Concrete Ultimate Strain Wrapped by Aramid Fiber-Reinforced Polymer: Application of Regression Analysis

Jingli WEN

doi:10.56748/ejse.24775

Authors

Jingli WEN Chongqing Technology and Business Institute

DOI:

https://doi.org/10.56748/ejse.24775

Keywords:

Aramid Fiber, Polymers, Concrete, Ultimate Strain, Least Square, Support Vector Regression, Feature Selection

Abstract

Concrete confinement using fiber-reinforced polymer (FRP) jackets is widely employed in structural retrofitting. A number of machine learning (ML) algorithms using tree-based methodologies were developed to forecast the ultimate strain (ε_cu) of circular columns wrapped in aramid fiber-reinforced polymer (AFRP). Hyperparameters are optimized using Artificial Hummingbird Optimizer (AHO) and Giant Trevally Optimizer (GTO) with least square support vector regression (LSSVR), leveraging AFRP-made concrete data from earlier studies to establish a suitable dataset. The AFRP jacket's total thickness (t_f), elastic modulus (E_f), ultimate tensile strength (f_f), the height of the column (L), unconfined compressive strength (f_co), and specimen diameter (d) are the input variables used in this approach. LSSVR(A) got the smallest uncertainty values (0.2893 and 0.2261) in training and evaluation. The values obtained during learning and evaluation were lower than LSSVR(G)'s 0.323 and 0.2476. The variation percentage between the two models for these measures, that is, at least 7% and sometimes 36%, depending on the variance percentage that was employed, shows the accuracy and reliability of the LSSVR(G). Regarding index values, throughout the training and assessment stages, the achieved values of 0.0676 and 0.0559, respectively, while the received the smallest values of 0.0591 and 0.0434.

Downloads

Download data is not yet available.

References

Abdel-Basset, M., Mohamed, R., Hezam, I. M., Sallam, K. M., & Hameed, I. A. (2024). An Efficient Binary Hybrid Equilibrium Algorithm for Binary Optimization Problems: Analysis, Validation, and Case Studies. International Journal of Computational Intelligence Systems, 17(1), 98. DOI: https://doi.org/10.1007/s44196-024-00458-z

Afkhami Hoor, S., & Esmaeili-Falak, M. (2024). Innovative Approaches for Mitigating Soil Liquefaction: A State-of-the-Art Review of Techniques and Bibliometric Analysis. Indian Geotechnical Journal. DOI: https://doi.org/10.1007/s40098-024-01120-3

Aghayari Hir, M., Zaheri, M., & Rahimzadeh, N. (2023). Prediction of rural travel demand by spatial regression and artificial neural network methods (Tabriz County). Journal of Transportation Research (Tehran), 20(4), 367–386.

Ahmad, A., Ahmad, W., Aslam, F., & Joyklad, P. (2022). Compressive strength prediction of fly ash-based geopolymer concrete via advanced machine learning techniques. Case Studies in Construction Materials, 16, e00840. DOI: https://doi.org/10.1016/j.cscm.2021.e00840

Ahmad, A., Chaiyasarn, K., Farooq, F., Ahmad, W., Suparp, S., & Aslam, F. (2021). Compressive strength prediction via gene expression programming (GEP) and artificial neural network (ANN) for concrete containing RCA. Buildings, 11(8), 324. DOI: https://doi.org/10.3390/buildings11080324

Amin, M. N., Ahmad, A., Khan, K., Ahmad, W., Nazar, S., Faraz, M. I., & Alabdullah, A. A. (2022). Split tensile strength prediction of recycled aggregate-based sustainable concrete using artificial intelligence methods. Materials, 15(12), 4296. DOI: https://doi.org/10.3390/ma15124296

Arabshahi, A., Gharaei Moghaddam, N., & Tavakkolizadeh, M. (2015). Proposed slenderness limit for FRP circular concrete column. Third Conference on Smart Monitoring, Assessment and Rehabilitation of Civil Structures, Antalya, Turkey.

Arabshahi, A., Gharaei-Moghaddam, N., & Tavakkolizadeh, M. (2020). Development of applicable design models for concrete columns confined with aramid fiber reinforced polymer using Multi-Expression Programming. Structures, 23, 225–244. DOI: https://doi.org/10.1016/j.istruc.2019.09.019

Babak, A., Shayan, R., P, S. M., Navid, C., S, F. A., & Mazdak, T. (2024). Cold-Formed Cross-Sectional Folds with Optimal Signature Curve. Journal of Engineering Mechanics, 150(8), 04024045. DOI: https://doi.org/10.1061/JENMDT.EMENG-7708

Bagherabad, M. B., Rivandi, E., & Mehr, M. J. (2025). Machine Learning for Analyzing Effects of Various Factors on Business Economic. Authorea Preprints. DOI: https://doi.org/10.36227/techrxiv.174429010.09842200/v1

Bemani, A., Xiong, Q., Baghban, A., Habibzadeh, S., Mohammadi, A. H., & Doranehgard, M. H. (2020). Modeling of cetane number of biodiesel from fatty acid methyl ester (FAME) information using GA-, PSO-, and HGAPSO-LSSVM models. Renewable Energy, 150, 924–934. DOI: https://doi.org/10.1016/j.renene.2019.12.086

Benemaran, R. S. (2023). Application of extreme gradient boosting method for evaluating the properties of episodic failure of borehole breakout. Geoenergy Science and Engineering, 226, 211837. DOI: https://doi.org/10.1016/j.geoen.2023.211837

Bennett, C. A. (2022). Principles of physical optics. John Wiley & Sons.

Cakiroglu, C. (2023). Explainable data-driven ensemble learning models for the mechanical properties prediction of concrete confined by aramid fiber-reinforced polymer wraps using generative adversarial networks. Applied Sciences, 13(21), 11991. DOI: https://doi.org/10.3390/app132111991

Chastre, C., & Silva, M. A. G. (2010). Monotonic axial behavior and modelling of RC circular columns confined with CFRP. Engineering Structures, 32(8), 2268–2277. DOI: https://doi.org/10.1016/j.engstruct.2010.04.001

Cheek, J., Formichella, N., Graetz, D., & Varasteh, S. (2011). The behaviour of ultra high strength concrete in FRP confined concrete systems under axial compression. Honours Bachelor’s Thesis, School of Civil, Environmental and Mining Engineering, Univ. of Adelaide, Adelaide, Australia.

Dai, J.-G., Bai, Y.-L., & Teng, J. G. (2011). Behavior and modeling of concrete confined with FRP composites of large deformability. Journal of Composites for Construction, 15(6), 963–973. DOI: https://doi.org/10.1061/(ASCE)CC.1943-5614.0000230

Dawei, Y., Bing, Z., Bingbing, G., Xibo, G., & Razzaghzadeh, B. (2023). Predicting the CPT-based pile set-up parameters using HHO-RF and PSO-RF hybrid models. Structural Engineering and Mechanics, An Int’l Journal, 86(5), 673–686.

Djafar-Henni, I., & Kassoul, A. (2018). Stress–strain model of confined concrete with Aramid FRP wraps. Construction and Building Materials, 186, 1016–1030. DOI: https://doi.org/10.1016/j.conbuildmat.2018.08.013

Ebrahim, H., & Mahzad, E.-F. (2024). Soil–Structure Interaction for Buried Conduits Influenced by the Coupled Effect of the Protective Layer and Trench Installation. Journal of Pipeline Systems Engineering and Practice, 15(2), 04024012. DOI: https://doi.org/10.1061/JPSEA2.PSENG-1547

Elsanadedy, H. M., Al-Salloum, Y. A., Alsayed, S. H., & Iqbal, R. A. (2012). Experimental and numerical investigation of size effects in FRP-wrapped concrete columns. Construction and Building Materials, 29, 56–72. DOI: https://doi.org/10.1016/j.conbuildmat.2011.10.025

Esmaeili-Falak, M., & Benemaran, R. S. (2024). Ensemble Extreme Gradient Boosting based models to predict the bearing capacity of micropile group. Applied Ocean Research, 151, 104149. DOI: https://doi.org/10.1016/j.apor.2024.104149

Esmaeili-Falak, M., Katebi, H., Vadiati, M., & Adamowski, J. (2019). Predicting triaxial compressive strength and Young’s modulus of frozen sand using artificial intelligence methods. Journal of Cold Regions Engineering, 33(3), 04019007. DOI: https://doi.org/10.1061/(ASCE)CR.1943-5495.0000188

Esmaeili‐Falak, M., & Sarkhani Benemaran, R. (2024). Application of optimization‐based regression analysis for evaluation of frost durability of recycled aggregate concrete. Structural Concrete, 25(1), 716–737. DOI: https://doi.org/10.1002/suco.202300566

Fardis, M. N., & Khalili, H. H. (1982). FRP-encased concrete as a structural material. Magazine of Concrete Research, 34(121), 191–202. DOI: https://doi.org/10.1680/macr.1982.34.121.191

Faustino, P., Chastre, C., & Paula, R. (2014). Design model for square RC columns under compression confined with CFRP. Composites Part B: Engineering, 57, 187–198. DOI: https://doi.org/10.1016/j.compositesb.2013.09.052

Gharaei-Moghaddam, N., Arabshahi, A., & Tavakkolizadeh, M. (2023). Predictive models for the peak stress and ultimate strain of FRP confined concrete cylinders with inclined fiber orientations. Results in Engineering, 18, 101044. DOI: https://doi.org/10.1016/j.rineng.2023.101044

Hadi, M. N. S., Khan, Q. S., & Sheikh, M. N. (2016). Axial and flexural behavior of unreinforced and FRP bar reinforced circular concrete filled FRP tube columns. Construction and Building Materials, 122, 43–53. DOI: https://doi.org/10.1016/j.conbuildmat.2016.06.044

Jiang, T., & Teng, J. G. (2007). Analysis-oriented stress–strain models for FRP–confined concrete. Engineering Structures, 29(11), 2968–2986. DOI: https://doi.org/10.1016/j.engstruct.2007.01.010

Jiang, T., & Teng, J. G. (2012). Theoretical model for slender FRP-confined circular RC columns. Construction and Building Materials, 32, 66–76. DOI: https://doi.org/10.1016/j.conbuildmat.2010.11.109

Khorasani, A. M. M., Esfahani, M. R., & Sabzi, J. (2019). The effect of transverse and flexural reinforcement on deflection and cracking of GFRP bar reinforced concrete beams. Composites Part B: Engineering, 161, 530–546. DOI: https://doi.org/10.1016/j.compositesb.2018.12.127

Kou, H., Quan, J., Guo, S., & Hassankhani, E. (2024). Light and normal weight concretes shear strength estimation using tree-based tunned frameworks. Construction and Building Materials, 452, 138955. DOI: https://doi.org/10.1016/j.conbuildmat.2024.138955

Kumarawadu, H., Weerasinghe, P., & Perera, J. S. (2024). Evaluating the Performance of Ensemble Machine Learning Algorithms over Traditional Machine Learning Algorithms for Predicting Fire Resistance in FRP Strengthened Concrete Beams. Electronic Journal of Structural Engineering, 24(3), 47–53. DOI: https://doi.org/10.56748/ejse.24661

Lam, L., & Teng, J. G. (2003). Design-oriented stress–strain model for FRP-confined concrete. Construction and Building Materials, 17(6–7), 471–489. DOI: https://doi.org/10.1016/S0950-0618(03)00045-X

Leung, H. Y., & Burgoyne, C. J. (2001). Compressive behaviour of concrete confined by aramid fibre spirals. In Structural Engineering, Mechanics and Computation (pp. 1357–1364). Elsevier. DOI: https://doi.org/10.1016/B978-008043948-8/50151-X

Li, D., Zhang, X., Kang, Q., & Tavakkol, E. (2023). Estimation of unconfined compressive strength of marine clay modified with recycled tiles using hybridized extreme gradient boosting method. Construction and Building Materials, 393, 131992. DOI: https://doi.org/10.1016/j.conbuildmat.2023.131992

Liang, R., & Bayrami, B. (2023). Estimation of frost durability of recycled aggregate concrete by hybridized Random Forests algorithms. Steel and Composite Structures, 49(1), 91–107.

Lim, J. C., & Ozbakkaloglu, T. (2015). Hoop strains in FRP-confined concrete columns: experimental observations. Materials and Structures, 48, 2839–2854. DOI: https://doi.org/10.1617/s11527-014-0358-8

Lobo, P. S., Faustino, P., Jesus, M., & Marreiros, R. (2018). Design model of concrete for circular columns confined with AFRP. Composite Structures, 200, 69–78. DOI: https://doi.org/10.1016/j.compstruct.2018.05.094

Muzata, T. S., Matuana, L. M., & Rabnawaz, M. (2024). Challenges in the mechanical recycling and upcycling of mixed postconsumer recovered plastics (PCR): A review. Current Research in Green and Sustainable Chemistry, 100407. DOI: https://doi.org/10.1016/j.crgsc.2024.100407

NadimiShahraki, K., & Reisi, M. (2020). Stress-strain based method for analysis and design of FRP wrapped reinforced concrete columns. Structures, 28, 1818–1830. DOI: https://doi.org/10.1016/j.istruc.2020.10.002

Nanni, A., & Bradford, N. M. (1995). FRP jacketed concrete under uniaxial compression. Construction and Building Materials, 9(2), 115–124. DOI: https://doi.org/10.1016/0950-0618(95)00004-Y

Nguyen, H. D., Choi, E., & Park, K. (2018). Dilation behavior of normal strength concrete confined by FRP wire jackets. Construction and Building Materials, 190, 728–739. DOI: https://doi.org/10.1016/j.conbuildmat.2018.09.081

Ozbakkaloglu, T. (2013). Compressive behavior of concrete-filled FRP tube columns: Assessment of critical column parameters. Engineering Structures, 51, 188–199. DOI: https://doi.org/10.1016/j.engstruct.2013.01.017

Ozbakkaloglu, T., & Akin, E. (2012). Behavior of FRP-confined normal-and high-strength concrete under cyclic axial compression. Journal of Composites for Construction, 16(4), 451–463. DOI: https://doi.org/10.1061/(ASCE)CC.1943-5614.0000273

Ozbakkaloglu, T., & Vincent, T. (2014). Axial compressive behavior of circular high-strength concrete-filled FRP tubes. Journal of Composites for Construction, 18(2), 04013037. DOI: https://doi.org/10.1061/(ASCE)CC.1943-5614.0000410

Pham, T. M., & Hadi, M. N. S. (2014). Confinement model for FRP confined normal-and high-strength concrete circular columns. Construction and Building Materials, 69, 83–90. DOI: https://doi.org/10.1016/j.conbuildmat.2014.06.036

Pham, T. M., & Hao, H. (2016). Review of concrete structures strengthened with FRP against impact loading. Structures, 7, 59–70. DOI: https://doi.org/10.1016/j.istruc.2016.05.003

Pour, A. F., Ozbakkaloglu, T., & Vincent, T. (2018). Simplified design-oriented axial stress-strain model for FRP-confined normal-and high-strength concrete. Engineering Structures, 175, 501–516. DOI: https://doi.org/10.1016/j.engstruct.2018.07.099

Reglero Ruiz, J. A., Trigo-López, M., García, F. C., & García, J. M. (2017). Functional aromatic polyamides. Polymers, 9(9), 414. DOI: https://doi.org/10.3390/polym9090414

Rivandi, E., & Jamili Oskouie, R. (2024). A Novel Approach for Developing Intrusion Detection Systems in Mobile Social Networks. Available at SSRN 5174811. DOI: https://doi.org/10.2139/ssrn.5174811

Rochette, P., & Labossiere, P. (2000). Axial testing of rectangular column models confined with composites. Journal of Composites for Construction, 4(3), 129–136. DOI: https://doi.org/10.1061/(ASCE)1090-0268(2000)4:3(129)

Rong, C., & Shi, Q. (2018). Axial-strength model for FRP-confined concrete based on the improved twin shear strength theory. Composite Structures, 202, 102–110. DOI: https://doi.org/10.1016/j.compstruct.2017.12.020

Rousakis, T. C., Karabinis, A. I., Kiousis, P. D., & Tepfers, R. (2008). Analytical modelling of plastic behaviour of uniformly FRP confined concrete members. Composites Part B: Engineering, 39(7–8), 1104–1113. DOI: https://doi.org/10.1016/j.compositesb.2008.05.001

Rousakis, T. C., Rakitzis, T. D., & Karabinis, A. I. (2012). Design-oriented strength model for FRP-confined concrete members. Journal of Composites for Construction, 16(6), 615–625. DOI: https://doi.org/10.1061/(ASCE)CC.1943-5614.0000295

Saadatmanesh, H., Ehsani, M. R., & Li, M.-W. (1994). Strength and ductility of concrete columns externally reinforced with fiber composite straps. Structural Journal, 91(4), 434–447. DOI: https://doi.org/10.14359/4151

Sabzi, J., & Esfahani, M. R. (2018). Effects of tensile steel bars arrangement on concrete cover separation of RC beams strengthened by CFRP sheets. Construction and Building Materials, 162, 470–479. DOI: https://doi.org/10.1016/j.conbuildmat.2017.12.053

Sadeeq, H. T., & Abdulazeez, A. M. (2022). Giant trevally optimizer (GTO): A novel metaheuristic algorithm for global optimization and challenging engineering problems. Ieee Access, 10, 121615–121640. DOI: https://doi.org/10.1109/ACCESS.2022.3223388

Sadeghian, P., & Fam, A. (2015). Improved design-oriented confinement models for FRP-wrapped concrete cylinders based on statistical analyses. Engineering Structures, 87, 162–182. DOI: https://doi.org/10.1016/j.engstruct.2015.01.024

Shaikh, F. U. A., & Alishahi, R. (2019). Behaviour of CFRP wrapped RC square columns under eccentric compressive loading. Structures, 20, 309–323. DOI: https://doi.org/10.1016/j.istruc.2019.04.012

Shang, L., Isleem, H. F., Almoghayer, W. J. K., & Khishe, M. (2025). Prediction of ultimate strength and strain in FRP wrapped oval shaped concrete columns using machine learning. Scientific Reports, 15(1), 10724. DOI: https://doi.org/10.1038/s41598-025-95272-8

Shang, M., Li, H., Ahmad, A., Ahmad, W., Ostrowski, K. A., Aslam, F., Joyklad, P., & Majka, T. M. (2022). Predicting the mechanical properties of RCA-based concrete using supervised machine learning algorithms. Materials, 15(2), 647. DOI: https://doi.org/10.3390/ma15020647

Siddiqui, N. A., Alsayed, S. H., Al-Salloum, Y. A., Iqbal, R. A., & Abbas, H. (2014). Experimental investigation of slender circular RC columns strengthened with FRP composites. Construction and Building Materials, 69, 323–334. DOI: https://doi.org/10.1016/j.conbuildmat.2014.07.053

Silva, M. A. G. (2011). Behavior of square and circular columns strengthened with aramidic or carbon fibers. Construction and Building Materials, 25(8), 3222–3228. DOI: https://doi.org/10.1016/j.conbuildmat.2011.03.007

Stylianidis, P. M., & Petrou, M. F. (2019). Study of the flexural behaviour of FRP-strengthened steel-concrete composite beams. Structures, 22, 124–138. DOI: https://doi.org/10.1016/j.istruc.2019.07.012

Sun, X., Dong, X., Teng, W., Wang, L., & Hassankhani, E. (2024). Creation of regression analysis for estimation of carbon fiber reinforced polymer-steel bond strength. Steel and Composite Structures, 51(5), 509–527.

Suter, R., & Pinzelli, R. (2001). Confinement of concrete columns with FRP sheets. Proc., 5th Int. Conf. on Fibre Reinforced Plastics for Reinforced Concrete Structures, 793–802.

Suykens, J. A. K., & Vandewalle, J. (1999). Least squares support vector machine classifiers. Neural Processing Letters, 9, 293–300. DOI: https://doi.org/10.1023/A:1018628609742

Teng, J. G., Huang, Y. L., Lam, L., & Ye, L. P. (2007). Theoretical model for fiber-reinforced polymer-confined concrete. Journal of Composites for Construction, 11(2), 201–210. DOI: https://doi.org/10.1061/(ASCE)1090-0268(2007)11:2(201)

Tian, Z. (2020). Short-term wind speed prediction based on LMD and improved FA optimized combined kernel function LSSVM. Engineering Applications of Artificial Intelligence, 91, 103573. DOI: https://doi.org/10.1016/j.engappai.2020.103573

Toutanji, H., & Deng, Y. (2002). Strength and durability performance of concrete axially loaded members confined with AFRP composite sheets. Composites Part B: Engineering, 33(4), 255–261. DOI: https://doi.org/10.1016/S1359-8368(02)00016-1

Vincent, T., & Ozbakkaloglu, T. (2013). Influence of fiber orientation and specimen end condition on axial compressive behavior of FRP-confined concrete. Construction and Building Materials, 47, 814–826. DOI: https://doi.org/10.1016/j.conbuildmat.2013.05.085

Wang, W., Sheikh, M. N., Al-Baali, A. Q., & Hadi, M. N. S. (2018). Compressive behaviour of partially FRP confined concrete: Experimental observations and assessment of the stress-strain models. Construction and Building Materials, 192, 785–797. DOI: https://doi.org/10.1016/j.conbuildmat.2018.10.105

Wang, Y., & Wu, H. (2010). Experimental investigation on square high-strength concrete short columns confined with AFRP sheets. Journal of Composites for Construction, 14(3), 346–351. DOI: https://doi.org/10.1061/(ASCE)CC.1943-5614.0000090

Wang, Y., & Wu, H. (2011). Size effect of concrete short columns confined with aramid FRP jackets. Journal of Composites for Construction, 15(4), 535–544. DOI: https://doi.org/10.1061/(ASCE)CC.1943-5614.0000178

Wang, Y., & Zhang, D. (2009). Creep-effect on mechanical behavior of concrete confined by FRP under axial compression. Journal of Engineering Mechanics, 135(11), 1315–1322. DOI: https://doi.org/10.1061/(ASCE)0733-9399(2009)135:11(1315)

Watanabe, K., Nakamura, H., Honda, Y., Toyoshima, M., Iso, M., Fujimaki, T., Kaneto, M., & Shirai, N. (1997). Confinement effect of FRP sheet on strength and ductility of concrete cylinders under uniaxial compression. Proc., 3rd Int. Symp. on Non-Metallic (FRP) Reinforcement for Concrete Structures, 1, 233–240.

Wu, G., Wu, Z. S., Lu, Z. T., & Ando, Y. B. (2008). Structural performance of concrete confined with hybrid FRP composites. Journal of Reinforced Plastics and Composites, 27(12), 1323–1348. DOI: https://doi.org/10.1177/0731684407084989

Wu, H.-L., Wang, Y.-F., Yu, L., & Li, X.-R. (2009). Experimental and computational studies on high-strength concrete circular columns confined by aramid fiber-reinforced polymer sheets. Journal of Composites for Construction, 13(2), 125–134. DOI: https://doi.org/10.1061/(ASCE)1090-0268(2009)13:2(125)

Yang, H., Song, H., & Zhang, S. (2015). Experimental investigation of the behavior of aramid fiber reinforced polymer confined concrete subjected to high strain-rate compression. Construction and Building Materials, 95, 143–151. DOI: https://doi.org/10.1016/j.conbuildmat.2015.07.084

Yaychi, B. M., & Esmaeili-Falak, M. (2024). Estimating Axial Bearing Capacity of Driven Piles Using Tuned Random Forest Frameworks. Geotechnical and Geological Engineering, 42(8), 7813–7834. DOI: https://doi.org/10.1007/s10706-024-02952-9

Yin, H. (2025). Ultimate strain estimation of concrete wrapped by aramid fiber employing coati optimization-based systems. Multiscale and Multidisciplinary Modeling, Experiments and Design, 8(1), 1–17. DOI: https://doi.org/10.1007/s41939-024-00668-0

Zarei, M., Mohseni, F., & Sohrabi, P. (2024). Correlates of spatial structure variability in Bushehr port-city: A comprehensive analysis using fuzzy cognitive mapping methodology. J. Infrastruct. Policy Dev, 8, 8789. DOI: https://doi.org/10.24294/jipd.v8i11.8789

Zhang, K., Zhang, Y., & Razzaghzadeh, B. (2024). Application of the optimal fuzzy-based system on bearing capacity of concrete pile. Steel and Composite Structures, 51(1), 25.

Zhao, W., Wang, L., & Mirjalili, S. (2022). Artificial hummingbird algorithm: A new bio-inspired optimizer with its engineering applications. Computer Methods in Applied Mechanics and Engineering, 388, 114194. DOI: https://doi.org/10.1016/j.cma.2021.114194

Zhou, Y., Liu, X., Xing, F., Cui, H., & Sui, L. (2016). Axial compressive behavior of FRP-confined lightweight aggregate concrete: An experimental study and stress-strain relation model. Construction and Building Materials, 119, 1–15. DOI: https://doi.org/10.1016/j.conbuildmat.2016.02.180