Analytical solution for design parameters of model box to simulate seismic spatial variability effect using double-array shaking tables

YU Hai-tao; CHEN Xi-zhuo; LI Pan

doi:10.11779/CJGE202008007

Volume 42 Issue 8

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Chinese Journal of Geotechnical Engineering > 2020 > 42(8): 1428-1434. > DOI: 10.11779/CJGE202008007

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. DOI: 10.11779/CJGE202008007

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Analytical solution for design parameters of model box to simulate seismic spatial variability effect using double-array shaking tables

YU Hai-tao^1,,
CHEN Xi-zhuo²,
LI Pan^{2, 3, ,}

1.
Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China
2.
Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China
3.
School of Rail Transportation, Soochow University, Suzhou 215131, China

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Received Date: July 28, 2019
Available Online: December 05, 2022

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Abstract

Abstract

Based on the multi-point shaking table tests on underground structures, the simulation of the seismic spatial variability effect can be realized by the design of model box, that is, the model container can be used to realize the equivalent transformation from the discrete multi-point shaking of the table into a continuous non-uniform seismic excitation. However, neither analytical solutions nor experimental data are available in the current literatures to obtain the design parameters of the model box. The simplified analysis model and boundary conditions of the model box are established for the typical double-array shaking table test system. According to the integral transformation and residue theorem, the analytical solution for dynamic response of the model box on the double-array shaking tables is derived, and thus the analytical relationship between the dynamic response and the parameters of the model box can be directly expressed from the proposed solution. By taking the continuous non-uniform seismic input as benchmark, the analytical expression for the design parameters of the model box is obtained. Finally, the proposed solution is verified by a series of shaking table tests. The analytical solution can be used for the design of the model box to simulate the seismic spatial variability effect based on double-array shaking tables.
- seismic input,
- spatial variability effect,
- shaking table,
- model box,
- analytical solution

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References (19)

References

[1]	禹海涛, 李翀, 袁勇, 等. 用于长隧道多点振动台试验的节段式模型箱及其适用性研究[J]. 中国公路学报, 2016, 29(12): 166-174. doi: 10.3969/j.issn.1001-7372.2016.12.021 YU Hai-tao, LI Chong, YUAN Yong, et al. Research on segmental model container and its validation for multi-point shaking table test of long tunnels[J]. China Journal of Highway and Transport, 2016, 29(12): 166-174. (in Chinese) doi: 10.3969/j.issn.1001-7372.2016.12.021
[2]	袁勇, 包蓁, 禹海涛, 等. 考虑行波效应的盾构隧道多点振动台试验[J]. 中国公路学报, 2017, 30(8): 174-182. doi: 10.3969/j.issn.1001-7372.2017.08.020 YUAN Yong, BAO Zhen, YU Hai-tao, et al. Multi-point shaking in consideration table test on shield tunnels of wave-passage effect[J]. China Journal of Highway and Transport, 2017, 30(8): 174-182. (in Chinese) doi: 10.3969/j.issn.1001-7372.2017.08.020
[3]	YU H, YUAN Y, QIAO Z, et al. Seismic analysis of a long tunnel based on multi-scale method[J]. Engineering Structures, 2013, 49(2): 572-587.
[4]	YU H T, YUAN Y, BOBET A. Multiscale method for long tunnels subjected to seismic loading[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37(4): 374-398. doi: 10.1002/nag.1102
[5]	刘鹏, 丁文其, 杨波. 深水超长沉管隧道接头及止水带地震响应[J]. 同济大学学报(自然科学版), 2013, 41(7): 984-988. doi: 10.3969/j.issn.0253-374x.2013.07.004 LIU Peng, DING Wen-qi, YANG Bo, et al. Research on joints and gasket seismic response of deep-water long immersed tube tunnels[J]. Journal of Tongji University (Natural Science), 2013, 41(7): 984-988. (in Chinese) doi: 10.3969/j.issn.0253-374x.2013.07.004
[6]	IIDA H, HIROTO T, YOSHIDA N, et al. Damage to Daikai subway station[J]. Soils and Foundations, 1996, 36: 283-330. doi: 10.3208/sandf.36.Special_283
[7]	VANZI I. Elastic and inelastic response of tunnels under longitudinal earthquake excitation[J]. Journal of Earthquake Engineering, 2000, 4(2): 161-182.
[8]	YAN X, YUAN J, YU H T, et al. Multi-point shaking table test design for long tunnels under non-uniform seismic loading[J]. Tunneling and Underground Space Technology, 2016, 59: 114-126. doi: 10.1016/j.tust.2016.07.002
[9]	LI P, SONG E X. Three-dimensional numerical analysis for the longitudinal seismic response of tunnels under an asynchronous wave input[J]. Computers and Geotechnics, 2015, 63: 229-243. doi: 10.1016/j.compgeo.2014.10.003
[10]	CHEN J, SHI X, LI J. Shaking table test of utility tunnel under non-uniform earthquake wave excitation[J]. Soil Dynamic & Earthquake Engineering, 2010, 30(11): 1400-1416.
[11]	李立云, 王成波, 韩俊艳, 等. 埋地管道–场地地震反应振动台试验研究的场地响应[J]. 地震工程与工程振动, 2015, 35(3): 166-176. https://www.cnki.com.cn/Article/CJFDTOTAL-DGGC201503021.htm LI Li-yun, WANG Cheng-bo, HAN Jun-yan, et al. Analysis of site responses during shaking table test for the interaction between pipeline and soil[J]. Earthquake Engineering and Engineering Dynamics, 2015, 35(3): 166-176. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-DGGC201503021.htm
[12]	YUAN Y, YU H T, LI C, et al. Multi-point shaking table test for long tunnels subjected to non-uniform seismic loadings: Part I theory and validation[J]. Soil Dynamics and Earthquake Engineering, 2018, 108: 177-186. doi: 10.1016/j.soildyn.2016.08.017
[13]	YU H T, YUAN Y, XU G, et al. Multi-point shaking table test for long tunnels subjected to non-uniform seismic loadings: Part II application to the HZM immersed tunnel[J]. Soil Dynamics and Earthquake Engineering, 2018, 108: 187-195. doi: 10.1016/j.soildyn.2016.08.018
[14]	YU H T, YAN X, BOBET A, et al. Multi-point shaking table test of a long tunnel subjected to non-uniform seismic loadings[J]. Bulletin of Earthquake Engineering, 2018, 16(2): 1041-1059. doi: 10.1007/s10518-017-0223-6
[15]	禹海涛, 袁勇. 长大隧道地震响应分析与试验方法新进展[J]. 中国公路学报, 2018, 31(10): 19-35. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201810002.htm YU Hai-tao, YUAN Yong. Review on seismic response analysis and test methods for long and large tunnels[J]. China Journal of Highway and Transport, 2018, 31(10): 19-35. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201810002.htm
[16]	袁勇, 禹海涛, 燕晓, 等. 超长沉管隧道多点振动台试验模拟与分析[J]. 中国公路学报, 2016, 29(12): 157-165. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201612023.htm YUAN Yong, YU Hai-tao, YAN Xiao, et al. Multi-point shaking table test simulation and analysis of a super-long immersed tunnel[J]. China Journal of Highway and Transport, 2016, 29(12): 157-165. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201612023.htm
[17]	燕晓, 禹海涛, 袁勇, 等. 沉管隧道基槽边坡振动台试验及动力特性[J]. 中国公路学报, 2016, 29(12): 149-156. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201612022.htm YAN Xiao, YU Hai-tao, YUAN Yong, et al. Shaking table test on seismic characteristics of trench slope of immersed tunnel[J]. China Journal of Highway and Transport, 2016, 29(12): 149-156. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201612022.htm
[18]	YU H T, YUAN Y. Analytical solution for an infinite Euler-Bernoulli beam on a viscoelastic foundation subjected to arbitrary dynamic loads[J]. Journal of Engineering Mechanics, 2014, 140(3): 542-551.
[19]	HASHASH Y M A, HOOK J J, SCHMIDT B, et al. Seismic design and analysis of underground structures[J]. Tunnelling and Underground Space Technology, 2001, 16(4): 247-293.