Prediction method for seismic responses of underground structures in shaking table tests
-
摘要: 考虑土–结构相互作用的地下结构大型振动台试验成本极高,周期长,通常难以在短期内多次重复开展,为保证试验顺利开展,在试验前对其响应开展预测工作具有重要意义。采用完全数值模拟进行预测的方法在模型试验中已得到广泛的使用,但这种方法有时会产生较大误差,特别是对于强非线性的地下结构振动台模型试验。为提高预测方法的准确性,提出了一种整体式反应位移法数值模拟与自由场试验相结合的方法来预测地下模型结构在振动台试验中的地震响应。首先,介绍采用自由场振动台试验获取整体式反应位移法计算参数的方法,基于此,分别采用所提出方法和传统全数值方法预测某地铁车站结构模型在振动台试验中的地震响应,并将预测结果与后续试验结果进行对比。结果表明：所提出方法预测结果准确性较传统全数值方法预测结果准确性有大幅提升,方法可用以定性地预测后续试验结果,并可在一定程度上指导和完善后续试验方案。Abstract: The large-scale shaking table tests on an underground structure embedded in soil need extremely high cost and long test period, and usually they can hardly be frequently conducted in a short time. In order to successfully conduct the tests, predicting their responses before the tests is meaningful. The fully-numerical prediction method has been widely applied in model tests, but sometimes the results may have a great error, especially under the strong non-linear condition. To improve the accuracy of the prediction, the method combining both the numerical analysis and the free-field shaking table tests is proposed to predict the seismic responses of underground model structures in shaking table tests. The method using the data of the free-field tests to estimate the parameters for the Integral Responses Displacement Method is firstly introduced. The seismic responses of underground model structures in shaking table tests are predicted using the proposed method and the traditional fully-numerical prediction method. The predicted results are then compared with those by the subsequent tests. It is shown that the accuracy of the predicted results by the proposed method is greatly improved compared with that by the traditional fully numerical method. The proposed method can be used to qualitatively predict the seismic responses of underground structures in shaking table tests and further improve the design of the subsequent tests.
-
-
![]()
图 4 0.4g阶段台面地震记录及其正则化傅里叶频谱(Ampk为傅里叶幅值)
Figure 4. Input seismic motions and normalized Fourier amplitudes with peak amplitude Ampk
![]()
图 5 土体的相对位移与加速度
Figure 5. Relative displacements and accelerations of soil at structural region
![]()
图 6 地震荷载作用下土体的剪应力–剪应变关系(IM-12)
Figure 6. Shear stress vs. shear strain hysteresis of sand under seismic motion at IM-12
![]()
图 7 自由场试验中土体的动剪应变–动剪切模量比估算结果(CH08, 0.4g阶段)
Figure 7. Estimated shear modulus degradation relationships obtained from shaking table tests (CH08, 0.4g stage)
![]()
图 8 整体式反应位移法有限元计算模型
Figure 8. Finite element model of integral response deformation method
表 1 动力荷载的输入顺序
Table 1 Sequence of input motions
工况序号 动力荷载 峰值加速度/g 试验阶段/g IM-1 第一次白噪声 0.05 IM-2 第一次脉冲 0.05 IM-3 Loma Prieta (LP) 0.20 0.20 IM-4 Kobe 0.20 IM-5 汶川 0.20 IM-6 北京人工记录 0.20 IM-7 第二次白噪声 0.05 IM-8 第二次脉冲 0.05 IM-9 Loma Prieta (LP) 0.40 0.40 IM-10 Kobe 0.40 IM-11 汶川 0.40 IM-12 北京人工记录 0.40 IM-13 第三次白噪声 0.05 IM-14 第三次脉冲 0.05 
下载: 导出CSV
表 2 土层的最大剪切模量Gmax估算结果
Table 2 Maximum shear moduli of soil layers
(MPa) 工况 土层1 土层2 土层3 第一次脉冲 5.0 21.7 55.4 第二次脉冲 4.0 12.0 32.4
下载: 导出CSV
表 3 整体式反应位移法计算中所使用的荷载参数
Table 3 Loads for integral response displacement method
工况 土体相对位移/mm 加速度/(m·s-2) 结构周围剪应力/kPa 顶板 底板 顶板 底板 左墙 右墙 IM-6 0.47 3.00 2.73 -0.70 -2.63 -0.97 0.97 IM-12 -1.23 -3.46 -3.14 0.81 3.08 1.14 -1.14
下载: 导出CSV
表 4 土层的材料属性G
Table 4 Estimated dynamic shear moduli G of soil
(MPa) 工况 土层1(G1) 土层2(G2) 土层3(G3) IM-6 1.8 7.9 25.9 IM-12 1.5 2.7 9.2
下载: 导出CSV
表 5 结构的材料与截面属性
Table 5 Properties of material and section
密度/(kg·m-3) 弹性模量/GPa 截面厚度/cm 底板 中板 顶板 墙 柱 2400 13.8 2.7 1.3 2.3 2.3 0.259
下载: 导出CSV
表 6 预测与后续试验结果对比
Table 6 Comparison between predicted and subsequent test results
工况 后续试验结果 本文方法预测结果 全数值方法预测结果 IM-6 顶一底板水平相对位移/mm 0.35 0.45 0.15 顶板右端竖向位移/mm 0.05 0.09 0.02 地下一层右侧柱底应变/με 2.15 5.54 7.32 地下一层右侧柱顶应变/με 1.95 6.10 7.24 地下一层左侧墙底应变/με 0.27 0.70 1.96 地下一层左侧墙顶应变/με 0.86 0.46 1.35 地下一层右侧墙底应变/με 0.44 0.75 1.96 地下二层右侧柱底应变/με 3.02 3.43 6.41 地下二层左侧柱底应变/με 1.48 3.45 6.39 地下二层左侧墙顶应变/με 0.81 0.79 2.47 地下二层右侧墙顶应变/με 0.76 0.80 2.47 地下二层右侧墙底应变/με 1.21 1.22 3.08 IM-12 顶-底板水平相对位移/mm 0.88 0.75 0.35 顶板右端竖向位移/mm 1.10 0.15 0.10 地下一层右侧柱底应变/με 5.01 7.93 13.33 地下一层右侧柱顶应变/με 7.80 7.94 14.32 地下一层左侧墙底应变/με 1.06 0.93 2.61 地下一层左侧墙顶应变/με 2.59 0.51 1.20 地下一层右侧墙底应变/με 1.63 0.93 2.44 地下二层右侧柱底应变/με 2.82 3.62 10.32 地下二层左侧柱底应变/με 3.36 3.59 10.28 地下二层左侧墙顶应变/με 2.79 0.93 3.28 地下二层右侧墙顶应变/με 1.82 0.92 3.39 地下二层右侧墙底应变/με 1.38 1.44 4.27 注： 表中的位移和应变均为相应地震工况作用下的峰值大小。
下载: 导出CSV
-
[1] TANG B Z, LI X J, CHEN S, et al. Investigations of seismic response to an irregular-section subway station structure located in a soft clay site[J]. Engineering Structures, 2020, 217: 110799. doi: 10.1016/j.engstruct.2020.110799
[2] WU W F, GE S P, YUAN Y, et al. Seismic response of subway station in soft soil: Shaking table testing versus numerical analysis[J]. Tunnelling and Underground Space Technology, 2020, 100: 103389. doi: 10.1016/j.tust.2020.103389
[3] 禹海涛, 陈希卓, 李攀. 基于双台阵模拟地震空间差动效应的模型箱参数解析[J]. 岩土工程学报, 2020, 42(8): 1428-1434. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC202008011.htm YU Hai-tao, CHEN Xi-zhuo, LI Pan. Analytical solution for design parameters of model box to simulate seismic spatial variability effect using double-array shaking tables[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(8): 1428-1434. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC202008011.htm
[4] 刘必灯, 郭迅. 西南交通大学8 m×10 m地震模拟振动台运行对场地振动的影响分析[J]. 中国地震, 2019, 35(2): 226-237. doi: 10.3969/j.issn.1001-4683.2019.02.002 LIU Bi-deng, GUO Xun. Experimental study of field vibration influence induced by the 8 m×10 m shake table of Southwest Jiaotong University[J]. Earthquake Research in China, 2019, 35(2): 226-237. (in Chinese) doi: 10.3969/j.issn.1001-4683.2019.02.002
[5] 陈学伟, 季静, 吴培烽, 等. E-Defense振动台试验预测性分析比赛的研究综述[J]. 世界地震工程, 2010, 26(3): 175-181. https://www.cnki.com.cn/Article/CJFDTOTAL-SJDC201003029.htm CHEN Xue-wei, JI Jing, WU Pei-feng, et al. Summary on research of blind analysis contest of E-Defense shaking table test[J]. World Earthquake Engineering, 2010, 26(3): 175-181. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-SJDC201003029.htm
[6] 孙严. 基于框架结构盲测试验OpenSEES建模参数敏感性分析[D]. 哈尔滨: 黑龙江科技大学, 2016. SUN Yan. Sensitivity Analysis of Modeling Parameters for OpenSees Based on Frame Blind Test[D]. Harbin: Heilongjiang University of Science and Technology, 2016. (in Chinese)
[7] 张震. 场地地震反应一维数值分析方法对比分析[D]. 廊坊: 防灾科技学院, 2020. ZHANG Zhen. Comparison on One Dimension Numerical Methods of Site Seismic Response Analysis[D]. Langfang: Institute of Disaster Prevention, 2020. (in Chinese)
[8] GRIFFITHS S C, COX B R, RATHJE E M. Challenges associated with site response analyses for soft soils subjected to high-intensity input ground motions[J]. Soil Dynamics and Earthquake Engineering, 2016, 85: 1-10. doi: 10.1016/j.soildyn.2016.03.008
[9] 杨林德, 季倩倩, 郑永来, 等. 软土地铁车站结构的振动台模型试验[J]. 现代隧道技术, 2003, 40(1): 7-11. doi: 10.3969/j.issn.1009-6582.2003.01.002 YANG Lin-de, JI Qian-qian, ZHENG Yong-lai, et al. Shaking table test on metro station structures in soft soil[J]. Modern Tunnelling Technology, 2003, 40(1): 7-11. (in Chinese) doi: 10.3969/j.issn.1009-6582.2003.01.002
[10] 李杰, 岳庆霞, 陈隽. 地下综合管廊结构振动台模型试验与有限元分析研究[J]. 地震工程与工程振动, 2009, 29(4): 41-45. https://www.cnki.com.cn/Article/CJFDTOTAL-DGGC200904005.htm LI Jie, YUE Qing-xia, CHEN Jun. Research on shaking-table test and finite element numerical simulation of utility tunnel[J]. Journal of Earthquake Engineering and Engineering Vibration, 2009, 29(4): 41-45. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-DGGC200904005.htm
[11] WANG Z Z, JIANG Y J, ZHU C A, et al. Shaking table tests of tunnel linings in progressive states of damage[J]. Tunnelling and Underground Space Technology, 2015, 50: 109-117. doi: 10.1016/j.tust.2015.07.004
[12] MOGHADAM M R, BAZIAR M H. Seismic ground motion amplification pattern induced by a subway tunnel: shaking table testing and numerical simulation[J]. Soil Dynamics and Earthquake Engineering, 2016, 83: 81-97. doi: 10.1016/j.soildyn.2016.01.002
[13] 陈国兴, 王炳辉, 孙田. 饱和南京细砂动剪切模量特性的大型振动台试验研究[J]. 岩土工程学报, 2012, 34(4): 582-590. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201204004.htm CHEN Guo-xing, WANG Bing-hui, SUN Tian. Dynamic shear modulus of saturated Nanjing fine sand in large scale shaking table tests[J]. Chinese Journal of Geotechnical Engineering, 2012, 34(4): 582-590. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201204004.htm
[14] DIHORU L, BHATTACHARYA S, MOCCIA F, et al. Dynamic testing of free field response in stratified granular deposits[J]. Soil Dynamics and Earthquake Engineering, 2016, 84: 157-168. doi: 10.1016/j.soildyn.2016.02.014
[15] TSAI C C, LIN W C, CHIOU J S. Identification of dynamic soil properties through shaking table tests on a large saturated sand specimen in a laminar shear box[J]. Soil Dynamics and Earthquake Engineering, 2016, 83: 59-68. doi: 10.1016/j.soildyn.2016.01.007
[16] 刘晶波, 王文晖, 赵冬冬, 等. 地下结构抗震分析的整体式反应位移法[J]. 岩石力学与工程学报, 2013, 32(8): 1618-1624. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201308015.htm LIU Jing-bo, WANG Wen-hui, ZHAO Dong-dong, et al. Integral response deformation method for seismic analysis of underground structure[J]. Chinese Journal of Rock Mechanics and Engineering, 2013, 32(8): 1618-1624. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201308015.htm
[17] 刘晶波, 王文晖, 赵冬冬, 等. 复杂断面地下结构地震反应分析的整体式反应位移法[J]. 土木工程学报, 2014, 47(1): 134-142. https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201401018.htm LIU Jing-bo, WANG Wen-hui, ZHAO Dong-dong, et al. Integral response deformation method in seismic analysis of complex section underground structures[J]. China Civil Engineering Journal, 2014, 47(1): 134-142. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201401018.htm
[18] 刘晶波, 王东洋, 谭辉, 等. 整体式反应位移法的理论推导及一致性证明[J]. 土木工程学报, 2019, 52(8): 18-23. https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201908003.htm LIU Jing-bo, WANG Dong-yang, TAN Hui, et al. Theorectical derivation and consistency proof of the integral response deformation method[J]. China Civil Engineering Journal, 2019, 52(8): 18-23. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201908003.htm
[19] ZENG X, SCHOFIELD A N. Design and performance of an equivalent-shear-beam container for earthquake centrifuge modelling[J]. Géotechnique, 1996, 46(1): 83-102.
[20] 倪克闯. 成层土中桩基与复合地基地震作用下工作性状振动台试验研究[D]. 北京: 中国建筑科学研究院, 2013. NI Ke-chuang. Shaking Table Test of Pile and Composite Foundations' Dynamic Behavior in Layered Soils Subjected to Earthquake Excitation[D]. Beijing: China Academy of Building Research, 2013. (in Chinese)
[21] SEED H B, IDRISS I M. Soil Moduli and Damping Factors for Dynamic Response Analyses[R]. Berkeley: Earthquake Engineering Research Center, University of California, 1970.
[22] SADREKARIMI A. Dynamic behavior of granular soils at shallow depths from 1g shaking table tests[J]. Journal of Earthquake Engineering, 2013, 17: 227-252.
[23] ANJALI M, VIVEK B, RAYCHOWDHURY P. Seismic response analysis of Ganga sand deposits using shake table tests[J]. International Journal of Geo-Engineering, 2015, 6(1): 11.
[24] ZEGHAL M, ELGAMAL A W. Analysis of site liquefaction using earthquake records[J]. Journal of Geotechnical Engineering, 1994, 120(6): 996-1017.
[25] LI Z, ESCOFFIER S, KOTRONIS P. Using centrifuge tests data to identify the dynamic soil properties: application to Fontainebleau sand[J]. Soil Dynamics and Earthquake Engineering, 2013, 52: 77-87.
[26] 地下结构抗震设计标准：GB/T 51336—2018[S]. 2018. Standard for Seismic Design of Underground Structures: GB/T 51336—2018[S]. 2018. (in Chinese)
[27] 江志伟. 装配式地铁隧道和车站结构抗震研究[D]. 北京: 北京工业大学, 2019. JIANG Zhi-wei. Aseismic Investigations on Precast Subway Tunnel and Station[D]. Beijing: Beijing University of Technology, 2019. (in Chinese)
[28] 刘洪涛, 许紫刚, 杜修力. 基于不同计算方法下的装配整体式地铁车站抗震性能研究[J]. 特种结构, 2019, 36(5): 71-76. https://www.cnki.com.cn/Article/CJFDTOTAL-TZJG201905013.htm LIU Hong-tao, XU Zi-gang, DU Xiu-li. Analysis of seismic performance of assembled monolithic subway station based on different calculation methods[J]. Special Structures, 2019, 36(5): 71-76. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TZJG201905013.htm
计量
- 文章访问数: 304
- HTML全文浏览量: 37
- PDF下载量: 170
