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New formulation for compressive strength of CFRP confined concrete cylinders using linear genetic programming

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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.

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Acknowledgment

The journal reviewers are thanked for their constructive comments that helped improve this paper.

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Correspondence to Amir Hossein Gandomi.

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):

$$ \begin{aligned} f_{{cc,{\text{NN}}}}^{\prime } ({\text{MPa}}) &\;=\;150 \times \left( {{\frac{2}{{1 + e^{ - 2W} }}}\; - 1} \right) \\ W &\;=\;0.63 \times \left( {{\frac{2}{{1 + e^{{ - 2U_{1} }} }}}\; - 1} \right)\;+\;0.74\;\times\;\left( {{\frac{2}{{1 + e^{{ - 2U_{2} }} }}}\; - 1} \right)\;-\;3.16\;\times\;\left( {{\frac{2}{{1 + e^{{ - 2U_{3} }} }}} \;- 1} \right)\;-\;2.62\;\times\;\left( {{\frac{2}{{1 + e^{{ - 2U_{4} }} }}} \;- 1} \right) \\ & \quad\;-\;0.68\;\times\;\left( {{\frac{2}{{1 + e^{{ - 2U_{5} }} }}} \;- 1} \right)\;+\;1.16\;\times\;\left( {{\frac{2}{{1 + e^{{ - 2U_{6} }} }}} \;- 1} \right)\;-\;1.36\;\times\;\left( {{\frac{2}{{1 + e^{{ - 2U_{7} }} }}} \;- 1} \right)\;+\;0.61\;\times\;\left( {{\frac{2}{{1 + e^{{ - 2U_{8} }} }}} \;- 1} \right) \\ & \quad\;+\;0.83\;\times\;\left( {{\frac{2}{{1 + e^{{ - 2U_{9} }} }}} \;- 1} \right)\;-\;0.52\;\times\;\left( {{\frac{2}{{1 + e^{{ - 2U_{10} }} }}} \;- 1} \right)\;-\;0.61\;\times\;\left( {{\frac{2}{{1 + e^{{ - 2U_{11} }} }}} \;- 1} \right)\;-\;2.57\;\times\;\left( {{\frac{2}{{1 + e^{{ - 2U_{12} }} }}} \;- 1} \right) \\ & \quad\;+\;1.60\;\times\;\left( {{\frac{2}{{1 + e^{{ - 2U_{13} }} }}} \;- 1} \right)\;+\;1.84\;\times\;\left( {{\frac{2}{{1 + e^{{ - 2U_{14} }} }}} \;- 1} \right)\;-\;3.77\;\times\;\left( {{\frac{2}{{1 + e^{{ - 2U_{15} }} }}} \;- 1} \right)\;+\;0.25 \\ \end{aligned} $$
$$ \begin{aligned} U_{1} & = (0.024 \times D) + (0.59 \times t) + (0.0004 \times E_{f} ) + (0.037 \times f_{co}^{\prime } ) + 14.02 \\ U_{2} & = (0.0217 \times D) + (1.56 \times t) + ( - 0.0003 \times E_{f} ) + (0.0346 \times f_{co}^{\prime } ) + 4.42 \\ U_{3} & = ( - 0.07 \times D) + ( - 0.1 \times t) + ( - 0.00013 \times E_{f} ) + (0.073 \times f^{\prime}_{co} ) + 16.12 \\ U_{4} & = (0.058 \times D) + ( - 0.96 \times t) + ( - 0.0028 \times E_{f} ) + ( - 0.041 \times f_{co}^{\prime } ) + 1.42 \\ U_{5} & = (0.061 \times D) + ( - 0.138 \times t) + ( - 0.0006 \times E_{f} ) + ( - 0.06 \times f_{co}^{\prime } ) - 4.02 \\ U_{6} & = ( - 0.0639 \times D) + ( - 0.6017 \times t) + ( - 0.0014 \times E_{f} ) + ( - 0.0327 \times f_{co}^{\prime } ) + 15.32 \\ U_{7} & = ( - 0.0365 \times D) + ( - 0.4598 \times t) + (0.0004 \times E_{f} ) + (0.0691 \times f^{\prime}_{co} ) + 2.07 \\ U_{8} & = ( - 0.0684 \times D) + (0.1734 \times t) + (0.0006 \times E_{f} ) + ( - 0.0381 \times f_{co}^{\prime } ) + 9.33 \\ U_{9} & = (0.044 \times D) + (0.2966 \times t) + (0.0008 \times E_{f} ) + (0.0736 \times f_{co}^{\prime } ) - 6.82 \\ U_{10} & = (0.0559 \times D) + (1.3957 \times t) + (0.0004 \times E_{f} ) + (0.016 \times f_{co}^{\prime } ) - 10.58 \\ U_{11} & = (0.0434 \times D) + ( - 0.7968 \times t) + (0.0014 \times E_{f} ) + ( - 0.0164 \times f_{co}^{\prime } ) + 3.41 \\ U_{12} & = ( - 0.0309 \times D) + ( - 1.0127 \times t) + ( - 0.0014 \times E_{f} ) + ( - 0.0326 \times f_{co}^{\prime } ) + 6.09 \\ U_{13} & = ( - 0.0638 \times D) + (0.7750 \times t) + (0.0003 \times E_{f} ) + (0.0633 \times f_{co}^{\prime } ) + 1.34 \\ U_{14} & = (0.092 \times D) + ( - 0.6339 \times t) + (0.0007 \times E_{f} ) + ( - 0.0032 \times f_{co}^{\prime } ) - 2.86 \\ U_{15} & = ( - 0.0288 \times D) + ( - 0.1202 \times t) + (0.0028 \times E_{f} ) + (0.0137 \times f_{co}^{\prime } ) - 5.91 \\ \end{aligned} $$
Table 6 Experimental database and comparative analysis of experimental and other models results

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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

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