University of Technology, Sweden
Fardis MN, Khalili H (1982) FRP-encased concrete as a structural material. Mag Concrete Res 34(121):191–202
Mirmiran A, Zagers K, Yuan W (2000) Nonlinear finite element modeling of concrete confined by fiber composites. Finite Elem Anal Des 35:79–96
Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection. MIT Press, Cambridge, Mass
Banzhaf W, Nordin P, Keller R, Francone F (1998) Genetic programming–an introduction. On the automatic evolution of computer programs and its application. Dpunkt/Morgan Kaufmann, Heidelberg/San Francisco
Brameier M, Banzhaf W (2007) Linear genetic programming. Springer Science+Business Media, LLC, New York
Oltean M, Grosan C (2003) A comparison of several linear genetic programming techniques. Adv Complex Syst 14(4):1–29
Gandomi AH, Alavi AH, Kazemi S, Alinia MM (2009) Behavior appraisal of steel semi-rigid joints using Linear Genetic Programming. J Constr Steel Res 65(8–9):1738–1750
Alavi AH, Heshmati AAR, Gandomi AH, Askarinejad A, Mirjalili M (2008) Utilisation of computational intelligence techniques for stabilised soil. In: Papadrakakis M, Topping BHV (eds) Proceedings of the 6th international conference on engineering computational technology. Civil-Comp Press, Paper 175, Edinburgh, Scotland
Alavi AH, Gandomi AH (2009) Energy-based numerical correlations for soil liquefaction assessment. Comput Geotech. doi:10.1016/j.compgeo.2009.08.003
Miyauchi K, Nishibayashi S, Inoue S (1997) Estimation of strengthening effects with carbon fiber sheet for concrete column. In: Proceedings of the 3rd international symposium (FRPRCS-3) on non-metallic (FRP) reinforcement for concrete structures, vol 1. Sapporo, Japan, pp 217–224
Kono S, Inazumi M, Kaku T (1998) Evaluation of confining effects of CFRP sheets on reinforced concrete members. In: Proceedings of the 2nd international conference on composites in infrastructure ICCI’98, pp 343–355
Matthys S, Taerwe L, Audenaert K (1999) Tests on axially loaded concrete columns confined by fiber reinforced polymer sheet wrapping. In: Proceedings of the 4th international symposium on fiber reinforced polymer reinforcement for reinforced concrete structures, pp 217–228
Shahawy M, Mirmiran A, Beitelmann T (2000) Tests and modeling of carbon-wrapped concrete columns. Compos Part B Eng 31:471–480
Rochette P, Labossiere P (2000) Axial testing of rectangular column models confined with composites. J Compos Const ASCE 4(3):129–136
Micelli F, Myers JJ, Murthy S (2001) Effect of environmental cycles on concrete cylinders confined with FRP. In: Proceedings of the CCC international conference on composites in construction. Porto, Portugal
Rousakis T (2001) Experimental investigation of concrete cylinders confined by carbon FRP sheets, under monotonic and cyclic axial compressive load. Research Report. Chalmers University of Technology, Goteborg, Sweden
Fardis MN, Khalili H (1981) Concrete encased in fiberglass-reinforced plastic. ACI J 8(6):440–446
Mander JB, Priestley MJN, Park R (1988) Theoretical stress–strain model for confined concrete. J Struct Eng 114(8):1804–1849
Samaan M, Mirmiram A, Shahawy M (1998) Model of concrete confined by fiber composites. J Struct Eng 124(9):1025–1031
Lam L, Teng JG (2001) Strength models for circular concrete columns confined by FRP composites. In: Burgoyne CJ (ed) Proceedings of the international conference on fibre reinforced plastics for reinforced concrete structures. London, pp 835–844
Toutanji H (1999) Stress–strain characteristics of concrete columns externally confined with advanced fiber composite sheets. ACI Mater J 96(3):397–404
Saafi M, Toutanji HA, Li Z (1999) Behavior of concrete columns confined with fiber reinforced polymer tubes. ACI Mater J 96(4):500–509
Spoelstra MR, Monti G (1999) FRP-confined concrete model. J Compos Const 3(3):143–150
Karbhari VM, Gao Y (1997) Composite jacketed concrete under uniaxial compression verification of simple design equation. J Mater Civil Eng 9(4):185–193
Richart FE, Brandtzaeg A, Brown RL (1928) A study of the failure of concrete under combined compressive stresses. Bulletin No. 185, University of Illinois, Engineering Experimental Station, Urbana, IL
Berthet JF, Ferrier E, Hamelin P (2006) Compressive behavior of concrete externally confined by composite jackets, Part B: modeling. Construct Build Mater 20:338–347
Vintzileou E, Panagiotidou E (2008) An empirical model for predicting the mechanical properties of FRP-confined concrete. Construct Build Mater 22:841–854
Xiao Y, Wu H (2000) Compressive behavior of concrete confined by carbon fiber composite jackets. J Mater Civil Eng 12(2):139–146
Li Y, Lin C, Sung Y (2003) A constitutive model for concrete confined with carbon fiber reinforced plastics. Mech Mater 35:603–619
Cevik A, Guzelbey IH (2008) Neural network modeling of strength enhancement for CFRP confined concrete cylinders. Build Environ 43:751–763
Bäck T (1996) Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithms. Adv Complex Syst 14(4):1–29
Ashour AF, Alvarez LF, Toropov VV (2003) Empirical modelling of shear strength of RC deep beams by genetic programming. Comput Struct 81:331–338
Baykasoglu A, Dereli T, Tanıs S (2004) Prediction of cement strength using soft computing techniques. Cem Concr Res 34(4):2083–2090
Gesoglu M, Guneyisi E (2007) Prediction of load-carrying capacity by soft computing techniques. Mater Struct 40:939–951
Alavi AH, Gandomi AH, Sahab MG, Gandomi M (2009) Multi expression programming: a new approach to formulation of soil classification. Eng Comput. doi:10.1007/s00366-009-0140-7
Cevik A, Cabalar AF (2009) Modelling damping ratio and shear modulus of sand–mica mixtures using genetic programming. Expert Syst Appl 36(4):7749–7757
Brameier M, Kantschik W, Dittrich P, Banzhaf W (1998) SYSGP – A C++ library of different GP variants. Technical Report [CI-98/48]. Collaborative Research Center 531, University of Dortmund, Germany
Nordin PJ (1994) A compiling genetic programming system that directly manipulates the machine code (Chapter 14). In: Kenneth E, Kinnear Jr (ed) Proceedings of the international conference on advances in genetic programming. MIT Press, USA, pp 311–331
Gandomi AH, Alavi AH, Sadat Hosseini SS (2008) A discussion on “Genetic programming for retrieving missing information in wave records along the west coast of India”. Appl Ocean Res 30(4):338–339
Francone F (2004) Discipulus™ owner’s manual, version 4.0. Register Machine Learning Technologies
Feldt R, Nordin P (2000) Using factorial experiments to evaluate the effect of genetic programming parameters. Proceedings of the EuroGP 2000, LNCS 1802, pp 271–282
Francone F (2000) Discipulus™ owner’s manual, version 3.0. Register Machine Learning Technologies
Rousakis TC, Karabinis AI, Kiousis PD, Tepfers R (2008) Analytical modelling of plastic behaviour of uniformly FRP confined concrete members. Compos Part B 39(7–8):1104–1113
Park TW, Na UJ, Feng MQ (2008) Compressive behavior of concrete cylinders confined by narrow strips of CFRP with spacing. Compos Part B 39(7–8):1093–1103
Acknowledgment
The journal reviewers are thanked for their constructive comments that helped improve this paper.
Author information
Authors and Affiliations
Corresponding author
Appendix
Appendix
Details of the explicit formulation of the NN model for the determination of strength enhancement of CFRP wrapped concrete cylinders [31] (see Table 6):
Rights and permissions
About this article
Cite this article
Gandomi, A.H., Alavi, A.H. & Sahab, M.G. New formulation for compressive strength of CFRP confined concrete cylinders using linear genetic programming. Mater Struct 43, 963–983 (2010). https://doi.org/10.1617/s11527-009-9559-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1617/s11527-009-9559-y