Explainable machine learning and application-oriented tool for predicting effective hoop strain of fiber-reinforced polymer-confined concrete

Abstract

The reliable prediction of hoop strain of fiber-reinforced polymer (FRP)-confined concrete is crucial for assessing confinement efficiency and ensuring structural integrity. Existing empirical models often fall short as a result of idealized assumptions and limited generalizability across diverse materials and geometries. This study presents a novel, data-driven machine learning (ML) approach to estimate the effective hoop strain of FRP-confined circular concrete columns. A refined database comprising 309 experimental specimens, including Carbon, glass, and aramid FRPs, was used. Eight ML algorithms, encompassing both single (K-Nearest Neighbors, Kernel Ridge Regression, Support Vector Regression, Decision Tree) and ensemble (AdaBoost, Gradient Boosting Machine, Extreme Gradient Boosting, Random Forest) models, were trained and optimized using Optuna with 10-fold cross-validation. The top-performing models have coefficient of determination of greater than 95% as well as low residual variance and error on the full data set. Accordingly, SHapley Additive exPlanations were incorporated for global and local interpretability of the model predictions. The best-performing model was deployed in a user-friendly graphical interface, aiding an accurate and interpretable tool for practitioners. The proposed framework significantly outperforms conventional empirical models, offering a scalable solution for assessing hoop strain of FRP-confined concrete.

Graphical abstract

Keywords

column confinement / FRP confinement / hoop strain / ML / predictive modeling

References

[1] Wang Y F , Wu H L . Size effect of concrete short columns confined with aramid FRP jackets. Journal of Composites for Construction, 2011, 15(4): 535–544

[2] Wu Y F , Zhou Y W . Unified strength model based on hoek-brown failure criterion for circular and square concrete columns confined by FRP. Journal of Composites for Construction, 2010, 14(2): 175–184

[3] Wei Y Y , Wu Y F . Unified stress-strain model of concrete for FRP-confined columns. Construction and Building Materials, 2012, 26(1): 381–392

[4] Ilki A , Peker O , Karamuk E , Demir C , Kumbasar N . FRP retrofit of low and medium strength circular and rectangular reinforced concrete columns. Journal of Materials in Civil Engineering, 2008, 20(2): 169–188

[5] Wu Y F , Jiang C . Effect of load eccentricity on the stress-strain relationship of FRP-confined concrete columns. Composite Structures, 2013, 98: 228–241

[6] Lam L , Teng J G . Design-oriented stress-strain model for FRP-confined concrete in rectangular columns. Journal of Reinforced Plastics and Composites, 2003, 22(13): 1149–1186

[7] Wu Y F , Jiang C . Quantification of bond-slip relationship for externally bonded FRP-to-concrete joints. Journal of Composites for Construction, 2013, 17(5): 673–686

[8] Tijani I A , Jiang C , Lim C W , Wu Y F . Eccentrically loaded concrete under nonuniform passive confinement. Journal of Structural Engineering, 2022, 148(1): 04021247

[9] Tijani I A , Jiang C , Lim C W , Wu Y F . Effect of load eccentricity on the mechanical response of FRP-confined predamaged concrete under compression. Journal of Composites for Construction, 2020, 24(5): 04020057

[10] Lam L , Teng J G . Design-oriented stress–strain model for FRP-confined concrete. Construction and Building Materials, 2003, 17(6–7): 471–489

[11] Mohammadi M , Wu Y F . Triaxial test for concrete under non-uniform passive confinement. Construction and Building Materials, 2017, 138: 455–468

[12] Tijani I A , Wu Y F , Lim C W . Aggregate size effects and general static loading response on mechanical behavior of passively confined concrete. Construction and Building Materials, 2019, 205: 61–72

[13] Chen Y , Li P , Zhang S . Experimental investigation on triaxial mechanical properties of coral coarse aggregate-sea sand seawater concrete. Construction and Building Materials, 2023, 409: 134213

[14] Mander J B , Priestley M J N , Park R . Theoretical stress‐strain model for confined concrete. Journal of Structural Engineering, 1988, 114(8): 1804–1826

[15] Benzaid R , Mesbah H . FRP-confined concrete cylinders: Axial compression experiments and strength model. Journal of Reinforced Plastics and Composites, 2010, 29(16): 2469–2488

[16] Rousakis T C , Karabinis A I , Kiousis P D . FRP-confined concrete members: Axial compression experiments and plasticity modelling. Engineering Structures, 2007, 29(7): 1343–1353

[17] Silva Lobo P , Faustino P , Jesus M , Marreiros R . Design model of concrete for circular columns confined with AFRP. Composite Structures, 2018, 200: 69–78

[18] Toutanji H A , Han M , Gilbert J , Matthys S . Behavior of large-scale rectangular columns confined with FRP composites. Journal of Composites for Construction, 2010, 14(1): 62–71

[19] Vincent T , Ozbakkaloglu T . Influence of fiber orientation and specimen end condition on axial compressive behavior of FRP-confined concrete. Construction and Building Materials, 2013, 47: 814–826

[20] Lim J C , Ozbakkaloglu T . Design model for FRP-confined normal- and high-strength concrete square and rectangular columns. Magazine of Concrete Research, 2014, 66(20): 1020–1035

[21] Arabshahi A , Gharaei-Moghaddam N , Tavakkolizadeh M . Development of applicable design models for concrete columns confined with aramid fiber reinforced polymer using Multi-Expression Programming. Structures, 2020, 23: 225–244

[22] Silva Lobo P , Jesus M , Freitas P S A . Prediction of the failure strain of FRP sheets on confined concrete columns with circular cross-section. International Journal of Structural Integrity, 2023, 14(1): 19–43

[23] Eshaghi M S , Anitescu C , Thombre M , Wang Y , Zhuang X , Rabczuk T . Variational Physics-informed Neural Operator (VINO) for solving partial differential equations. Computer Methods in Applied Mechanics and Engineering, 2025, 437: 117785

[24] Es-haghi M S , Anitescu C , Rabczuk T . Methods for enabling real-time analysis in digital twins: A literature review. Computers and Structures, 2024, 297: 107342

[25] Liu B , Liu P , Wang Y , Li Z , Lv H , Lu W , Olofsson T , Rabczuk T . Explainable machine learning for multiscale thermal conductivity modeling in polymer nanocomposites with uncertainty quantification. Composite Structures, 2025, 370: 119292

[26] Liu B , Lu W , Olofsson T , Zhuang X , Rabczuk T . Stochastic interpretable machine learning based multiscale modeling in thermal conductivity of Polymeric graphene-enhanced composites. Composite Structures, 2024, 327: 117601

[27] Liu B , Vu-Bac N , Zhuang X , Fu X , Rabczuk T . Stochastic integrated machine learning based multiscale approach for the prediction of the thermal conductivity in carbon nanotube reinforced polymeric composites. Composites Science and Technology, 2022, 224: 109425

[28] Liu B , Vu-Bac N , Zhuang X , Fu X , Rabczuk T . Stochastic full-range multiscale modeling of thermal conductivity of Polymeric carbon nanotubes composites: A machine learning approach. Composite Structures, 2022, 289: 115393

[29] Liu B , Vu-Bac N , Rabczuk T . A stochastic multiscale method for the prediction of the thermal conductivity of Polymer nanocomposites through hybrid machine learning algorithms. Composite Structures, 2021, 273: 114269

[30] Liu B , Vu-Bac N , Zhuang X , Lu W , Fu X , Rabczuk T . Al-DeMat: A web-based expert system platform for computationally expensive models in materials design. Advances in Engineering Software, 2023, 176: 103398

[31] Zhou C , Wang W , Zheng Y . Data-driven shear capacity analysis of headed stud in steel-UHPC composite structures. Engineering Structures, 2024, 321: 118946

[32] Tang Y , Zhou C , Wang W , Zhang W , Cheng Y . Machine learning driven bond performance prediction between FRP bars and coral aggregate concrete. Construction and Building Materials, 2024, 442: 137684

[33] Zhou C , Xie Y , Wang W , Zheng Y . Machine learning driven post-impact damage state prediction for performance-based crashworthiness design of bridge piers. Engineering Structures, 2023, 292: 116539

[34] TijaniI ADaudaJ AKareemM ALawalA I. Genetic programming-based model for estimating maximum pull load of fiber-reinforced polymer-to-concrete bond interfaces with graphical user interface implementation. Structural Concrete, 2025

[35] Lam L , Teng J G . Ultimate condition of fiber reinforced polymer-confined concrete. Journal of Composites for Construction, 2004, 8(6): 539–548

[36] Lam L , Teng J G , Cheung C H , Xiao Y . FRP-confined concrete under axial cyclic compression. Cement and Concrete Composites, 2006, 28(10): 949–958

[37] Lee J Y , Yi C K , Jeong H S , Kim S W , Kim J K . Compressive response of concrete confined with steel spirals and FRP composites. Journal of Composite Materials, 2010, 44(4): 481–504

[38] Liang M , Wu Z M , Ueda T , Zheng J J , Akogbe R . Experiment and modeling on axial behavior of carbon fiber reinforced polymer confined concrete cylinders with different sizes. Journal of Reinforced Plastics and Composites, 2012, 31(6): 389–403

[39] KonoSInazumiMKakuT. Evaluation of confining effects of CFRP sheets on reinforced concrete members. In: Second International Conference on Composites in Infrastructure. Washington, D.C.: Transportation Research Board, 1998, 343–355

[40] Abbasnia R , Ziaadiny H . Experimental investigation and strength modeling of CFRP-confined concrete rectangular prisms under axial monotonic compression. Materials and Structures, 2015, 48(1–2): 485–500

[41] Al-Salloum Y A . Influence of edge sharpness on the strength of square concrete columns confined with FRP composite laminates. Composites Part B: Engineering, 2007, 38(5–6): 640–650

[42] BulloS. Experimental study of the effects of the ultimate strain of fiber reinforced plastic jackets on the behavior of confined concrete. In: International Conference on Composite Construction. Cosenza, Italy: University of Calabria, 2003, 465–470

[43] Cui C , Sheikh S A . Experimental study of normal- and high-strength concrete confined with fiber-reinforced polymers. Journal of Composites for Construction, 2010, 14(5): 553–561

[44] Eid R , Roy N , Paultre P . Normal- and high-strength concrete circular elements wrapped with FRP composites. Journal of Composites for Construction, 2009, 13(2): 113–124

[45] Micelli F , Modarelli R . Experimental and analytical study on properties affecting the behaviour of FRP-confined concrete. Composites Part B: Engineering, 2013, 45(1): 1420–1431

[46] Elsanadedy H M , Al-Salloum Y A , Alsayed S H , Iqbal R A . Experimental and numerical investigation of size effects in FRP-wrapped concrete columns. Construction and Building Materials, 2012, 29: 56–72

[47] Harries K A , Carey S A . Shape and “gap” effects on the behavior of variably confined concrete. Cement and Concrete Research, 2003, 33(6): 881–890

[48] Saenz N , Pantelides C P . Short and medium term durability evaluation of FRP-confined circular concrete. Journal of Composites for Construction, 2006, 10(3): 244–253

[49] Shahawy M , Mirmiran A , Beitelman T . Tests and modeling of carbon-wrapped concrete columns. Composites Part B: Engineering, 2000, 31(6–7): 471–480

[50] Tamuzs V , Valdmanis V , Tepfers R , Gylltoft K . Stability analysis of CFRP-wrapped concrete columns strengthened with external longitudinal CFRP sheets. Mechanics of Composite Materials, 2008, 44(3): 199–208

[51] Toutanji H A . Stress-strain characteristics of concrete columns externally confined with advanced fiber composite sheets. ACI Materials Journal, 1999, 96(3): 397–404

[52] Wu G , Wu Z S , Lu Z T , Ando Y B . Structural Performance of Concrete Confined with Hybrid FRP Composites. Journal of Reinforced Plastics and Composites, 2008, 27(12): 1323–1348

[53] Valdmanis V , De Lorenzis L , Rousakis T , Tepfers R . Behaviour and capacity of CFRP-confined concrete cylinders subjected to monotonic and cyclic axial compressive load. Structural Concrete, 2007, 8(4): 187–200

[54] Wang L M , Wu Y F . Effect of corner radius on the performance of CFRP-confined square concrete columns. Engineering Structures, 2008, 30(2): 493–505

[55] Watanabe K , Nakamura H , Honda Y , Toyoshima M , Iso M , Fujimaki T , Kaneto M , Shirai N . Confinement effect of FRP sheet on strength and ductility of concrete cylinders under uniaxial compression. In: Third International Symposium on Non-Metallic (FRP) Reinforcement for Concrete Structures. Sapporo, Japan: Japan Society of Civil Engineers, 1997, 1: 233–240

[56] RousakisTTepfersR. Experimental investigation of concrete cylinders confined by carbon FRP sheets, under monotonic and cyclic axial compressive load. KTH Technical Report KTH-R-01-44. 2001

[57] Shehata I A E M , Carneiro L A V , Shehata L C D . Strength of short concrete columns confined with CFRP sheets. Materials and Structures, 2002, 35(1): 50–58

[58] Song X , Gu X , Li Y , Chen T , Zhang W . Mechanical behavior of FRP-strengthened concrete columns subjected to concentric and eccentric compression loading. Journal of Composites for Construction, 2013, 17(3): 336–346

[59] Xiao Y , Wu H . Compressive behavior of concrete confined by carbon fiber composite jackets. Journal of Materials in Civil Engineering, 2000, 12(2): 139–146

[60] Aire C , Gettu R , Casas J R . Study of the compressive behavior of concrete confined by fiber reinforced composites. Journal of Composites for Construction, 2001, 5(4): 239–243

[61] Harries K A , Kharel G . Behavior and modeling of concrete subject to variable confining pressure. ACI Materials Journal, 2002, 99: 180–189

[62] Silva M A G , Rodrigues C C . Size and relative stiffness effects on compressive failure of concrete columns wrapped with glass FRP. Journal of Materials in Civil Engineering, 2006, 18(3): 334–342

[63] Dai J G , Bai Y L , Teng J G . Behavior and modeling of concrete confined with FRP composites of large deformability. Journal of Composites for Construction, 2011, 15(6): 963–973

[64] Rochette P , Labossière P . Axial testing of rectangular column models confined with composites. Journal of Composites for Construction, 2000, 4(3): 129–136

[65] Toutanji H , Deng Y . Strength and durability performance of concrete axially loaded members confined with AFRP composite sheets. Composites Part B: Engineering, 2002, 33(4): 255–261

[66] Vincent T , Ozbakkaloglu T . Influence of concrete strength and confinement method on axial compressive behavior of FRP confined high- and ultra high-strength concrete. Composites Part B: Engineering, 2013, 50: 413–428

[67] PicherFRochettePLabossiereP. Confinement of concrete cylinders with CFRP. In: 1st International Conference on Composites in Infrastructures, ICCI’96. Tucson, Arizona: American Concrete Institute, 1996, 829–841

[68] ParrettiRNanniA. Axial testing of concrete columns confined with carbon FRP: Effect of fiber orientation. In: 2nd International Conference on Composites in Infrastructures, ICCI. Tucson, Arizona: American Concrete Institute, 2002: 1–10

[69] Ozbakkaloglu T , Akin E . Behavior of FRP-confined normal- and high-strength concrete under cyclic axial compression. Journal of Composites for Construction, 2012, 16(4): 451–463

[70] Micelli F , Myers J J . Durability of FRP-confined concrete. Proceedings of the Institution of Civil Engineers—Construction Materials, 2008, 161(4): 173–185

[71] Berthet J F , Ferrier E , Hamelin P . Compressive behavior of concrete externally confined by composite jackets: Part B: Modeling. Construction and Building Materials, 2006, 20(5): 338–347

[72] Matthys S , Taerwe L , Audenaert K . Tests on axially loaded concrete columns confined by fiber reinforced polymer sheet wrapping. Special Publication, 1999, 188: 217–228

[73] Wu Y F , Jiang J F . Effective strain of FRP for confined circular concrete columns. Composite Structures, 2013, 95: 479–491

[74] HastieTTibshiraniRFriedmanJ. The Elements of Statistical Learning. New York: Springer, 2009

[75] Evgeniou T , Pontil M , Poggio T . Regularization Networks and Support Vector Machines. Advances in Computational Mathematics, 2000, 13(1): 1–50

[76] Cortes C , Vapnik V . Support-vector networks. Machine Learning, 1995, 20(3): 273–297

[77] Freund Y , Schapire R E . A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences, 1997, 55(1): 119–139

[78] ChenTGuestrinC. XGBoost: A scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, California: Association for Computing Machinery, 2016, 13–17

[79] KeGMengQFinleyTWangTChenWMaWYeQLiuT. LightGBM: A highly efficient gradient boosting decision tree. In: Advances in Neural Information Processing Systems. Long Beach, California: Neural Information Processing Systems Foundation, 2017

[80] Lundberg S M , Lee S I . A unified approach to interpreting model predictions. Advances in Neural Information Processing Systems, 2017, 30: 4766–4775

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