Probabilistic seismic demand modeling of continuous concrete box-girder bridges: emphasizing hysteretic energy and residual demands

Abstract

Energy-based seismic design is an innovative approach that systematically incorporates energy-related demands of ground motion to analyze and design structures, particularly in near-field regions. This study investigates the seismic behavior of three multi-span continuous concrete box-girder (MSCC-BG) bridges subjected to 328 ground motions, including pulse-like and non-pulse records, using the OpenSees framework. Twenty-eight energy-related, residual, and displacement-based demands and thirty-six intensity measures (IMs) from horizontal and vertical earthquake components are analyzed. Key correlations between these demands and various IMs are identified, focusing on the most critical demands under pulse-like earthquakes. A multi-variable probabilistic seismic demand model (PSDM) is developed using Lasso and stepwise regression for critical demands, such as column hysteretic energy and residual drift ratio. While the multi-variable PSDM demonstrates improved prediction accuracy compared to single-IM models, the improvement for the examined demands is modest. These findings highlight the importance of incorporating horizontal and vertical ground motion IMs in PSDMs to enhance predictive accuracy and provide a foundation for further refinement in energy-based seismic design methodologies.

Keywords

Box-girder highway bridges / Near-field ground motion / Energy-related demands / Residual displacement / Lasso regression / Stepwise regression / Engineering / Civil Engineering / Earth Sciences / Geophysics

References

[1] Akaike, Hirotogu. “Information Theory and an Extension of the Maximum Likelihood Principle.” In Selected Papers of Hirotugu Akaike, pp. 199–213. New York, NY: Springer New York, 1998. https://doi.org/10.1007/978-1-4612-1694-0_15

[2] American Concrete Institute. 2014. Building Code Requirements for Structural Concrete (ACI 318–14): Commentary on Building Code Requirements for Structural Concrete (ACI 318R-14): An ACI Report. American Concrete Institute. ACI

[3] Arias, A. 1970. “A Measure of Earthquake Intensity.” In Seismic Design for Nuclear Plants, 438–483

[4] ArroyoD, OrdazM. On the Estimation of Hysteretic Energy Demands for SDOF Systems. Earthquake Eng Struct Dynam, 2007, 36152365-2382.

[5] ASCE 7–16 Minimum Design Loads and Associated Criteria for Buildings and Other Structures, American Society of Civil Engineers, 2017

[6] Baker, J. W., T. Lin, S. K. Shahi, and N. Jayaram. 2011. “New Ground Motion Selection Procedures and Selected Motions for the PEER Transportation Research Program.” PEER Report, 3

[7] Bianchini, M., P. Diotallevi, and J. W. Baker. 2009. “Prediction of Inelastic Structural Response Using an Average of Spectral Accelerations.” In 10th International Conference on Structural Safety and Reliability (ICOSSAR09), Osaka, Japan.fbbs

[8] BommerJJ, Martínez-PereiraA. The Effective Duration of Earthquake Strong Motion. J Earthquake Eng, 1999, 302127-172.

[9] Caltrans. 2007. Reinforced Concrete Bridge Capacity Assessment Training Manual. Structure Maintenance and Investigations Rep., Sacramento, CA

[10] Chang, G. A., and J. B. Mander. 1994. “Seismic Energy-Based Fatigue Damage Analysis of Bridge Columns: Part I-Evaluation of Seismic Capacity.” Buffalo, NY: National Center for Earthquake Engineering Research

[11] ChatterjeeS, HadiASRegression Analysis by Example, 2015John Wiley & Sons

[12] Choi, E. 2002. “Seismic Analysis and Retrofit of Mid-America Bridges.” Doctoral dissertation, School of Civil and Environmental Engineering, Georgia Institute of Technology. https://smartech.gatech.edu/handle/1853/21538

[13] CornellCA, JalayerF, HamburgerRO, FoutchDA. Probabilistic Basis for 2000 SAC Federal Emergency Management Agency Steel Moment Frame Guidelines. J Struct Eng, 2002, 1284526-533.

[14] DabaghiMNStochastic Modeling and Simulation of Near-Fault Ground Motions for Performance-Based Earthquake Engineering, 2014BerkeleyUniversity of California

[15] DaiK, WangJ, LiB, HongHP. Use of Residual Drift for Post-Earthquake Damage Assessment of R.C. Buildings. Eng Struct, 2017, 147: 242-255.

[16] DecaniniLD, MollaioliF. An Energy-Based Methodology for the Assessment of Seismic Demand. Soil Dyn Earthq Eng, 2001, 212113-137.

[17] EslamniaH, MalekzadehH, JalaliSA, MoghadamAS. Seismic Energy Demands and Optimal Intensity Measures for Continuous Concrete Box-Girder Bridges. Soil Dyn Earthq Eng, 2023, 165. 107657

[18] FajfarP, VidicT. Consistent Inelastic Design Spectra: Hysteretic and Input Energy. Earthquake Eng Struct Dynam, 1994, 235523-537.

[19] FayazJ, MedallaM, ZareianF. Sensitivity of the Response of Box-Girder Seat-Type Bridges to the Duration of Ground Motions Arising from Crustal and Subduction Earthquakes. Eng Struct, 2020, 219. 110845

[20] Filippou, F. C., E. P. Popov, and V. V. Bertero. 1983. “Effects of Bond Deterioration on Hysteretic Behavior of Reinforced Concrete Joints.”

[21] GentileR, GalassoC. Hysteretic Energy-Based State-Dependent Fragility for Ground-Motion Sequences. Earthquake Eng Struct Dynam, 2020, 5041187-1203.

[22] GuoJWW, ChristopoulosC. A Probabilistic Framework for Estimating the Residual Drift of Idealized SDOF Systems of Non-Degrading Conventional and Damped Structures. Earthquake Eng Struct Dynam, 2018, 472479-496.

[23] GuoJ, AlamMS, WangJ, LiS, YuanW. Optimal Intensity Measures for Probabilistic Seismic Demand Models of a Cable-Stayed Bridge Based on Generalized Linear Regression Models. Soil Dyn Earthq Eng, 2020, 131. 106024

[24] Housner, G. 1956. “Limit Design of Structures to Resist Earthquakes.” In Proceedings of the 1st World Conference on Earthquake Engineering, Berkeley, CA, USA, June 1956

[25] HousnerGW. Behavior of Structures During Earthquakes. J Eng Mech Div, 1959, 854109-130.

[26] Jalali SA, Eslamnia H, Malekzadeh H (2021) Commits to OpenSees in GitHub Repository. https://github.com/OpenSeesHouse/OpenSeesH. Accessed 20 Apr 2021

[27] JamesG, WittenD, HastieT, TibshiraniRAn Introduction to Statistical Learning, 2013New YorkSpringer.

[28] KawashimaK, TakahashiY, GeH, WuZ, ZhangJ. Reconnaissance Report on Damage of Bridges in 2008 Wenchuan, China, Earthquake. J Earthquake Eng, 2009, 137965-996.

[29] KramerSLGeotechnical Earthquake Engineering, 1996New Jersey, USAPrentice-Hall

[30] LeeCS, JeonJS. Probabilistic Residual Deformation Prediction Model for Rectangular Reinforced Concrete Columns. Earthquake Eng Struct Dynam, 2022, 5191994-2015.

[31] LiS, WangJQ, AlamMS. Seismic Performance Assessment of a Multi-Span Continuous Isolated Highway Bridge with Super Elastic Shape Memory Alloy Reinforced Piers and Restraining Devices. Earthquake Eng Struct Dynam, 2021, 502673-691.

[32] LiuTT, LuDG, YuXH. Development of a Compound Intensity Measure Using Partial Least-Squares Regression and Its Statistical Evaluation Based on Probabilistic Seismic Demand Analysis. Soil Dyn Earthq Eng, 2019, 125. 105725

[33] Malekzadeh H, Hosseini M, Abbasi H, Aziminejad A, Adib Ramazani M (2021) Developing a multi-variable vulnerability function for a class of multi-span continuous concrete box-girder highway bridges with emphasis on near-field earthquakes. Eur J Environ Civ Eng 2021:1–37. https://doi.org/10.1080/19648189.2021.1899991

[34] ManfrediG. Evaluation of Seismic Energy Demand. Earthquake Eng Struct Dynam, 2001, 304485-499.

[35] McKennaF. OpenSees: A Framework for Earthquake Engineering Simulation. Computing in Science & Engineering, 2011, 13458-66.

[36] Megally, S. H., P. F. Silva, and F. Seible. 2002. “Seismic Response of Sacrificial Exterior Keys in Bridge Abutments.”

[37] Menegotto, M. 1973. “Method of Analysis for Cyclically Loaded R.C. Plane Frames, Including Changes in Geometry and Non-Elastic Behavior of Elements under Combined Normal Force and Bending.” In Proc. of IABSE Symposium on Resistance and Ultimate Deformability of Structures Acted on by Well-Defined Repeated Loads, 15–22

[38] MuthukumarS, DesRochesR. A Hertz Contact Model with Nonlinear Damping for Pounding Simulation. Earthquake Eng Struct Dynam, 2006, 357811-828.

[39] NBI (National Bridge Inventory). 2010. “National Bridge Inventory Data.” U.S. Dept. of Transportation, Federal Highway Administration, Washington, DC

[40] Nielson, B. G. 2005. “Analytical Fragility Curves for Highway Bridges in Moderate Seismic Zones.” Doctoral dissertation, Georgia Institute of Technology. https://smartech.gatech.edu/handle/1853/7542

[41] NIST, G. 2011. “GCR 11–917–15: Selecting and Scaling Earthquake Ground Motions for Performing Response-History Analyses.”

[42] Nuttli, O. W. 1979. “The Relation of Sustained Maximum Ground Acceleration and Velocity to Earthquake Intensity and Magnitude.” Report No. S-73–1, U.S. Army Waterways Experimental Station, Vicksburg, MS

[43] Ramanathan, K. N. 2012. “Next-Generation Seismic Fragility Curves for California Bridges Incorporating the Evolution in Seismic Design Philosophy.” Doctoral dissertation, Georgia Institute of Technology. https://smartech.gatech.edu/handle/1853/44883?show=full

[44] RamanathanK, PadgettJE, DesRochesR. Temporal Evolution of Seismic Fragility Curves for Concrete Box-Girder Bridges in California. Eng Struct, 2015, 97: 29-46.

[45] ReedJW, KassawaraRP. A Criterion for Determining Exceedance of the Operating Basis Earthquake. Nucl Eng des, 1990, 1232–3387-396.

[46] RiddellR, GarciaJE. Hysteretic Energy Spectrum and Damage Control. Earthquake Eng Struct Dynam, 2001, 30121791-1816.

[47] Sarma, S. K., and K. S. Yang. 1987. “An Evaluation of Strong Motion Records and a New Parameter A95.” Earthquake Engineering & Structural Dynamics15 (1): 119–132. https://doi.org/10.1002/eqe.4290150109

[48] Schwarz, G. 1978. “Estimating the Dimension of a Model.” *The Annals of Statistics* 6 (2): 461–464

[49] SDC (2004). Seismic Design Criteria. Version 1.3. California Department of Transportation, Sacramento, CA

[50] SDC (2010). Seismic Design Criteria. Version 1.6. California Department of Transportation, Sacramento, CA

[51] ShamsabadiA, Khalili-TehraniP, StewartJP, TacirogluE. Validated Simulation Models for Lateral Response of Bridge Abutments with Typical Backfills. J Bridg Eng, 2010, 153302-311.

[52] ShamsabadiA, RollinsKM, KapuskarM. Nonlinear Soil–Abutment–Bridge Structure Interaction for Seismic Performance-Based Design. Journal of Geotechnical and Geo-Environmental Engineering, 2007, 1336707-720.

[53] SoleimaniF, HajializadehD. State-of-the-Art Review on Probabilistic Seismic Demand Models of Bridges: Machine-Learning Application. Infrastructures, 2022, 7564.

[54] SoleimaniF, LiuX. Artificial Neural Network Application in Predicting Probabilistic Seismic Demands of Bridge Components. Earthquake Eng Struct Dynam, 2021, 513612-629.

[55] SoleimaniF, VidakovicB, DesRochesR, PadgettJ. Identification of the Significant Uncertain Parameters in the Seismic Response of Irregular Bridges. Eng Struct, 2017, 141: 356-372.

[56] Tabachnick, B. G., and L. S. Fidell. 2013. Using Multivariate Statistics. Pearson

[57] TaniguchiM, TakewakiI. Bound of Earthquake Input Energy to Building Structure Considering Shallow and Deep Ground Uncertainties. Soil Dyn Earthq Eng, 2015, 77: 267-273.

[58] TibshiraniR. Regression Shrinkage and Selection via the Lasso: A Retrospective. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2011, 733273-282.

[59] Vidakovic, B. 2011. Statistics for Bioengineering Sciences: With MATLAB and WinBUGS Support. Springer Science

[60] Von Thun, J. L. 1988. “Earthquake Ground Motions for Design and Analysis of Dams.” In Earthquake Engineering and Soil Dynamics II - Recent Advances in Ground-Motion Evaluation

[61] WangX, ShafieezadehA, YeA. Optimal Intensity Measures for Probabilistic Seismic Demand Modeling of Extended Pile-Shaft-Supported Bridges in Liquefied and Laterally Spreading Ground. Bull Earthq Eng, 2018, 161229-257.

[62] WangY, ZhengZ, JiD, PanX, TianA. Machine Learning-Driven Probabilistic Seismic Demand Model with Multiple Intensity Measures and Applicability in Seismic Fragility Analysis for Nuclear Power Plants. Soil Dyn Earthq Eng, 2023, 171. 107966

[63] Wei B, Jia J, Bai Y, Du X, Guo B, Guo H (2023) Seismic Resilience Assessment of Bridges Considering Both Maximum and Residual Displacements. Eng Struct 291. https://doi.org/10.1016/j.engstruct.2023.116420

[64] XiangN, LiJ. Experimental and Numerical Study on Seismic Sliding Mechanism of Laminated Rubber Bearings. Eng Struct, 2017, 141: 159-174.

[65] ZhaiC, JiD, WenW, LiC, LeiW, XieL. Hysteretic Energy Prediction Method for Mainshock-Aftershock Sequences. Earthq Eng Eng Vib, 2018, 172277-291.

[66] ZhongJ, JeonJS, ShaoYH, ChenL. Optimal Intensity Measures in Probabilistic Seismic Demand Models of Cable-Stayed Bridges Subjected to Pulse-Like Ground Motions. J Bridge Eng, 2019, 24204018118.

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