Seismic vulnerability analysis of bridge structure based on BOX-COX transformation

PDF(1806 KB)

Journal of Vibration and Shock ›› 2021, Vol. 40 ›› Issue (1) : 192-198.

ZHANG Penghui, GUO Junjun, ZHOU Lianxu, YUAN Wancheng

Author information +

History +

Abstract

The cloud chart method is one of the main methods for calculating theoretical vulnerability curves, but its assumptions of linearity, normality and homoscedasticity to simplify calculation often deviate from the reality. Here, in order to solve this problem, a new vulnerability analysis method was proposed by combining BOX-COX transformation and Monte Carlo sampling technique. It was shown that this method doesn’t increase the number of nonlinear time history analysis, and it doesn’t need to satisfy 3 basic assumptions of the cloud chart method. A 3-span pre-stressed concrete continuous girder bridge was taken as an example to verify the effectiveness of the proposed method. The calculation results obtained with the proposed method were compared to those with the cloud chart method taking significance levels of determination coefficient, kernel density estimation curve, and rank-correlation coefficient as the evaluation indexes. Results showed that BOX-COX transformation can improve linearity, normality and homoscedasticity of the probabilistic seismic demand model (PSDM) to ensure the correctness of vulnerability analysis results; when PSDM has heteroscedasticity, using the cloud chart method can cause distortion of structural vulnerability curve calculation results, and the higher the damage degree corresponding to the limit state, the more obvious the vulnerability curve deviates from the reality.

Key words

BOX-COX transformation / Monte Carlo sampling / vulnerability analysis / probabilistic seismic demand model (PSDM) / cloud chart method

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

ZHANG Penghui, GUO Junjun, ZHOU Lianxu, YUAN Wancheng. Seismic vulnerability analysis of bridge structure based on BOX-COX transformation[J]. Journal of Vibration and Shock, 2021, 40(1): 192-198

References

[1] NIELSON B G, DESROCHES R. Analytical seismic fragility curves for typical bridges in the central and southeastern united states [J]. Earthquake Spectra, 2007, 23(3): 615-633.
[2] MUNTASIR BILLAH A H M, SHAHRIA ALAM M. Seismic fragility assessment of highway bridges: A state-of-the-art review [J]. Structure and Infrastructure Engineering, 2015, 11(6): 804-832.
[3] 张菊辉, 管仲国. 规则连续梁桥地震易损性研究 [J]. 振动与冲击, 2014, 33(20): 140-145. (ZHANG Juhui, GUAN Zhongguo. Seismic vulnerability analysis of regular continuous girder bridges [J]. Journal of Vibration and Shock, 2014, 33(20): 140-145.)
[4] BAKER J W. Probabilistic structural response assessment using vector-valued intensity measures [J]. Earthquake Engineering & Structural Dynamics, 2007, 36(13): 1861-1883.
[5] KARAMLOU A, BOCCHINI P. Quantification of the approximations introduced by assumptions made on marginal distributions of the demand for highway bridge fragility analysis [C]// Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM 2014), 2014: 13-16.
[6] MACKIE K, STOJADINOVIĆ B. Comparison of incremental dynamic, cloud, and stripe methods for computing probabilistic seismic demand models [C]//Structures Congress 2005: Metropolis and Beyond. 2005: 1-11.
[7] PADGETT J E, NIELSON B G, DESROCHES R. Selection of optimal intensity measures in probabilistic seismic demand models of highway bridge portfolios [J]. Earthquake Engineering & Structural Dynamics, 2008, 37(5): 711-725.
[8] PAN Y, AGRAWAL A K, GHOSN M. Seismic fragility of continuous steel highway bridges in new york state [J]. Journal of Bridge Engineering, 2007, 12(6): 689-699.
[9] MACKIE K R, STOJADINOVIĆ B. Fragility basis for california highway overpass bridge seismic decision making [R]: Pacific Earthquake Engineering Research Center, 2005.
[10] MACKIE K, STOJADINOVIC B. Relation between probabilistic seismic demand analysis and incremental dynamic analysis [C]// 7th US National Conference on Earthquake Engineering, 2002: 21-25.
[11] CORNELL C A, JALAYER F, HAMBURGER RONALD O, et al. Probabilistic basis for 2000 sac federal emergency management agency steel moment frame guidelines [J]. Journal of Structural Engineering, 2002, 128(4): 526-533.
[12] KARAMLOU A, BOCCHINI P. Optimal bridge restoration sequence for resilient transportation networks [C]//Structures Congress 2014. 2014: 1437-1447.
[13] BOX G E P, COX D R. An analysis of transformations [J]. Journal of the Royal Statistical Society: Series B (Methodological), 1964, 26(2): 211-243.
[14] 何晓群. 应用回归分析(r语言版) [M] 电子工业出版社. 北京. 2017: 115-119+192. (HE Xiaoqun. Applied regression analysis (R language edition) [M]. Beijing: Publishing House of Electronics Industry, 2017. 115-119+192.)
[15] COLLINS S. Prediction techniques for box–cox regression models [J]. Journal of Business & Economic Statistics, 1991, 9(3): 267-277.
[16] NIELSON B G, DESROCHES R. Seismic fragility methodology for highway bridges using a component level approach [J]. Earthquake Engineering & Structural Dynamics, 2007, 36(6): 823-839.
[17] 钟剑, 庞于涛, 曹飒飒, et al. 基于构件的rc连续梁桥地震体系易损性分析 [J]. 同济大学学报(自然科学版), 2015, 43(02): 193-198. (ZHONG Jian, Pang Yutao, CAO Sasa, et al. Seismic fragility methodology for RC continuous bridges based on components correlation [J]. Journal of Tongji University (Natural S cience), 2015, 43(02): 193-198.)
[18] SCOTT B, PARK R, PRIESTLEY M. Stress-strain behavior of concrete confined by overlapping hoops at low and high strain ratio rates [D]. Lulea: Lulea University of Technology, 1989.
[19] MUTHUKUMAR S. A contact element approach with hysteresis damping for the analysis and design of pounding in bridges [D]. Atlanta: Georgia Institute of Technology, 2003.
[20] 郭军军, 钟剑, 袁万城, et al. 考虑桥台性能影响的连续梁桥地震易损性分析 [J]. 哈尔滨工程大学学报, 2017, 38(04): 532-537. (GUO Junjun, ZHONG Jian, YUAN Wancheng, et al. Seismic fragility analysis of a continuous bridge considering the performance of abutments [J]. Journal of Harbin Engineering University, 2017, 38(04): 532-537.)
[21] NIELSON B G. Analytical fragility curves for highway bridges in moderate seismic zones [D]. Atlanta: Georgia Institute of Technology, 2005.
[22] BAKER J W, LEE C. An improved algorithm for selecting ground motions to match a conditional spectrum [J]. Journal of Earthquake Engineering, 2018, 22(4): 708-723.
[23] 焦驰宇. 基于性能的大跨斜拉桥地震易损性分析 [D]: 同济大学, 2008. (JIAO Chiyu. Seismic fragility analysis of long-span cablestayed bridges [D]. Shanghai: Tongji University, 2008.)
[24] BOORE D M, STEWART J P, SEYHAN E, et al. Nga-west2 equations for predicting pga, pgv, and 5% damped psa for shallow crustal earthquakes [J]. Earthquake Spectra, 2013, 30(3): 1057-1085.
[25] RIDDELL R. On ground motion intensity indices [J]. Earthquake Spectra, 2007, 23(1): 147-173.
[26] MOSCHONAS I F, KAPPOS A J, PANETSOS P, et al. Seismic fragility curves for greek bridges: Methodology and case studies [J]. Bulletin of Earthquake Engineering, 2008, 7(2): 439-468.
[27] 谷音, 黄怡君, 卓卫东. 高墩大跨连续刚构桥梁地震易损性分析 [J]. 地震工程与工程振动, 2011, 31(02): 91-97. (GU Yin, HUANG Yijun, ZHUO Weidong. Study on seismic vulnerability of long-span continuous rigid frame bridge with high piers [J]. Journal of Earthquake Engineering and Engineering Vibration, 2011, 31(02): 91-97.)
[28] 吴文朋, 李立峰. 桥梁结构系统地震易损性分析方法研究 [J]. 振动与冲击, 2018, 37(21): 273-280. (wu Wenpeng, LI Lifeng. System seismic fragility analysis methods for bridge structures [J]. Journal of Vibration and Shock, 2018, 37(21): 273-280)
[29] HWANG H, LIU J B, CHIU Y H. Seismic fragility analysis of highway bridges [R]. Urbana: Mid-America Earthquake Center, 2001.
[30] FENG R, WANG X, YUAN W, et al. Impact of seismic excitation direction on the fragility analysis of horizontally curved concrete bridges [J]. Bulletin of Earthquake Engineering, 2018, 16(10): 4705-4733.
[31] JEON J-S, SHAFIEEZADEH A, LEE D H, et al. Damage assessment of older highway bridges subjected to three-dimensional ground motions: Characterization of shear–axial force interaction on seismic fragilities [J]. Engineering Structures, 2015, 87: 47-57.