Seismic performance assessment of subway station structures considering fuzzy probability of damage states
-
摘要: 在基于性能的地震工程理论框架下，地下结构易损性分析及抗震性能评价当中结构损伤状态的划分多采用确定性的损伤状态阈值。基于传统地下结构易损性分析框架基础上进一步提出了考虑损伤界限模糊性的地下结构易损性分析方法，以三层三跨地铁车站结构为例建立二维非线性土–结构相互作用分析模型，选取21条地表天然地震动反演到基岩面并调幅作为非线性增量动力分析的输入地震动，引入三角形和拟正态形隶属度函数计算不同损伤状态下最大层间位移角的隶属度得到不同地震动强度等级下的模糊失效概率，通过极大似然估计方法拟合计算结果并建立考虑损伤界限模糊性的地铁车站结构易损性曲线。分析结果表明：采用模糊性评价方法所给出的地下结构地震易损性曲线总体上更趋于安全；考虑损伤界限的模糊性，会增加结构地震易损性曲线的离散性；而且隶属度函数类型的选取对模糊地震易损性分析结果影响可忽略不计。Abstract: Quantification of structural damage states in the fragility analysis and seismic performance evaluation of underground structures usually adopts the deterministic threshold values, which is a limitation in the framework of performance-based seismic engineering. A new seismic fragility analysis method considering the fuzzy probability of damage states of the underground structures is proposed based on the fragility analysis framework of the traditional underground structures. A two-dimensional nonlinear finite element model for a three-story and three-span subway station structure is established fully considering the soil-structure interaction (SSI). The input ground motions used in the nonlinear incremental dynamic analysis of the SSI model are back-calculated from an ensemble of 21 actual earthquake records on the ground surfaces. The triangle and quasi-normal membership functions are introduced to compute the membership degrees of the maximum interlayer drift ratios for different damage states so as to derive the fuzzy failure probability under different intensity levels of ground motions. The maximum likelihood estimation method is used to fit the numerical results and establish the seismic fragility curves of subway station structures considering the fuzzy probability of damage states. The results of the numerical study indicate that the seismic fragility curves of the underground structures derived from the proposed method generally give a safer estimation of the seismic performance of the structures. The dispersions of the seismic fragility curves increase with the consideration of the fuzzy probability of damage states. Besides, the influences of the membership function types on the results of the fuzzy seismic fragility analysis can be ignored.
-
-
![]()
图 1 考虑损伤界限模糊性的地下结构地震易损性分析流程
Figure 1. Seismic fragility analysis of underground structures considering fuzzy probability of damage states
![]()
图 2 地铁车站结构横断面及有限元模型示意图
Figure 2. Schematic diagram of cross-section of subway station structures
![]()
图 4 三层三跨地铁车站结构IDA曲线
Figure 4. IDA curves of three-story and three-span metro station structures
![]()
图 5 本文基于MIDR的地铁车站结构损伤状态定义
Figure 5. Definition of damage states of subway station structures based on MIDR in this paper
![]()
图 6 MIDR的频率分布及损伤指标隶属度函数图
Figure 6. Probability distribution and membership function of MIDR
![]()
图 7 极大似然估计法拟合地铁车站结构地震易损性曲线
Figure 7. Seismic fragility curves of subway station structure using maximum likelihood estimation method
![]()
图 10 损伤界限模糊性对易损性分析的影响程度
Figure 10. Influence degrees of fuzzy damage states on fragility analysis
表 1 Ⅱ类场地土层物理参数
Table 1 Physical parameters of type Ⅱ site soil
土层序号 土类 土层厚度/m 密度/(kg·m-3) 剪切波速/(m·s-1) 1 人工填土 5.0 1750 180 2 粉质黏土 10.0 1900 250 3 细中砂 10.0 2000 300 4 细粉砂 15.0 2000 320 5 卵石 20.0 2280 500 
下载: 导出CSV
表 2 本文选用的地震动记录
Table 2 Ground motion records selected in this paper
序号 地震 台站 震中距/km PGA/g 1 San Fernando LA - Hollywood Stor FF 22.77 0.225 2 Friuli Italy-01 Tolmezzo 14.97 0.357 3 Imperial_Valley-06 Delta 22.03 0.236 4 Imperial_Valley-06 El Centro Array #11 12.56 0.367 5 Superstition Hills-02 El Centro Imp. Co. Cent 18.20 0.357 6 Superstition Hills-02 Poe Road (temp) 11.16 0.475 7 Loma Prieta Capitola 8.65 0.511 8 Loma Prieta Gilroy Array #3 12.23 0.559 9 Landers Coolwater 19.74 0.284 10 Landers Yermo Fire Station 23.62 0.245 11 Northridge-01 Beverly Hills - 14145 Mulhol 9.44 0.443 12 Northridge-01 Canyon Country - W Lost Cany 11.39 0.404 13 Kobe Japan Nishi-Akashi 7.08 0.483 14 Kobe Japan Shin-Osaka 19.14 0.225 15 Kocaeli Turkey Arcelik 10.56 0.210 16 Kocaeli Turkey Duzce 131.17 0.312 17 Chi-Chi Taiwan CHY101 9.94 0.340 18 Chi-Chi Taiwan TCU045 26.00 0.473 19 Duzce Turkey Bolu 12.02 0.740 20 Manjil Iran Abbar 12.55 0.515 21 Hector Mine Hector 10.35 0.265
下载: 导出CSV
表 3 单条地震动作用下的结构损伤评价矩阵（以PGA为0.4g时的序号21地震动为例）
Table 3 Evaluation matrices of structural damage under single strip ground motion
隶属度 基本完好 轻微破坏 中等破坏 严重破坏 倒塌 不考虑模糊性 0 0 0 1.00 0 三角形隶属度函数 0 0 0 0.69 0.31 拟正态形隶属度函数 0 0 0.01 0.72 0.27
下载: 导出CSV
表 4 考虑损伤界限模糊性计算的不同地震动强度下各损伤状态的出现概率和超越概率（以三角形隶属度函数为例）
Table 4 Occurrence and exceeding probabilities of damage states under different ground motion intensities calculated considering their fuzzy probability
(%) 损伤状态 峰值加速度（PGA） 0.05g 0.1g 0.2g 0.3g 0.4g 0.6g 0.8g 基本完好 67.76/100 32.79/100 7.85/100 4.48/100 3.06/100 0/100 0/100 轻微破坏 32.24/32.24 63.91/67.21 61.57/92.15 33.06/95.52 17.64/96.94 8.67/100 0.79/100 中等破坏 0/0 3.30/3.30 27.20/30.57 40.36/62.46 44.61/79.30 28.21/91.33 17.90/99.21 严重破坏 0/0 0/0 3.37/3.37 14.23/22.11 16.87/34.69 20.84/63.13 25.18/81.31 倒塌 0/0 0/0 0/0 7.87/7.87 17.82/17.82 42.29/42.29 56.13/56.13
下载: 导出CSV
表 5 不考虑损伤界限模糊性计算的不同地震动强度下各损伤状态的出现概率和超越概率
Table 5 Occurrence and exceeding probabilities of damage states under different ground motion intensities calculated considering their fuzzy probability
(%) 损伤状态 峰值加速度（PGA） 0.05g 0.1g 0.2g 0.3g 0.4g 0.6g 0.8g 基本完好 90.48/100 19.05/100 9.52/100 4.76/100 4.76/100 0/100 0/100 轻微破坏 9.52/9.52 80.95/80.95 57.14/95.24 23.81.6/95.2 4.76/95.24 4.76/100 0/100 中等破坏 0/0 0/0 28.57/71.43 47.62/66.7 47.62/90.48 19.05/95.24 14.29/100 严重破坏 0/0 0/0 4.76/4.8 9.52/23.81 19.05/42.86 28.57/76.19 19.05/85.71 倒塌 0/0 0/0 0/0 14.29/14.29 23.81/23.81 47.62/47.62 66.67/66.67 注：“/”左右侧分别为给定损伤等级出现概率和超越概率。
下载: 导出CSV
表 6 易损性曲线拟合参数
Table 6 Fitting parameters of fragility curves
拟合参数 轻微破坏 中等破坏 严重破坏 倒塌 Smi 模糊 0.071g 0.261g 0.492g 0.697g 不模糊 0.084g 0.244g 0.439g 0.613g β 模糊 0.807 0.532 0.543 0.567 不模糊 0.683 0.419 0.501 0.567
下载: 导出CSV
-
[1] 杜修力, 李 洋, 许成顺, 等. 1995年日本阪神地震大开地铁车站震害原因及成灾机理分析研究进展[J]. 岩土工程学报, 2018, 40(2): 223–236. http://manu31.magtech.com.cn/Jwk_ytgcxb/CN/abstract/abstract17276.shtml DU Xiu-li, LI Yang, XU Cheng-shun, et al. Review on damage causes and disaster mechanism of Daikai subway station during 1995 Osaka-Kobe Earthquake[J]. Chinese Journal of Geotechnical Engineering, 2018, 40(2): 223–236. (in Chinese) http://manu31.magtech.com.cn/Jwk_ytgcxb/CN/abstract/abstract17276.shtml
[2] TSINIDIS G, DE Silva F, ANASTASOPOULOS I, et al. Seismic behaviour of tunnels: from experiments to analysis[J]. Tunnelling and Underground Space Technology, 2020, 99: 103334. doi: 10.1016/j.tust.2020.103334
[3] ZHONG Z L, SHEN Y Y, ZHAO M, et al. Seismic fragility assessment of the Daikai subway station in layered soil[J]. Soil Dynamics and Earthquake Engineering, 2020, 132: 106044. doi: 10.1016/j.soildyn.2020.106044
[4] FEMA P58-1, Seismic Performance Assessment of Buildings[R]. Washington: Federal Emergency Management Agency, 2018.
[5] WILLIAMS M S, SEXSMITH R G. Seismic damage indices for concrete structures: a state-of-the-art review[J]. Earthquake Spectra, 1995, 11(2): 319–349. doi: 10.1193/1.1585817
[6] 黄忠凯, 张冬梅. 地下结构地震易损性研究进展[J]. 同济大学学报(自然科学版), 2021, 49(1): 49–59, 115. https://www.cnki.com.cn/Article/CJFDTOTAL-TJDZ202101007.htm HUANG Zhong-kai, ZHANG Dong-mei. Recent advance in seismic fragility research of underground structures[J]. Journal of Tongji University (Natural Science), 2021, 49(1): 49–59, 115. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TJDZ202101007.htm
[7] ARGYROUDIS S A, PITILAKIS K D. Seismic fragility curves of shallow tunnels in alluvial deposits[J]. Soil Dynamics and Earthquake Engineering, 2012, 35: 1–12. doi: 10.1016/j.soildyn.2011.11.004
[8] NGUYEN D D, PARK D, SHAMSHER S, et al. Seismic vulnerability assessment of rectangular cut-and-cover subway tunnels[J]. Tunnelling and Underground Space Technology, 2019, 86: 247–261 doi: 10.1016/j.tust.2019.01.021
[9] HE Z M, CHEN Q J. Vertical seismic effect on the seismic fragility of large-space underground structures[J]. Advances in Civil Engineering, 2019, 2019: 9650294.
[10] JIANG J W, EL Nggar H M, XU C S, et al. Effect of ground motion characteristics on seismic fragility of subway station[J]. Soil Dynamics and Earthquake Engineering, 2021, 143: 106618. doi: 10.1016/j.soildyn.2021.106618
[11] 钟紫蓝, 申轶尧, 郝亚茹, 等. 基于IDA方法的两层三跨地铁地下结构地震易损性分析[J]. 岩土工程学报, 2020, 42(5): 916–924. http://manu31.magtech.com.cn/Jwk_ytgcxb/CN/abstract/abstract18204.shtml ZHONG Zi-lan, SHEN Yi-yao, HAO Ya-ru, et al. Seismic fragility analysis of two-story and three-span metro station structures based on IDA method[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(5): 916–924. (in Chinese) http://manu31.magtech.com.cn/Jwk_ytgcxb/CN/abstract/abstract18204.shtml
[12] 钟紫蓝, 严智豪, 史跃波, 等. 基于IDA方法的地铁车站结构抗震性能评价[J]. 北京工业大学学报, 2021, 47(7): 680–690. https://www.cnki.com.cn/Article/CJFDTOTAL-BJGD202107003.htm ZHONG Zi-lan, YAN Zhi-hao, SHI Yue-bo, et al. Seismic performance evaluation of station structures based on IDA method[J]. Journal of Beijing University of Technology, 2021, 47(7): 680–690. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-BJGD202107003.htm
[13] 钟紫蓝, 申轶尧, 甄立斌, 等. 地震动强度参数与地铁车站结构动力响应指标分析[J]. 岩土工程学报, 2020, 42(3): 486–494. http://manu31.magtech.com.cn/Jwk_ytgcxb/CN/abstract/abstract18148.shtml ZHONG Zi-lan, SHEN Yi-yao, ZHEN Li-bin, et al. Ground motion intensity measures and dynamic response indexes of metro station structures[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(3): 486–494. (in Chinese) http://manu31.magtech.com.cn/Jwk_ytgcxb/CN/abstract/abstract18148.shtml
[14] LIU T, CHEN Z Y, YUAN Y, et al. Fragility analysis of a subway station structure by incremental dynamic analysis[J]. Advances in Structural Engineering, 2017, 20(7): 1111–1124. doi: 10.1177/1369433216671319
[15] DU X L, JIANG J W, EL NAGGAR M H, et al. Interstory drift ratio associated with performance objectives for shallow-buried multistory and span subway stations in inhomogeneous soil profiles[J]. Earthquake Engineering & Structural Dynamics, 2021, 50(2): 655–672.
[16] 杜修力, 蒋家卫, 许紫刚, 等. 浅埋矩形框架地铁车站结构抗震性能指标标定研究[J]. 土木工程学报, 2019, 52(10): 111–119, 128. https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201910012.htm DU Xiu-li, JIANG Jia-wei, XU Zi-gang, et al. Study on quantification of seismic performance index for rectangular frame subway station structure[J]. China Civil Engineering Journal, 2019, 52(10): 111–119, 128. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201910012.htm
[17] ZADEH L A. Fuzzy sets[J]. Information and Control, 1965, 8(3): 338–353.
[18] THINLEY K, HAO H. Seismic performance of reinforced concrete frame buildings in Bhutan based on fuzzy probability analysis[J]. Soil Dynamics and Earthquake Engineering, 2017, 92: 604–620.
[19] LI Z F, WU Z Y, CHEN J K, et al. Fuzzy seismic fragility analysis of gravity dams considering spatial variability of material parameters[J]. Soil Dynamics and Earthquake Engineering, 2021, 140: 106439.
[20] 王 媛, 李泽发, 吴震宇, 等. 考虑损伤状态阈值模糊性的重力坝地震易损性分析[J]. 工程科学与技术, 2020, 52(2): 110–120. https://www.cnki.com.cn/Article/CJFDTOTAL-SCLH202002014.htm WANG Yuan, LI Ze-fa, WU Zhen-yu, et al. Seismic fragility analysis of gravity dams considering the fuzziness of damage states thresholds[J]. Advanced Engineering Sciences, 2020, 52(2): 110–120. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-SCLH202002014.htm
[21] 何浩祥, 李瑞峰, 闫维明. 基于多元模糊评定的桥梁综合地震易损性分析[J]. 振动工程学报, 2017, 30(2): 270–279. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201702013.htm HE Hao-xiang, LI Rui-feng, YAN Wei-ming. Bridge seismic fragility analysis method based on multiple fuzzy evaluation[J]. Journal of Vibration Engineering, 2017, 30(2): 270–279. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201702013.htm
[22] GU X M, LU Y. A fuzzy-random analysis model for seismic performance of framed structures incorporating structural and non-structural damage[J]. Earthquake Engineering & Structural Dynamics, 2005, 34(10): 1305–1321.
[23] COLANGELO F. A simple model to include fuzziness in the seismic fragility curve and relevant effect compared with randomness[J]. Earthquake Engineering & Structural Dynamics, 2012, 41(5): 969–986.
[24] WU C Q, HAO H, ZHOU Y X. Fuzzy-random probabilistic analysis of rock mass responses to explosive loads[J]. Computers and Geotechnics, 1999, 25(4): 205–225.
[25] BAKER J W. Efficient analytical fragility function fitting using dynamic structural analysis[J]. Earthquake Spectra, 2015, 31(1): 579–599.
[26] SHINOZUKA M, FENG M Q, LEE J, et al. Statistical analysis of fragility curves[J]. Journal of Engineering Mechanics, 2000, 126(12): 1224–1231.
[27] STORN R, PRICE K. Differential evolution–A simple and efficient heuristic for global optimization over continuous spaces[J]. Journal of Global Optimization, 1997, 11: 341–359.
[28] 城市轨道交通结构抗震设计规范: GB 50909—2014[S]. 北京: 中国标准出版社, 2014. Code for Seismic Design of Urban Rail Transit Structures: GB50909—2014[S]. Beijing: China Planning Publishing House, 2014. (in Chinese)
[29] 曲 哲, 叶列平. 基于有效累积滞回耗能的钢筋混凝土构件承载力退化模型[J]. 工程力学, 2011, 28(6): 45–51. https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201106009.htm QU Zhe, YE Lie-ping. Strength deterioration model based on effective hysteretic energy dissipation for rc members under cyclic loading[J]. Engineering Mechanics, 2011, 28(6): 45–51. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201106009.htm
[30] BARDET JP, ICHII K, LIN CH. EERA—A computer program for equivalent-linear earthquake site response analyses[R]. LosAngeles: Department of Civil Engineering, University of Southern California, 2000.
[31] 杜修力, 许紫刚, 许成顺, 等. 基于等效线性化的土–地下结构整体动力时程分析方法研究[J]. 岩土工程学报, 2018, 40(12): 2155–2163. http://manu31.magtech.com.cn/Jwk_ytgcxb/CN/abstract/abstract17626.shtml DU Xiu-li, XU Zi-gang, XU Cheng-shun, et al. Time-history analysis method for soil-underground structure system based on equivalent linear method[J]. Chinese Journal of Geotechnical Engineering, 2018, 40(12): 2155–2163. (in Chinese) http://manu31.magtech.com.cn/Jwk_ytgcxb/CN/abstract/abstract17626.shtml
[32] TSINIDIS G, PITILAKIS K, TRIKALIOTI A D. Numerical simulation of round robin numerical test on tunnels using a simplified kinematic hardening model[J]. Acta Geotechnica, 2014, 9(4): 641–659.
[33] VAMVATSIKOS D, FRAGIADAKIS M. Incremental dynamic analysis for estimating seismic performance sensitivity and uncertainty[J]. Earthquake Engineering & Structural Dynamics, 2009: 141–163.
[34] FERSON S, TUCKER W T. Sensitivity analysis using probability bounding[J]. Reliability Engineering & System Safety, 2006, 91(10/11): 1435–1442.
计量
- 文章访问数: 0
- HTML全文浏览量: 0
- PDF下载量: 0
