Probabilistic Design Models for Ultimate Strength and Strain of FRP-Confined Concrete
Publication: Journal of Composites for Construction
Volume 20, Issue 6
Abstract
This paper presents a probabilistic procedure for deriving design models for the ultimate strength and strain of fiber–reinforced-polymer (FRP)-confined concrete. First, a large database of axial compression tests performed on circular FRP-confined concrete specimens is collected for calibrating an ultimate strength model, based on the Drucker-Prager criterion, and an ultimate strain model, based on the ultimate dilation rate. The database is also employed for deriving a probabilistic model for the FRP strain efficiency factor. The calibrated models, though simple, show superior performance over some of the models in the literature. Then, using the Central Limit Theorem and considering uncertainty in the mechanical properties of the concrete and FRP material as well as their correlation, analytical probabilistic design models for the ultimate strength and strain of FRP-confined concrete are derived. These models can be used in the design and reliability analysis of FRP-confined columns.
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References
ACI (American Concrete Institute). (2008). “Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures.” ACI 440.2R-08, Farmington Hills, MI.
Aire, C., Gettu, R., Casas, J., Marques, S., and Marques, D. (2010). “Concrete laterally confined with fibre-reinforced polymers (FRP): Experimental study and theoretical model.” Materiales de Construcción, 60(297), 19–31.
Akogbe, R. K., Liang, M., and Wu, Z. M. (2011). “Size effect of axial compressive strength of CFRP confined concrete cylinders.” Int. J. Concr. Struct. Mater., 5(1), 49–55.
Almusallam, T. H. (2007). “Behavior of normal and high-strength concrete cylinders confined with E-glass/epoxy composite laminates.” Composit. Part B: Eng., 38(5–6), 629–639.
Atadero, R., Lee, L., and Karbhari, V. M. (2005). “Consideration of material variability in reliability analysis of FRP strengthened bridge decks.” Compos. Struct., 70(4), 430–443.
Atadero, R. A. (2006). “Development of load and resistance factor design for FRP strengthening of reinforced concrete structures.” Ph.D. thesis, Univ. of California, San Diego.
Atadero, R. A., and Karbhari, V. M. (2009). “Sources of uncertainty and design values for field-manufactured FRP.” Compos. Struct., 89(1), 83–93.
Bartlett, F. M., and Macgregor, J. G. (1996). “Statistical analysis of the compressive strength of concrete in structures.” ACI Mater. J., 93(2), 158–168.
Benjamin, J., and Cornell, C. (1975). Probability, statistics and decision for civil engineers, McGraw-Hill, New York.
Benzaid, R., Mesbah, H., and Chikh, N. E. (2010). “FRP-confined concrete cylinders: Axial compression experiments and strength model.” J. Reinf. Plast. Compos., 29(16), 2469–2488.
Berthet, J., Ferrier, E., and Hamelin, P. (2005). “Compressive behavior of concrete externally confined by composite jackets. Part A: Experimental study.” Constr. Build. Mater., 19(3), 223–232.
Berthet, J., Ferrier, E., and Hamelin, P. (2006). “Compressive behavior of concrete externally confined by composite jackets: Part B: Modeling.” Constr. Build. Mater., 20(5), 338–347.
Binici, B. (2008). “Design of FRPs in circular bridge column retrofits for ductility enhancement.” Eng. Struct., 30(3), 766–776.
Bisby, L. A., and Take, W. A. (2009). “Strain localisations in FRP-confined concrete: New insights.” Proc. ICE-Struct. Build., 162(5), 301–309.
Bullo, S. (2003). “Experimental study of the effects of the ultimate strain of fiber reinforced plastic jackets on the behavior of confined concrete.” Proc., Int. Conf. of Composite in Construction, D. Brung, G. Spadea, and R. N. Swamy, eds., Univ. of Calabria, Cosenza, Italy, 465–470.
Cairns, S. W. (2001). “Circular concrete columns externally reinforced with pre-fabricated carbon polymer shells.” Master’s thesis, Univ. of Toronto, Toronto.
Carey, S. A., and Harries, K. A. (2005). “Axial behavior and modeling of confined small-, medium-, and large-scale circular sections with carbon fiber-reinforced polymer jackets.” ACI Struct. J., 102(4), 596–604.
Chastre, C., and Silva, M. A. G. (2010). “Monotonic axial behavior and modelling of RC circular columns confined with CFRP.” Eng. Struct., 32(8), 2268–2277.
Chen, W.-F. (2007). Plasticity in reinforced concrete, J. Ross Publishing, Fort Lauderdale, FL.
Ciupala, M., Pilakoutas, K., and Mortazavi, A. (2007). “Effectiveness of FRP composites in confined concrete.” Proc., 8th Int. Symp. on Fiber Reinforced Polymer Reinforcement for Concrete Structures, Univ. of Patras, Patras, Greece, 1–10.
Cui, C. (2009). “Behaviour of normal and high strength concrete confined with fibre reinforced polymers (FRP).” Ph.D. thesis, Univ. of Toronto, Toronto.
Cui, C., and Sheikh, S. (2010). “Experimental study of normal- and high-strength concrete confined with fiber-reinforced polymers.” J. Compos. Constr., 553–561.
De Lorenzis, L., Micelli, F., and La Tegola, A. (2002). “Influence of specimen size and resin type on the behaviour of FRP-confined concrete cylinders.” Proc., ACIC-2002, Thomas Telford, U.K., 281–290.
De Lorenzis, L., and Tepfers, R. (2003). “Comparative study of models on confinement of concrete cylinders with fiber-reinforced polymer composites.” J. Compos. Constr., 219–237.
Demers, M., and Neale, K. (1994). “Strengthening of concrete columns with unidirectional composite sheets.” Proc., 4th Int. Conf. on Short and Medium Span Bridges, A. A. Mufti, B. Bakht, and L. G. Jaeger, eds., Canadian Society for Civil Engineering, Montreal, 895–905.
Demers, M., and Neale, K. (1999). “Confinement of reinforced concrete columns with fibre-reinforced composite sheets—An experimental study.” Can. J. Civ. Eng., 26(2), 226–241.
Dias da Silva, V., and Santos, J. (2001). “Strengthening of axially loaded concrete cylinders by surface composites.” Proc., Int. Conf. Composites in Constructions, AA Balkema Publishers, Lisse, Netherlands, 257–262.
Doran, B., Koksal, H. O., and Turgay, T. (2009). “Nonlinear finite element modeling of rectangular/square concrete columns confined with FRP.” Mater. Des., 30(8), 3066–3075.
EC2 (Eurocode No. 2). (2004). “Design of concrete structures: Part 1: General rules and rules for buildings.” EN 1990-1-1:2003E, European Committee for Standardization, Brussels, Belgium.
Eid, R., and Paultre, P. (2007). “Plasticity-based model for circular concrete columns confined with fibre-composite sheets.” Eng. Struct., 29(12), 3301–3311.
Ellingwood, B., Galambos, T., McGregor, J., and Cornell, C. (1980). “Development of a probability-based load criteria for American Standard A 58.” U.S. Dept. of Commerce, National Bureau of Standards, Washington, DC.
Elsanadedy, H. M., Al-Salloum, Y. A., Alsayed, S. H., and Iqbal, R. A. (2012). “Experimental and numerical investigation of size effects in FRP-wrapped concrete columns.” Constr. Build. Mater., 29, 56–72.
Faella, C., Realfonzo, R., and Salerno, N. (2004). “Sulla resistenza e deformazione di elementi in ca confinati con tessuti in FRP.” Proc., 11th National Congress “L’ingegneria sismica in Italia,” Genova, Italia (in Italian).
Fardis, M. N., and Khalili, H. H. (1982). “FRP-encased concrete as a structural material.” Mag. Concr. Res., 34(121), 191–202.
Grubbs, F. E. (1969). “Procedures for detecting outlying observations in samples.” Technometrics, 11(1), 1–21.
Gu, D.-S., Wu, G., Wu, Z.-S., and Wu, Y.-F. (2010). “Confinement effectiveness of FRP in retrofitting circular concrete columns under simulated seismic load.” J. Compos. Constr., 531–540.
Harries, K. A., and Carey, S. A. (2003). “Shape and “gap” effects on the behavior of variably confined concrete.” Cem. Concr. Res., 33(6), 881–890.
Harries, K. A., and Kharel, G. (2003). “Experimental investigation of the behavior of variably confined concrete.” Cem. Concr. Res., 33(6), 873–880.
He, Z., and Li, X. (2008). “Progress in developing a reliability-based design philosophy for FRP-strengthened concrete structures.” Proc., 4th Int. Conf. on FRP Composites in Civil Engineering (CICE2008), Zürich, Switzerland, 1–6.
Ilki, A., Kumbasar, N., and Koc, V. (2002). “Strength and deformability of low strength concrete confined by carbon fiber composite sheets.” Proc., 15th ASCE Engineering Mechanics Conf., Columbia Univ., New York.
Imran, I., and Pantazopoulou, S. J. (1996). “Experimental study of plain concrete under triaxial stress.” ACI Mater. J., 93(6), 589–601.
Iravani, S. (1996). “Mechanical properties of high-performance concrete.” ACI Mater. J., 93(5), 416–426.
Jaffry, S. A. D. (2001). “Concrete filled glass fibre reinforced polymer (GFRP) shells under concentric compression.” Master’s thesis, Univ. of Toronto, Toronto.
Jiang, T., and Teng, J. (2007). “Analysis-oriented stress-strain models for FRP-confined concrete.” Eng. Struct., 29(11), 2968–2986.
Karabinis, A. I., and Rousakis, T. C. (2002). “Concrete confined by FRP material: A plasticity approach.” Eng. Struct., 24(7), 923–932.
Karbhari, V. M., and Gao, Y. (1997). “Composite jacketed concrete under uniaxial compression-verification of simple design equations.” J. Mater. Civ. Eng., 185–193.
Kono, S., Inazumi, M., and Kaku, T. (1998). “Evaluation of confining effects of CFRP sheets on reinforced concrete members.” Proc., 2nd Int. Conf. on Composites in Infrastructure ICCI’98, Univ. of Arizona, Tucson, AZ, 343–355.
Kshirsagar, S., Lopez-Anido, R. A., and Gupta, R. K. (2000). “Environmental aging of fiber-reinforced polymer-wrapped concrete cylinders.” ACI Mater. J., 97(6), 703–712.
Lam, L., and Teng, J. (2003a). “Design-oriented stress-strain model for FRP-confined concrete.” Constr. Build. Mater., 17(6), 471–489.
Lam, L., and Teng, J. (2003b). “Design-oriented stress-strain model for FRP-confined concrete in rectangular columns.” J. Reinf. Plast. Compos., 22(13), 1149–1186.
Lam, L., and Teng, J. (2004). “Ultimate condition of fiber reinforced polymer-confined concrete.” J. Compos. Constr., 539–548.
Lam, L., Teng, J. G., Cheung, C. H., and Xiao, Y. (2006). “FRP-confined concrete under axial cyclic compression.” Cem. Concr. Compos., 28(10), 949–958.
Liang, M., Wu, Z. M., Ueda, T., Zheng, J. J., and Akogbe, R. (2012). “Experiment and modeling on axial behavior of carbon fiber reinforced polymer confined concrete cylinders with different sizes.” J. Reinf. Plast. Compos., 31(6), 389–403.
Lim, J. C., and Ozbakkaloglu, T. (2013). “Confinement model for FRP-confined high-strength concrete.” J. Compos. Constr., .
Lim, J. C., and Ozbakkaloglu, T. (2015a). “Hoop strains in FRP-confined concrete columns: Experimental observations.” Mater. Struct., 48(9), 2839–2854.
Lim, J. C., and Ozbakkaloglu, T. (2015b). “Investigation of the influence of the application path of confining pressure: Tests on actively confined and FRP-confined concretes.” J. Struct. Eng., 04014203.
Logan, A. T. (2005). “Short-term material properties of high-strength concrete.” Ph.D. thesis, North Carolina State Univ., Raleigh, NC.
Mastrapa, J. (1997). “Effect of construction bond on confinement with fiber composites.” Master’s thesis, Univ. of Central Florida, Orlando, FL.
Matthys, S., Taerwe, L., and Audenaert, K. (1999). “Tests on axially loaded concrete columns confined by fiber reinforced polymer sheet wrapping.” Proc., 4th Int. Symp. on Fiber Reinforced Polymer Reinforcement for Reinforced Concrete Structures, Detroit.
Matthys, S., Toutanji, H., Audenaert, K., and Taerwe, L. (2005). “Axial load behavior of large-scale columns confined with fiber-reinforced polymer composites.” ACI Struct. J., 102(2), 258–267.
Micelli, F., and Modarelli, R. (2013). “Experimental and analytical study on properties affecting the behaviour of FRP-confined concrete.” Compos. Part B: Eng., 45(1), 1420–1431.
Micelli, F., Myers, J., and Murthy, S. (2001). “Effect of environmental cycles on concrete cylinders confined with FRP.” Proc., Int. Conf. Composites in Constructions, Balkema Publishers, Lisse, Netherlands, 317–322.
Mirmiran, A., and Shahawy, M. (1997). “Dilation characteristics of confined concrete.” Mech. Cohesive-Frict. Mater., 2(3), 237–249.
Mirmiran, A., Shahawy, M., Samaan, M., El Echary, H., Mastrapa, J. C., and Pico, O. (1998). “Effect of column parameters on FRP-confined concrete.” J. Compos. Constr., 175–185.
Mirmiran, A., Zagers, K., and Yuan, W. (2000). “Nonlinear finite element modeling of concrete confined by fiber composites.” Finite Ele. Anal. Des., 35(1), 79–96.
Mirza, S. A., and MacGregor, J. G. (1979). “Variations in dimensions of reinforced concrete members.” J. Struct. Div., 105(4), 751–766.
Mirza, S. A., MacGregor, J. G., and Hatzinikolas, M. (1979). “Statistical descriptions of strength of concrete.” J. Struct. Div., 105(6), 1021–1037.
Miyauchi, K., Nishibayashi, S., and Inoue, S. (1997). “Estimation of strengthening effects with carbon fiber sheet for concrete column.” 3rd Int. Symp. of Non-metallic (FRP) Reinforcement for Concrete Structures, Sapporo, Japan, 217–224.
Mohamed, H. M., and Masmoudi, R. (2010). “Axial load capacity of concrete-filled FRP tube columns: Experimental versus theoretical predictions.” J. Compos. Constr., 231–243.
Noguchi Laboratory Data. (2015). “Database for mechanical properties of concrete.” ⟨http://bme.t.u-tokyo.ac.jp/index_e.html⟩ (18 Aug. 2015).
Nowak, A. S., and Szerszen, M. M. (2003). “Calibration of design code for buildings (ACI 318): Part 1—Statistical models for resistance.” ACI Struct. J., 100(3), 377–382.
Owen, L. M. (1998). “Stress-strain behavior of concrete confined by carbon fiber jacketing.” Master’s thesis, Univ. of Washington, Seattle.
Ozbakkaloglu, T., and Lim, J. C. (2013). “Axial compressive behavior of FRP-confined concrete: Experimental test database and a new design-oriented model.” Compos. Part B: Eng., 55, 607–634.
Ozbakkaloglu, T., Lim, J. C., and Vincent, T. (2013). “FRP-confined concrete in circular sections: Review and assessment of stress-strain models.” Eng. Struct., 49, 1068–1088.
Ozbakkaloglu, T., and Saatcioglu, M. (2006). “Seismic behavior of high-strength concrete columns confined by fiber-reinforced polymer tubes.” J. Compos. Constr., 538–549.
Ozbakkaloglu, T., and Vincent, T. (2013). “Axial compressive behavior of circular high-strength concrete-filled FRP tubes.” J. Compos. Constr., .
Ozcan, O., Binici, B., and Ozcebe, G. (2010). “Seismic strengthening of rectangular reinforced concrete columns using fiber reinforced polymers.” Eng. Struct., 32(4), 964–973.
Pessiki, S., Harries, K. A., Kestner, J. T., Sause, R., and Ricles, J. M. (2001). “Axial behavior of reinforced concrete columns confined with FRP jackets.” J. Compos. Constr., 237–245.
Picher, F., Rochette, P., and Labossiére, P. (1996). “Confinement of concrete cylinders with CFRP.” Proc., 1st Int. Conf. on Composite Infrastructures, Univ. of Arizona, Tucson, AZ, 829–841.
Purba, B. K., and Mufti, A. A. (1999). “Investigation of the behavior of circular concrete columns reinforced with carbon fiber reinforced polymer (CFRP) jackets.” Can. J. Civ. Eng., 26(5), 590–596.
Realfonzo, R., and Napoli, A. (2011). “Concrete confined by FRP systems: Confinement efficiency and design strength models.” Compos. Part B: Eng., 42(4), 736–755.
Realfonzo, R., and Napoli, A. (2013). “Confining concrete members with FRP systems: Predictive vs design strain models.” Compos. Struct., 104, 304–319.
Richart, F. E., Brandtzaeg, A., and Brown, R. L. (1928). “A study of the failure of concrete under combined compressive stresses.” Engineering Experimental Station, Univ. of Illinois, Champaign, IL.
Rochette, P., and Labossiere, P. (1996). “A plasticity approach for concrete columns confined with composite materials.” Proc., 2nd Int. Conf. on Advanced Composite Materials in Bridges and Structures, Canadian Society of Civil Engineering, Montreal, 359–366.
Ross, S. M. (2014). Introduction to probability and statistics for engineers and scientists, Academic Press, Burlington, VT.
Rousakis, T., and Tepfers, R. (2001). “Experimental investigation of concrete cylinders confined by carbon FRP sheets, under monotonic and cyclic axial compressive load.” Chalmers Univ. of Technology, Division of Building Technology, Goteborg, Sweden, 87.
Rousakis, T., You, C.-S., De Lorenzis, L., Tamužs, V., and Tepfers, R. (2003). “Concrete cylinders confined by CFRP sheets subjected to cyclic axial compressive load.” Proc., 6th Int. Symp. on FRP Reinforcement for Concrete Structures, Singapore, 571–580.
Rousakis, T. C., Rakitzis, T. D., and Karabinis, A. I. (2012). “Design-oriented strength model for FRP-confined concrete members.” J. Compos. Constr., 615–625.
Saadatmanesh, H., Ehsani, M. R., and Li, M. W. (1994). “Strength and ductility of concrete columns externally reinforced with fiber composite straps.” ACI Struct. J., 91(4), 434–447.
Saafi, M., Toutanji, H., and Li, Z. (1999). “Behavior of concrete columns confined with fiber reinforced polymer tubes.” ACI Mater. J., 96(4), 500–509.
Saenz, N., and Pantelides, C. P. (2006). “Short and medium term durability evaluation of FRP-confined circular concrete.” J. Compos. Constr., 244–253.
Samaan, M., Mirmiran, A., and Shahawy, M. (1998). “Model of concrete confined by fiber composites.” J. Struct. Eng., 1025–1031.
Samdani, S., and Sheikh, S. A. (2003). “Analytical study of FRP-confined concrete columns.” Proc., 4th Int. Conf. on Concrete Under Severe Conditions, Korea Concrete Institute, Seoul, 27–30.
Shahawy, M., Mirmiran, A., and Beitelman, T. (2000). “Tests and modeling of carbon-wrapped concrete columns.” Compos. Part B: Eng., 31(6), 471–480.
Shehata, I., Carneiro, L., and Shehata, L. (2007). “Strength of confined short concrete columns.” Proc., 8th Int. Symp. on Fiber Reinforced Polymer Reinforcement for Concrete Structures, Univ. of Patras, Patron, Greece, 1–10.
Silva, M. A., and Rodrigues, C. C. (2006). “Size and relative stiffness effects on compressive failure of concrete columns wrapped with glass FRP.” J. Mater. Civ. Eng., 334–342.
Song, X., Gu, X., Li, Y., Chen, T., and Zhang, W. (2013). “Mechanical behavior of FRP-strengthened concrete columns subjected to concentric and eccentric compression loading.” J. Compos. Constr., 336–346.
Spoelstra, M. R., and Monti, G. (1999). “FRP-confined concrete model.” J. Compos. Constr., 143–150.
Tamuzs, V., Tepfers, R., and Sparnins, E. (2006a). “Behavior of concrete cylinders confined by carbon composite: 2. Prediction of strength.” Mech. Compos. Mater., 42(2), 109–118.
Tamuzs, V., Tepfers, R., Zile, E., and Ladnova, O. (2006b). “Behavior of concrete cylinders confined by a carbon composite: 3. Deformability and the ultimate axial strain.” Mech. Compos. Mater., 42(4), 303–314.
Tamuzs, V., Valdmanis, V., Tepfers, R., and Gylltoft, K. (2008). “Stability analysis of CFRP-wrapped concrete columns strengthened with external longitudinal CFRP sheets.” Mech. Compos. Mater., 44(3), 199–208.
Teng, J., Jiang, T., Lam, L., and Luo, Y. (2009). “Refinement of a design-oriented stress-strain model for FRP-confined concrete.” J. Compos. Constr., 269–278.
Teng, J., Yu, T., Wong, Y., and Dong, S. (2007). “Hybrid FRP-oncrete-steel tubular columns: Concept and behavior.” Constr. Build. Mater., 21(4), 846–854.
Theriault, M., Neale, K. W., and Claude, S. (2004). “Fiber-reinforced polymer-confined circular concrete columns: Investigation of size and slenderness effects.” J. Compos. Constr., 323–331.
Toutanji, H. (1999). “Stress-strain characteristics of concrete columns externally confined with advanced fiber composite sheets.” ACI Mater. J., 96(3), 397–404.
Valdmanis, V., De Lorenzis, L., Rousakis, T., and Tepfers, R. (2007). “Behaviour and capacity of CFRP-confined concrete cylinders subjected to monotonic and cyclic axial compressive load.” Struct. Concr., 8(4), 187–200.
Vincent, T., and Ozbakkaloglu, T. (2013). “Influence of concrete strength and confinement method on axial compressive behavior of FRP confined high- and ultra high-strength concrete.” Compos. Part B: Eng., 50, 413–428.
Wang, F., and Cheong, K. (2001). “RC columns strengthened by FRP under uniaxial compression.” Proc., Int. Conf. on FRP Composites in Civil Engineering, Hong Kong, 327–334.
Wang, L.-M., and Wu, Y.-F. (2008). “Effect of corner radius on the performance of CFRP-confined square concrete columns: Test.” Eng. Struct., 30(2), 493–505.
Wang, Z., Wang, D., Smith, S. T., and Lu, D. (2012). “Experimental testing and analytical modeling of CFRP-confined large circular RC columns subjected to cyclic axial compression.” Eng. Struct., 40, 64–74.
Watanabe, K., et al. (1997). “Confinement effect of FRP sheet on strength and ductility of concrete cylinders under uniaxial compression.” Proc., Non-Metallic (FRP) Reinforcement for Concrete Structures, Japan Concrete Institute, Sapporo, Japan, 233–240.
Wiśniewski, D. F., Cruz, P. J., Henriques, A. A. R., and Simões, R. A. (2012). “Probabilistic models for mechanical properties of concrete, reinforcing steel and pre-stressing steel.” Struct. Infrastruct. Eng., 8(2), 111–123.
Wu, G., Lü, Z., and Wu, Z. (2006). “Strength and ductility of concrete cylinders confined with FRP composites.” Constr. Build. Mater., 20(3), 134–148.
Wu, Y. F., and Jiang, J. F. (2013). “Effective strain of FRP for confined circular concrete columns.” Compos. Struct., 95(1), 479–491.
Wu, Y.-F., Yun, Y., Wei, Y., and Zhou, Y. (2014). “Effect of predamage on the stress-strain relationship of confined concrete under monotonic loading.” J. Struct. Eng., 04014093.
Xiao, Q., Teng, J., and Yu, T. (2010). “Behavior and modeling of confined high-strength concrete.” J. Compos. Constr., 249–259.
Xiao, Y., and Wu, H. (2000). “Compressive behavior of concrete confined by carbon fiber composite jackets.” J. Mater. Civ. Eng., 139–146.
Yan, Z., Pantelides, C. P., and Reaveley, L. D. (2006). “Fiber-reinforced polymer jacketed and shape-modified compression members: I—Experimental behavior.” ACI Struct. J., 103(6), 885–893.
Yu, T., Teng, J., Wong, Y., and Dong, S. (2010). “Finite element modeling of confined concrete: I—Drucker-Prager type plasticity model.” Eng. Struct., 32(3), 665–679.
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Journal of Composites for Construction
Volume 20 • Issue 6 • December 2016
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© 2016 American Society of Civil Engineers.
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Received: Oct 13, 2015
Accepted: Feb 16, 2016
Published online: May 5, 2016
Discussion open until: Oct 5, 2016
Published in print: Dec 1, 2016
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