Title:
Stochasticity on Long-Term Behavior of Steel-/Carbon Fiber-Reinforced Polymer Prestressed Girders
Author(s):
Yail J. Kim and David Micnhimer
Publication:
Structural Journal
Volume:
118
Issue:
2
Appears on pages(s):
33-47
Keywords:
carbon fiber-reinforced polymer (CFRP); long-term; modeling; prestressing; stochastic
DOI:
10.14359/51723512
Date:
3/1/2021
Abstract:
This paper presents the long-term behavior of bridge girders prestressed with steel strands and carbon fiber-reinforced polymer (CFRP) tendons, based on a stochastic process called polynomial chaos expansion (PCE). Benchmark girders are designed pursuant to existing specifications, and their time-dependent responses are predicted up to 100 years by the incremental time steps and modified step function methods, alongside variable performance levels dependent upon the extent of corrosion. The loss of prestress in the steel-prestressed girders is influenced by the degree of corrosion current density up to 45.4%, while the loss of the CFRP-prestressed girders is stable at a maximum of 15.5%. The geometric
configuration of the girders dominates the sensitivity of the flexural capacity when subjected to corrosion. The deflections of both steel and CFRP-prestressed girders, including the corrosion-damaged cases, are within the limit of the American Association of State Highway Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) Bridge Design Specifications. Published design provisions on the camber and deflection of those girders are assessed. Additional practical interests lie in the evaluation of deformability for the CFRP-prestressed girders.
Related References:
1. Federal Highway Administration, “National Bridge Inventory,” FHWA, Washington, DC, 2016.
2. Precast/Prestressed Concrete Institute, “PCI Design Handbook,” PCI, Chicago, IL, 2010.
3. American Association of State Highway and Transportation Officials, “AASHTO LRFD Bridge Design Specifications,” eighth edition, AASHTO, Washington, DC, 2017.
4. Garber, D. B.; Gallardo, J. M.; Deschenes, D. J.; and Bayrak, O., “Experimental Investigation of Prestress Losses in Full-Scale Bridge Girders,” ACI Structural Journal, V. 112, No. 5, Sept.-Oct. 2015, pp. 553-564. doi: 10.14359/51687909
5. ACI Committee 440, “Prestressing Concrete Structures with FRP Tendons (ACI 440.4R-04),” American Concrete Institute, Farmington Hills, MI, 2004.
6. Rizkalla, S. H., and Tadros, G., “First Smart Highway Bridge in Canada,” Concrete International, V. 16, No. 6, June 1994, pp. 42-44.
7. Dolan, C. W., “FRP Prestressing in the USA,” Concrete International, V. 21, No. 10, Oct. 1999, pp. 21-24.
8. Frankhauser, W.; Elkaissi, J.; Kahl, S.; McMillan, S.; Potter, W.; Rister, D.; and Wilson, D., “Advances in Fiber-Reinforced Polymer (FRP) Composites in Transportation Infrastructure,” US Domestic Scan Program, NCHRP Project 20-68A, Scan 13-03, Transportation Research Board, Washington, DC, 2016.
9. Nanni, A., and Tanigaki, M., “Pretensioned Prestressed Concrete Members with Bonded Fiber Reinforced Plastic Tendons: Development and Flexural Bond Lengths (Static),” ACI Structural Journal, V. 89, No. 4, July-Aug. 1992, pp. 433-441.
10. Lees, J. M., “Fibre-Reinforced Polymers in Reinforced and Prestressed Concrete Applications: Moving Forward,” Progress in Structural Engineering and Materials, V. 3, No. 2, 2001, pp. 122-131. doi: 10.1002/pse.60
11. Grace, N.; Ushijima, K.; Matsagar, V.; and Wu, C., “Performance of AASHTO-Type Bridge Model Prestressed with Carbon Fiber-Reinforced Polymer Reinforcement,” ACI Structural Journal, V. 110, No. 3, May-June 2013, pp. 491-501.
12. Braimah, A.; Green, M. F.; and Soudki, K. A., “Long-Term Behavior of CFRP Prestressed Concrete Beams,” PCI Journal, V. 48, No. 2, 2003, pp. 98-107.
13. Zou, P. X. W., “Theoretical Study on Short-Term and Long-Term Deflections of Fiber Reinforced Polymer Prestressed Concrete Beams,” Journal of Composites for Construction, ASCE, V. 7, No. 4, 2003, pp. 285-291. doi: 10.1061/(ASCE)1090-0268(2003)7:4(285)
14. Youkim, S. A., and Karbhari, V. M., “An Approach to Determine Long-Term Behavior of Concrete Members Prestressed with FRP Tendons,” Construction and Building Materials, V. 21, No. 5, 2007, pp. 1052-1060. doi: 10.1016/j.conbuildmat.2006.02.006
15. Mertol, H. C.; Rizkalla, S. H.; Scott, P.; Lees, J. M.; and El-Hacha, R., “Durability of Concrete Beams Prestressed with CFRP,” Case Histories and Use of FRP for Prestressing Applications, SP-245, R. El-Hacha and S. H. Rizkalla, eds., American Concrete Institute, Farmington Hills, MI, Apr. 2007, pp. 1-20.
16. Sepahvand, K., and Marburg, S., “On Construction of Uncertain Material Parameter Using Generalized Polynomial Chaos Expansion from Experimental Data,” Procedia IUTAM, V. 6, Apr. 2013, pp. 4-17. doi: 10.1016/j.piutam.2013.01.001
17. Spiridonakos, M. D.; Chatzi, E. N.; and Sudret, B., “Polynomial Chaos Expansion Models for the Monitoring of Structures under Operational Variability,” Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, V. 2, No. 3, 2016, p. B4016003. doi: 10.1061/AJRUA6.0000872
18. Xiu, D., “Fast Numerical Methods for Stochastic Computations: A Review,” Communications in Computational Physics, V. 5, No. 2-4, 2009, pp. 242-272.
19. Hadigol, M., and Doostan, A., “Least Squares Polynomial Chaos Expansion: A Review of Sampling Strategies,” Computer Methods in Applied Mechanics and Engineering, V. 332, Apr, 2018, pp. 382-407. doi: 10.1016/j.cma.2017.12.019
20. Wiener, N., “The Homogeneous Chaos,” American Journal of Mathematics, V. 60, No. 4, 1938, pp. 897-936. doi: 10.2307/2371268
21. Oladyshkin, S., and Nowak, W., “Data-Driven Uncertainty Quantification Using the Arbitrary Polynomial Chaos Expansion,” Reliability Engineering & System Safety, V. 106, Oct, 2012, pp. 179-190. doi: 10.1016/j.ress.2012.05.002
22. Maccone, C., Deep Space Flight and Communications, Springer, Berlin, Germany, 2009.
23. Precast/Prestressed Concrete Institute, Bridge Design Manual, PCI, Chicago, IL, 2004.
24. Barr, P. J.; Eberhard, M. O.; and Stanton, J. F., “Live-Load Distribution Factors in Prestressed Concrete Girder Bridges,” Journal of Bridge Engineering, ASCE, V. 6, No. 5, 2001, pp. 298-306. doi: 10.1061/(ASCE)1084-0702(2001)6:5(298)
25. Michhimer, D., and Kim, Y. J., “Chaos Expansion for Long-Term Behavior of Carbon Fiber-Reinforced Polymer-Strengthened Reinforced Concrete Beams,” ACI Structural Journal, V. 117, No. 2, Mar. 2020, pp. 105-116.
26. ACI Committee 318, “Building Code Requirements for Structural Concrete and Commentary (ACI 318-14) and Commentary (ACI 318R-14),” American Concrete Institute, Farmington Hills, MI, 2014.
27. ACI Committee 209, “Guide for Modeling and Calculating Shrinkage and Creep in Hardened Concrete (ACI 209.2R-08),” American Concrete Institute, Farmington Hills, MI, 2008.
28. Tadros, M. K., “Designing for Deflection,” Seminar, PCI Seminar on Advanced Design Concepts in Precast Prestressed Concrete, PCI Convention, Dallas, TX, October, Prestressed Concrete Institute, Chicago, IL, 1979.
29. Nawy, E. G., Prestressed Concrete, fifth edition, Prentice Hall, Upper Saddle River, NJ, 2009.
30. Enomoto, T.; Harada, T.; Ushijima, K.; and Khin, M., “Long-Term Relaxation Characteristics of CFRP Cables,” Proceedings, Fourth International Conference on Construction and Materials (ConMat09), Nagoya, Japan, 2009, pp. 1205-1210.
31. Gar, S. P.; Mander, J. B.; and Hurlebaus, S., “Deflection of FRP Prestressed Concrete Beams,” Journal of Composites for Construction, ASCE, V. 22, No. 2, 2017, p. 04017049
32. Branson, D. E., “The Deformation of Noncomposite and Composite Prestressed Concrete Members,” SP-43, Deflections of Concrete Structures, American Concrete Institute, Farmington Hills, MI, Jan. 1974, pp. 83-128.
33. Thoft-Christensen, P.; Jensen, F. M.; Middleton, C. R.; and Blackmore, A., “Assessment of the Reliability of Concrete Slab Bridges,” Proceedings, Seventh IFIP WG 7.5 Working Conference, Boulder, CO, 1996, pp. 1-8.
34. Ahmad, Z., Principles of Corrosion Engineering and Corrosion Control, Butterworth-Heinemann, Oxford, 2006.
35. Kayser, J. R., and Nowak, A. S., “Reliability of Corroded Steel Girder Bridges,” Structural Safety, V. 6, No. 1, 1989, pp. 53-63. doi: 10.1016/0167-4730(89)90007-6
36. Darmawan, M. S., and Stewart, M. G., “Spatial Time-Dependent Reliability Analysis of Corroding Pretensioned Prestressed Concrete Bridge Girders,” Structural Safety, V. 29, No. 1, 2007, pp. 16-31. doi: 10.1016/j.strusafe.2005.11.002
37. Transportation Research Board, “Bridges for Service Life Beyond 100 Years: Service Limit State Design (SHRP R19B),” TRB, Washington, DC, 2015.
38. Vu, K. A. T., and Stewart, M. G., “Structural Reliability of Concrete Bridges Including Improved Chloride-Induced Corrosion Models,” Structural Safety, V. 22, No. 4, 2000, pp. 313-333. doi: 10.1016/S0167-4730(00)00018-7
39. Broomfield, J. P.; Rodriguez, J.; Ortega, L. M.; and Garcia, A. M., “Corrosion Rate Measurements in Reinforced Concrete Structures by a Linear Polarization Device,” Concrete Bridges in Aggressive Environments, SP-151, R. E. Weyers, ed., American Concrete Institute, Farmington Hills, MI, July 1994, pp. 163-182.
40. Liu, T., and Weyers, R. W., “Modeling the Dynamic Corrosion Process in Chloride Contaminated Concrete Structures,” Cement and Concrete Research, V. 28, No. 3, 1998, pp. 365-379. doi: 10.1016/S0008-8846(98)00259-2
41. Okeil, A.; El-Tawil, S.; and Shahawy, M., “Flexural Reliability of Reinforced Concrete Bridge Girders Strengthened with Carbon Fiber-Reinforced Polymer Laminates,” Journal of Bridge Engineering, ASCE, V. 7, No. 5, 2002, pp. 290-299. doi: 10.1061/(ASCE)1084-0702(2002)7:5(290)
42. Nowak, A. S., and Collins, K. R., Reliability of Structures, CRC Press, Boca Raton, FL, 2013.
43. Mirza, S. A.; Kikuchi, D. K.; and MacGregor, J. G., “Flexural Strength Reduction Factor for Bonded Prestressed Concrete Beams,” ACI Journal Proceedings, V. 77, No. 4, Apr. 1980, pp. 237-246.
44. Atadero, R. A., and Karbhari, V. M., “Calibration of Resistance Factors for Reliability-Based Design of Externally-Bonded FRP Composites,” Composites. Part B, Engineering, V. 39, No. 4, 2008, pp. 665-679. doi: 10.1016/j.compositesb.2007.06.004
45. Sanchez-Heres, L.; Ringsberg, J. W.; and Johnson, E., “Influence of Mechanical and Probabilistic Models on the Reliability Estimates of Fibre-Reinforced Cross-Ply Laminates,” Structural Safety, V. 51, Nov. 2014, pp. 35-46. doi: 10.1016/j.strusafe.2014.06.001
46. Joint Committee on Structural Safety, “JCSS Probabilistic Model Code,” JCSS, Copenhagen, Denmark, 2014.
47. Papakonstantinou, K. G., and Shinozuka, M., “Probabilistic Model for Steel Corrosion in Reinforced Concrete Structures of Large Dimensions Considering Crack Effects,” Engineering Structures, V. 57, Dec, 2013, pp. 306-326. doi: 10.1016/j.engstruct.2013.06.038
48. Stewart, M. G., and Rosowsky, D. V., “Time-Dependent Reliability of Deteriorating Reinforced Concrete Bridge Decks,” Structural Safety, V. 20, No. 1, 1998, pp. 91-109. doi: 10.1016/S0167-4730(97)00021-0
49. Smith, J. L., and Viramani, Y. P., “Materials and Methods for Corrosion Control of Reinforced and Prestressed Concrete Structures in New Construction,” Report No. FHWA-RD-00-081, Federal Highway Administration, Washington, DC, 2000.
50. Kim, Y. J., and Nickle, R. W., “Long-Term Multipliers and Deformability of Fiber-Reinforced Polymer Prestressed Concrete,” ACI Structural Journal, V. 115, No. 1, Jan. 2018, pp. 223-234. doi: 10.14359/51700988
51. Kim, Y. J., “Flexural Response of Concrete Beams Prestressed with AFRP Tendons: Numerical Investigation,” Journal of Composites for Construction, ASCE, V. 14, No. 6, 2010, pp. 647-658. doi: 10.1061/(ASCE)CC.1943-5614.0000128