Genetic Programming–Based Drift Ratio Limit Models for Segmental Posttensioned Precast Concrete Piers
Publication: Journal of Bridge Engineering
Volume 28, Issue 2
Abstract
Segmental posttensioned precast concrete (SPPC) is a promising approach to accelerated bridge construction (ABC). However, an impediment to the performance-based design of SPPC piers lies in the challenge of defining appropriate damage states and corresponding engineering demand parameter (EDP) limits. To address this, in this study, genetic programming (GP), a form of artificial intelligence, is used to develop drift ratio–based EDP limit models in order to identify the onset of four damage levels that are particularly introduced herein for SPPC piers. In this respect, a finite-element model using ABAQUS is developed and experimentally validated to simulate the response of SPPC piers under seismic loading. The model is then utilized to generate a data set of 316 cases, all within the feasible design space of SPPC piers. This data set is subsequently used to develop GP-based predictive equations that map the relationship between different SPPC pier design parameters (e.g., posttensioning strand ratio, concrete compressive strength, and gravity load level) and EDP (i.e., drift ratio) limits. The performance of the developed equations is evaluated through different measures, including fitness function and performance index. Ultimately, parametric and sensitivity analyses are conducted to demonstrate that the GP-based equations are robust enough to characterize the four damage states for SPPC piers.
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References
Abonyi, J. 2022. “Genetic programming MATLAB toolbox.” MATLAB Central File Exchange. Accessed November 10, 2021. https://www.mathworks.com/matlabcentral/fileexchange/47197-genetic-programming-matlab-toolbox.
ACI (American Concrete Institute). 2019. Building code requirements for structural concrete. ACI 318-19. Farmington Hills, MI: ACI.
ASTM. 2013. Standard specification for low alloy steel deformed and plain bars for concrete reinforcement. A706/A706M-13. West Conshohocken, PA: ASTM.
ASTM. 2018. Standard specification for low-relaxation, seven-wire steel strand for prestressed concrete. ASTM A416/A416M-18. West Conshohocken, PA: ASTM.
ASTM. 2020. Standard specification for deformed and plain carbon-steel bars for concrete reinforcement. ASTM A615/A615-20. West Conshohocken, PA: ASTM.
Billah, A. H. M. M., and M. S. Alam. 2016. “Performance-based seismic design of shape memory alloy–reinforced concrete bridge piers. I: Development of performance-based damage states.” J. Struct. Eng. 142 (12): 04016140. https://doi.org/10.1061/(asce)st.1943-541x.0001458.
Bu, Z., J. Guo, R. Zheng, J. Song, and G. C. Lee. 2016a. “Cyclic performance and simplified pushover analyses of precast segmental concrete bridge columns with circular section.” Earthquake Eng. Eng. Vibr. 15 (2): 297–312. https://doi.org/10.1007/s11803-016-0323-3.
Bu, Z. Y., Y. C. Ou, J. W. Song, N. S. Zhang, and G. C. Lee. 2016b. “Cyclic loading test of unbonded and bonded posttensioned precast segmental bridge columns with circular section.” J. Bridge Eng. 21 (2): 04015043. https://doi.org/10.1061/(asce)be.1943-5592.0000807.
Caltrans (California Department of Transportation). 2016. Caltrans seismic design specifications for steel bridges. Sacramento, CA: Caltrans.
Chou, J. S., N. T. Ngo, and A. D. Pham. 2016. “Shear strength prediction in reinforced concrete deep beams using nature-inspired metaheuristic support vector regression.” J. Comput. Civ. Eng. 30 (1): 04015002. https://doi.org/10.1061/(asce)cp.1943-5487.0000466.
Cladera, A., J. L. Pérez-Ordóñez, and F. Martínez-Abella. 2014. “Shear strength of RC beams. Precision, accuracy, safety and simplicity using genetic programming.” Comput. Concr. 14 (4): 479–501. https://doi.org/10.12989/cac.2014.14.4.479.
CSA (Canadian Standards Association). 2016. Precast concrete - Materials and construction. CSA A23.4. Rexdale, ON, Canada: CSA.
CSA (Canadian Standards Association). 2019. Canadian highway bridge design code. CSA S6. Rexdale, ON, Canada: CSA.
CSA (Canadian Standards Association). 2021. Carbon steel bars for concrete reinforcement. CSA G30.18. Rexdale, ON, Canada: CSA.
Dawood, H., M. ElGawady, and W. Cofer. 2011. Seismic behavior and design of segmental precast post-tensioned concrete pier. No. TNW2011-17. Washington, DC: Transportation Northwest Organization.
ElGawady, M. A., and A. Sha’lan. 2011. “Seismic behavior of self-centering precast segmental bridge bents.” J. Bridge Eng. 16 (3): 328–339. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000174.
FIB (International Federation for Structural Concrete). 2010. FIB model code for concrete structures. Lausanne, Switzerland: FIB.
Gandomi, A. H., and D. A. Roke. 2015. “Assessment of artificial neural network and genetic programming as predictive tools.” Adv. Eng. Software 88: 63–72. https://doi.org/10.1016/j.advengsoft.2015.05.007.
Gandomi, A. H., G. J. Yun, and A. H. Alavi. 2013. “An evolutionary approach for modeling of shear strength of RC deep beams.” Mater. Struct. 46 (12): 2109–2119. https://doi.org/10.1617/s11527-013-0039-z.
Gerin, M., D. Mitchell, and D. Kennedy. 2019. “CSA-S6-19 section 4-the 2nd generation of performance based seismic design provisions.” In Proc., 12th Canadian Conf. on Earthquake Engineering. Vancouver, BC: The Canadian Association for Earthquake Engineering.
Gondia, A., M. Ezzeldin, and W. El-Dakhakhni. 2020. “Mechanics-guided genetic programming expression for shear-strength prediction of squat reinforced concrete walls with boundary elements.” J. Struct. Eng. 146 (11): 04020223. https://doi.org/10.1061/(asce)st.1943-541x.0002734.
Hewes, J. T., and M. J. N. Priestley. 2002. “Seismic tests on precast segmental concrete columns with unbonded tendons.” Bridge Struct. 3 (3–4): 215–227.
Jeon, J. S., A. Shafieezadeh, and R. Desroches. 2014. “Statistical models for shear strength of RC beam-column joints using machine-learning techniques.” Earthquake Eng. Struct. Dyn. 43 (14): 2075–2095. https://doi.org/10.1002/eqe.2437.
Karsan, I. D., and J. O. Jirsa. 1969. “Behavior of concrete under compressive loadings.” J. Struct. Div. 95 (12): 2543–2564. https://doi.org/10.1061/JSDEAG.0002424.
Khaleghi, B., E. Schultz, S. Seguirant, L. Marsh, O. Haraldsson, M. Eberhard, and J. Stanton. 2012. “Accelerated bridge construction in Washington state: From research to practice.” PCI J. 57 (4): 34–49. https://doi.org/10.15554/pcij.09012012.34.49.
Khan, M. A. 2014. Accelerated bridge construction: Best practices and techniques. Amsterdam, Netherlands: Elsevier.
Kim, T. H., Y. J. Kim, H. T. Kang, and H. M. Shin. 2007. “Performance assessment of reinforced concrete bridge columns using a damage index.” Can. J. Civ. Eng. 34 (7): 843–855. https://doi.org/10.1139/l07-003.
Koza, J. R. 1992. Vol. 2 of Genetic programming: On the programming of computers by means of natural selection. Cambridge, MA: MIT Press.
Kwan, W. P., and S. L. Billington. 2003. “Unbonded posttensioned concrete bridge piers. I: Monotonic and cyclic analyses.” J. Bridge Eng. 8 (2): 92–101. https://doi.org/10.1061/(asce)1084-0702(2003)8:2(92).
Lee, J., and G. L. Fenves. 1998. “Plastic-damage model for cyclic loading of concrete structures.” J. Eng. Mech. 124 (8): 892–900. https://doi.org/10.1061/(asce)0733-9399(1998)124:8(892).
Lee, T. H., and K. M. Mosalam. 2005. “Seismic demand sensitivity of reinforced concrete shear-wall building using FOSM method.” Earthquake Eng. Struct. Dyn. 34 (14): 1719–1736. https://doi.org/10.1002/eqe.506.
Lehman, D., J. Moehle, S. Mahin, A. Calderone, and L. Henry. 2004. “Experimental evaluation of the seismic performance of reinforced concrete bridge columns.” J. Struct. Eng. 130 (6): 869–879. https://doi.org/10.1061/(ASCE)0733-9445(2004)130.
Li, C., H. Hao, X. Zhang, and K. Bi. 2018. “Experimental study of precast segmental columns with unbonded tendons under cyclic loading.” Adv. Struct. Eng. 21 (3): 319–334. https://doi.org/10.1177/1369433217717119.
Lim, J. C., T. Ozbakkaloglu, A. Gholampour, T. Bennett, and R. Sadeghi. 2016. “Finite-element modeling of actively confined normal-strength and high-strength concrete under uniaxial, biaxial, and triaxial compression.” J. Struct. Eng. 142 (11): 04016113. https://doi.org/10.1061/(asce)st.1943-541x.0001589.
Lubliner, J., J. Oliver, S. Oller, and E. Oñate. 1989. “A plastic-damage model for concrete.” Int. J. Solids Struct. 25 (3): 299–326. https://doi.org/10.1016/0020-7683(89)90050-4.
Luo, H., and S. G. Paal. 2021. “Metaheuristic least squares support vector machine-based lateral strength modelling of reinforced concrete columns subjected to earthquake loads.” Structures 33: 748–758. https://doi.org/10.1016/j.istruc.2021.04.048.
Luong, C. N., C. Yang, and M. Ezzeldin. 2022. “Data-driven models for predicting drift ratio limits of segmental post-tensioned precast concrete bridge piers.” In Proc., Annual Conf. on Canadian Society of Civil Engineering. Montreal: Canadian Society for Civil Engineering (CSCE).
Mackie, K. R., and B. Stojadinovic. 2007. “Performance-based seismic bridge design for damage and loss limit states.” Pac. Conf. Earthquake Eng. 36 (13): 1953–1971. https://doi.org/10.1002/eqe.
Mander, J. B. 1983. Seismic design of bridge piers. Canterbury, New Zealand: Univ. of Canterbury.
Mander, J. B., M. J. N. Priestley, and R. Park. 1988. “Theoretical stress-strain model for confined concrete.” J. Struct. Eng. 114 (8): 1804–1826.
Mangalathu, S., G. Heo, and J. S. Jeon. 2018. “Artificial neural network based multi-dimensional fragility development of skewed concrete bridge classes.” Eng. Struct. 162: 166–176. https://doi.org/10.1016/j.engstruct.2018.01.053.
Marriott, D., S. Pampanin, and A. Palermo. 2009. “Quasi-static and pseudo-dynamic testing of unbonded post-tensioned rocking bridge piers with external replaceable dissipaters.” Earthquake Eng. Struct. Dyn. 38: 331–354. https://doi.org/10.1002/eqe.857.
Marsh, M. L., J. F. Stanton, M. Wernli, M. O. Eberhard, B. E. Garrett, and M. D. Weinert. 2011. Vol. 698 of Application of accelerated bridge construction connections in moderate-to-high seismic regions. Washington, DC: Transportation Research Board.
Marsh, M. L., and S. J. Stringer. 2013. Performance-based seismic bridge design. Washington, DC: Transportation Research Board.
Musselman, E., M. Fournier, P. McAlpine, and S. Sritharan. 2015. “Behavior of unbonded post-tensioning monostrand anchorage systems under short duration, high amplitude cyclical loading.” Eng. Struct. 104: 116–125. https://doi.org/10.1016/j.engstruct.2015.09.022.
NZT (Transit New Zealand). 2016. New Zealand bridge manual. Wellington, New Zealand: NZT.
Ou, Y. C. 2007. “Precast segmental post-tensioned concrete bridge columns for seismic regions.” Ph.D. thesis, Dept of Civil, Structural, and Environmental Engineering, State Univ. of New York at Buffalo.
Ou, Y. C., M.-S. Tsai, K. C. Chang, and G. C. Lee. 2010a. “Cyclic behavior of precast segmental concrete bridge columns with high performance or conventional steel reinforcing bars as energy dissipation bars.” Earthquake Eng. Struct. Dyn. 39: 1181–1198. https://doi.org/10.1002/eqe.986.
Ou, Y. C., P. H. Wang, M. s. Tsai, K. C. Chang, and G. C. Lee. 2010b. “Large-scale experimental study of precast segmental unbonded posttensioned concrete bridge columns for seismic regions.” J. Struct. Eng. 136 (3): 255–264. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000110.
Palermo, A., S. Pampanin, and D. Marriott. 2007. “Design, modeling, and experimental response of seismic resistant bridge piers with posttensioned dissipating connections.” J. Struct. Eng. 133 (11): 1648–1661. https://doi.org/10.1061/(asce)0733-9445(2007)133:11(1648).
Pampanin, S., M. J. N. Priestley, and S. Sritharan. 2001. “Analytical modelling of the seismic behaviour of precast concrete frames designed with ductile connections.” J. Earthquake Eng. 5 (3): 329–367.
PCI (Precast/Prestressed Concrete Institute). 2010. “Design aid 15.3.3 typical design stress-strain curve, 7-wire low-relaxation prestressing strand.” In PCI design handbook. 7th ed. 15–32. Chicago: PCI.
Pérez, J. L., A. Cladera, J. R. Rabuñal, and F. Martínez-Abella. 2012. “Optimization of existing equations using a new genetic programming algorithm: Application to the shear strength of reinforced concrete beams.” Adv. Eng. Software 50 (1): 82–96. https://doi.org/10.1016/j.advengsoft.2012.02.008.
Popovics, S. 1973. “A numerical approach to the complete stress-strain curve of concrete.” Cem. Concr. Res. 3 (5): 583–599. https://doi.org/10.1016/0008-8846(73)90096-3.
Priestley, M. N., F. Seible, and G. M. Calvi. 1996. Seismic design and retrofit of bridges. Hoboken, NJ: Wiley.
Reed-Hill, R. E., R. Abbaschian, and R. Abbaschian. 1973. Physical metallurgy principles. New York: Van Nostrand.
Roh, H., and A. M. Reinhorn. 2009. “Analytical modeling of rocking elements.” Eng. Struct. 31 (5): 1179–1189. https://doi.org/10.1016/j.engstruct.2009.01.014.
Saatcioglu, M., and S. R. Razvi. 1992. “Strength and ductility of confined concrete.” J. Struct. Eng. 118 (6): 1590–1607. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:6(1590).
Shokrgozar, A., M. Torabi, A. Ebrahimpour, and M. Mashal. 2020. “Seismic analysis of a precast pier system in ABC.” In Structures Congress, edited by J. G. Soules, 172–182. Reston, VA: ASCE.
Siam, A., M. Ezzeldin, and W. El-Dakhakhni. 2019. “Machine learning algorithms for structural performance classifications and predictions: Application to reinforced masonry shear walls.” Struct. 22: 252–265. https://doi.org/10.1016/j.istruc.2019.06.017.
Sideris, P., A. J. Aref, and A. Filiatrault. 2014. “Quasi-static cyclic testing of a large-scale hybrid sliding-rocking segmental column with slip-dominant joints.” J. Bridge Eng. 19 (10): 04014036. https://doi.org/10.1061/(asce)be.1943-5592.0000605.
Sinha, B. P., K. H. Gerstle, and L. G. Tulin. 1964. “Stress-strain relations for concrete under cyclic loading.” ACI Struct. J. 61 (2): 195–212.
To, D., and J. Moehle. 2017. “Seismic performance of beams with high-strength reinforcement.” In Proc., 16th World Conf. on Earthquake Engineering. Tokyo: International Association for Earthquake Engineering.
Walsh, K. Q., and Y. C. Kurama. 2010. “Behavior of unbonded posttensioning monostrand anchorage systems under monotonic tensile loading.” PCI J. 55 (1): 97–117. https://doi.org/10.15554/pcij.01012010.97.117.
Wang, H. C., Y. C. Ou, K. C. Chang, and G. C. Lee. 2008. “Large-scale seismic tests of tall concrete bridge columns with precast segmental construction.” Earthquake Eng. Struct. Dyn. 37 (12): 1449–1465. https://doi.org/10.1002/eqe.
Wang, J., Z. Wang, Y. Tang, T. Liu, and J. Zhang. 2018. “Cyclic loading test of self-centering precast segmental unbonded posttensioned UHPFRC bridge columns.” Bull. Earthquake Eng. 16 (11): 5227–5255. https://doi.org/10.1007/s10518-018-0331-y.
Yang, C. 2019. “Reducing earthquake-induced damage to precast concrete bridge piers.” Ph.D. thesis, Dept of Civil, Structural and Environmental Engineering, State Univ. of New York at Buffalo.
Yang, C., and P. Okumus. 2017. “Ultrahigh-performance concrete for posttensioned precast bridge piers for seismic resilience.” J. Struct. Eng. 143 (12): 1–13. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001906.
Zhang, J., G. Ma, Y. Huang, J. Sun, F. Aslani, and B. Nener. 2019. “Modelling uniaxial compressive strength of lightweight self-compacting concrete using random forest regression.” Constr. Build. Mater. 210: 713–719. https://doi.org/10.1016/j.conbuildmat.2019.03.189.
Zhang, Q., and M. S. Alam. 2020a. “Drift-based design criteria for reinforced concrete columns and hybrid rocking columns.” In IABSE-JSCE Joint Conf. on Advances in Bridge Engineering. Zürich, Switzerland: International Association for Bridge and Structural Engineering and Japan Society of Civil Engineers.
Zhang, Q., and M. S. Alam. 2020b. “State-of-the-art review of seismic-resistant precast bridge columns.” J. Bridge Eng. 25 (10): 03120001. https://doi.org/10.1061/(asce)be.1943-5592.0001620.
Zhuo, W., T. Tong, and Z. Liu. 2019. “Analytical pushover method and hysteretic modeling of precast segmental bridge piers with high-strength bars based on cyclic loading test.” J. Struct. Eng. 145 (7): 04019050. https://doi.org/10.1061/(asce)st.1943-541x.0002318.
Information & Authors
Information
Published In
Journal of Bridge Engineering
Volume 28 • Issue 2 • February 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Apr 10, 2022
Accepted: Oct 3, 2022
Published online: Dec 13, 2022
Published in print: Feb 1, 2023
Discussion open until: May 13, 2023
ASCE Technical Topics:
- Analysis (by type)
- Bridge engineering
- Bridges
- Bridges (by material)
- Computer programming
- Computing in civil engineering
- Concrete
- Concrete bridges
- Engineering fundamentals
- Engineering materials (by type)
- Hydraulic engineering
- Hydraulic structures
- Materials engineering
- Materials processing
- Mathematics
- Parameters (statistics)
- Piers
- Ports and harbors
- Post tensioning
- Post-tensioned concrete
- Precast concrete
- Prestressed concrete
- Sensitivity analysis
- Statistics
- Structural engineering
- Water and water resources
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