Analytical solution for longitudinal response of pipeline structure under fault dislocation based on Pasternak foundation model

TAO Lian-jin; WANG Zhi-gang; SHI Cheng; AN Shao; JIA Zhi-bo

doi:10.11779/CJGE202209002

Volume 44 Issue 9

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Chinese Journal of Geotechnical Engineering > 2022 > 44(9): 1577-1586. > DOI: 10.11779/CJGE202209002

TAO Lian-jin, WANG Zhi-gang, SHI Cheng, AN Shao, JIA Zhi-bo. Analytical solution for longitudinal response of pipeline structure under fault dislocation based on Pasternak foundation model[J]. Chinese Journal of Geotechnical Engineering, 2022, 44(9): 1577-1586. DOI: 10.11779/CJGE202209002

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Analytical solution for longitudinal response of pipeline structure under fault dislocation based on Pasternak foundation model

Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing 100124, China

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Received Date: August 26, 2021
Available Online: September 22, 2022

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Abstract

The fault dislocation causes the rupture of the overlying soil on the site, resulting in enormous damage to the underground pipeline structures across the overlying soil. Through the researches on the longitudinal response of the pipeline structures of the overlying soil layer under the fault dislocation, the Pasternak double-parameter model is introduced so as to take the nonlinear interaction between the pipeline and the foundation into consideration, and an analytical solution for the longitudinal response of the pipeline structures is derived using the complementary error function. The calculated results of analytical solution are consistent with those of the model tests and numerical simulations, which proves the correctness of the analytical solution. Through the parameter sensitivity analysis, the influences of the shear stiffness of the elastic layer, the coefficient of subgrade reaction and the fault dip on the longitudinal response of the underground pipeline structures are discussed. The research results show that the longitudinal response of the pipeline structures under fault dislocation based on the two-parameter Pasternak foundation model is more accurate than that of the Winkler foundation model. The shear stiffness and reaction coefficient of the subgrade will change the maximum bending moment and shear force of the underground pipeline structures. In contrast, the coefficient of subgrade reaction and fault dip will change the influence area and the maximum value of the bending moment and shear force. In the influence area, the bending moment and shear force of the pipeline structures are several times higher than those in other locations, and the structures are prone to shear failure, which is the main disaster occurrence area.
- fault dislocation,
- analytical solution,
- Pasternak foundation model,
- complementary error function,
- longitudinal response

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[1]	SHEN Y S, GAO B, YANG X M, et al. Seismic damage mechanism and dynamic deformation characteristic analysis of mountain tunnel after Wenchuan earthquake[J]. Engineering Geology, 2014, 180: 85–98. doi: 10.1016/j.enggeo.2014.07.017
[2]	HSU L P, WENG S L. The geological treatment for railway tunnel after seismic damage–a case study of Sanyi No. 1 railway tunnel[J]. Treat Technol Engineering Geology Tunnel, 2000: 125–153.
[3]	崔光耀, 王明年, 于丽, 等. 汶川地震公路隧道洞口结构震害分析及震害机理研究[J]. 岩土工程学报, 2013, 35(6): 1084–1091. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201306015.htm CUI Guang-yao, WANG Ming-nian, YU Li, et al. Seismic damage and mechanism of portal structure of highway tunnels in Wenchuan Earthquake[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(6): 1084–1091. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201306015.htm
[4]	高波, 王峥峥, 袁松, 等. 汶川地震公路隧道震害启示[J]. 西南交通大学学报, 2009, 44(3): 336–341, 374. doi: 10.3969/j.issn.0258-2724.2009.03.005 GAO Bo, WANG Zheng-zheng, YUAN Song, et al. Lessons learnt from damage of highway tunnels in Wenchuan earthquake[J]. Journal of Southwest Jiaotong University, 2009, 44(3): 336–341, 374. (in Chinese) doi: 10.3969/j.issn.0258-2724.2009.03.005
[5]	WANG W L, WANG T T, SU J J, et al. Assessment of damage in mountain tunnels due to the Taiwan Chi-Chi Earthquake[J]. Tunnelling and Underground Space Technology, 2001, 16(3): 133–150. doi: 10.1016/S0886-7798(01)00047-5
[6]	DALGIÇ S. Tunneling in squeezing rock, the bolu tunnel, Anatolian motorway, Turkey[J]. Engineering Geology, 2002, 67(1/2): 73–96. http://www.sciencedirect.com/science/article/pii/S0013795202001461
[7]	TAKADA S, HASSANI N, FUKUDA K. A new proposal for simplified design of buried steel pipes crossing active faults[J]. Earthquake Engineering & Structural Dynamics, 2001, 30(8): 1243–1257. http://ci.nii.ac.jp/naid/130003801718
[8]	ZHANG Y, TAO L J, ZHAO X, et al. An analytical model for face stability of shield tunnel in dry cohesionless soils with different buried depth[J]. Computers and Geotechnics, 2022, 142: 104565. doi: 10.1016/j.compgeo.2021.104565
[9]	YANG Y R, HU J C, LIN M L. Evolution of coseismic fault-related folds induced by the Chi-Chi earthquake: a case study of the Wufeng site, Central Taiwan by using 2D distinct element modeling[J]. Journal of Asian Earth Sciences, 2014, 79: 130–143. doi: 10.1016/j.jseaes.2013.08.034
[10]	杨步云, 陈俊涛, 肖明. 跨断层地下隧洞衬砌结构地震响应及损伤机理研究[J]. 岩土工程学报, 2020, 42(11): 2078–2087. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC202011017.htm YANG Bu-yun, CHEN Jun-tao, XIAO Ming. Seismic response and damage mechanism of lining structures for underground tunnels across fault[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(11): 2078–2087. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC202011017.htm
[11]	YU H T, ZHANG Z W, CHEN J T, et al. Analytical solutionfor longitudinal seismic response of tunnel liners with sharp stiffness transition[J]. Tunnelling and Underground Space Technology, 2018, 77: 103–114. doi: 10.1016/j.tust.2018.04.001
[12]	林存刚, 黄茂松. 基于Pasternak地基的盾构隧道开挖非连续地下管线的挠曲[J]. 岩土工程学报, 2019, 41(7): 1200–1207. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201907004.htm LIN Cun-gang, HUANG Mao-song. Deflections of discontinuous buried pipelines induced by shield tunnelling based on Pasternak foundation[J]. Chinese Journal of Geotechnical Engineering, 2019, 41(7): 1200–1207. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201907004.htm
[13]	徐日庆, 程康, 应宏伟, 等. 考虑埋深与剪切效应的基坑卸荷下卧隧道的形变响应[J]. 岩土力学, 2020, 41(增刊1): 195–207. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX2020S1023.htm XU Ri-qing, CHENG Kang, YING Hong-wei, et al. Deformation response of a tunnel under foundation pit unloading considering buried depth and shearing effect[J]. Rock and Soil Mechanics, 2020, 41(S1): 195–207. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX2020S1023.htm
[14]	刘国钊, 乔亚飞, 何满潮, 等. 活动性断裂带错动下隧道纵向响应的解析解[J]. 岩土力学, 2020, 41(3): 923–932. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX202003023.htm LIU Guo-zhao, QIAO Ya-fei, HE Man-chao, et al. An analytical solution of longitudinal response of tunnels under dislocation of active fault[J]. Rock and Soil Mechanics, 2020, 41(3): 923–932. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX202003023.htm
[15]	刘学增, 王煦霖, 林亮伦. 75°倾角正断层黏滑错动对公路隧道影响的模型试验研究[J]. 岩石力学与工程学报, 2013, 32(8): 1714–1720. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201308026.htm LIU Xue-zeng, WANG Xu-lin, LIN Liang-lun. Model experiment on effect of normal fault with 75°dip angle stick-slip dislocation on highway tunnel[J]. Chinese Journal of Rock Mechanics and Engineering, 2013, 32(8): 1714–1720. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201308026.htm
[16]	刘学增, 王煦霖, 林亮伦. 45°倾角正断层黏滑错动对隧道影响试验分析[J]. 同济大学学报(自然科学版), 2014, 42(1): 44–50. https://www.cnki.com.cn/Article/CJFDTOTAL-TJDZ201401009.htm LIU Xue-zeng, WANG Xu-lin, LIN Liang-lun. Modeling experiment on effect of normal fault with 45° dip angle stick-slip dislocation on tunnel[J]. Journal of Tongji University (Natural Science), 2014, 42(1): 44–50. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TJDZ201401009.htm
[17]	刘学增, 刘金栋, 李学锋, 等. 逆断层铰接式隧道衬砌的抗错断效果试验研究[J]. 岩石力学与工程学报, 2015, 34(10): 2083–2090. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201510018.htm LIU Xue-zeng, LIU Jin-dong, LI Xue-feng, et al. Experimental research on effect of anti-dislocation of highway tunnel lining with hinge joints in thrust fault[J]. Chinese Journal of Rock Mechanics and Engineering, 2015, 34(10): 2083–2090. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201510018.htm
[18]	王道远, 李粮余, 袁金秀, 等. 逆断层黏滑错动下隧道抗错断力学机制研究[J]. 铁道工程学报, 2019, 36(6): 62–66. https://www.cnki.com.cn/Article/CJFDTOTAL-TDGC201906013.htm WANG Dao-yuan, LI Liang-yu, YUAN Jin-xiu, et al. Research on the mechanical response of dislocation fracture of tunnel under stick-slip of reverse fault[J]. Journal of Railway Engineering Society, 2019, 36(6): 62–66. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TDGC201906013.htm
[19]	孙飞, 张志强, 易志伟. 正断层黏滑错动对地铁隧道结构影响的模型试验研究[J]. 岩土力学, 2019, 40(8): 3037–3044, 3053. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201908020.htm SUN Fei, ZHANG Zhi-qiang, YI Zhi-wei. Model experimental study of the influence of normal fault with stick-slip dislocation on subway tunnel structure[J]. Rock and Soil Mechanics, 2019, 40(8): 3037–3044, 3053. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201908020.htm
[20]	KIANI M, AKHLAGHI T, GHALANDARZADEH A. Experimental modeling of segmental shallow tunnels in alluvial affected by normal faults[J]. Tunnelling and Underground Space Technology, 2016, 51: 108–119. doi: 10.1016/j.tust.2015.10.005
[21]	DEMIRCI H E, BHATTACHARYA S, KARAMITROS D, et al. Experimental and numerical modelling of buried pipelines crossing reverse faults[J]. Soil Dynamics and Earthquake Engineering, 2018, 114: 198–214. doi: 10.1016/j.soildyn.2018.06.013
[22]	马亚丽娜, 崔臻, 盛谦, 等. 正断层错动对围岩–衬砌体系响应影响的离散–连续耦合模拟研究[J]. 岩土工程学报, 2020, 42(11): 2088–2097. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC202011018.htm MA Yalina, CUI Zhen, SHENG Qian, et al. Influences of normal fault dislocation on response of surrounding rock and lining system based on discrete-continuous coupling simulation[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(11): 2088–2097. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC202011018.htm
[23]	安韶, 陶连金, 边金, 等. 跨活动断裂带城市浅埋地铁隧道结构两阶段设计方法研究[J]. 中南大学学报(自然科学版), 2020, 51(9): 2558–2570. https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD202009021.htm AN Shao, TAO Lian-jin, BIAN Jin, et al. Study on two-level design method of urban shallow subway tunnel structure crossing active fault[J]. Journal of Central South University (Science and Technology), 2020, 51(9): 2558–2570. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD202009021.htm
[24]	BAZIAR M H, NABIZADEH A, MEHRABI R, et al. Evaluation of underground tunnel response to reverse fault rupture using numerical approach[J]. Soil Dynamics and Earthquake Engineering, 2016, 83: 1–17. doi: 10.1016/j.soildyn.2015.11.005
[25]	汪振, 钟紫蓝, 黄景琦, 等. 走滑断层错动下山岭隧道关键断面变形及损伤演化[J]. 建筑结构学报, 2020, 41(增刊1): 425–433. https://www.cnki.com.cn/Article/CJFDTOTAL-JZJB2020S1048.htm WANG Zhen, ZHONG Zi-lan, HUANG Jing-qi, et al. Deformation and damage evolution of critical cross section of mountain tunnels under strike-slip fault movement[J]. Journal of Building Structures, 2020, 41(S1): 425–433. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JZJB2020S1048.htm
[26]	ZHANG L S, ZHAO X B, YAN X Z, et al. A new finite element model of buried steel pipelines crossing strike-slip faults considering equivalent boundary springs[J]. Engineering Structures, 2016, 123: 30–44. doi: 10.1016/j.engstruct.2016.05.042
[27]	耿萍, 曾冠雄, 郭翔宇, 等. 近场脉冲地震作用下穿越断层带隧道地震响应[J]. 中国公路学报, 2020, 33(5): 122–131. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL202005011.htm GENG Ping, ZENG Guan-xiong, GUO Xiang-yu, et al. Seismic response of tunnel structures passing through fault zone under near-field pulsed earthquakes[J]. China Journal of Highway and Transport, 2020, 33(5): 122–131. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL202005011.htm
[28]	FADAEE M, FARZANEGANPOUR F, ANASTASOPOULOS I. Response of buried pipeline subjected to reverse faulting[J]. Soil Dynamics and Earthquake Engineering, 2020, 132: 106090. http://www.sciencedirect.com/science/article/pii/S0267726119303781
[29]	PASTERNAK P L. On a new method of analysis of an elastic foundation by means of two foundation constants[C]// Cosudarstrennoe Izd Lit po Stroit i Arkhitekture, Moscow, USSR 1954.
[30]	CAI Q P, NG C W W. Analytical approach for estimating ground deformation profile induced by normal faulting in undrained clay[J]. Canadian Geotechnical Journal, 2013, 50(4): 413–422. http://d.wanfangdata.com.cn/periodical/168945325ce21718e8d4fb20910e6d18
[31]	AHMED I. Pipeline Response to Excavation-Induced Ground Movements[D]. Cornell: Cornell University, 1990.
[32]	ROBOSKI J, FINNO R J. Distributions of ground movements parallel to deep excavations in clay[J]. Canadian Geotechnical Journal, 2006, 43(1): 43–58.
[33]	LOUKIDIS D, BOUCKOVALAS G D, PAPADIMITRIOU A G. Analysis of fault rupture propagation through uniform soil cover[J]. Soil Dynamics and Earthquake Engineering, 2009, 29(11/12): 1389–1404. http://www.sciencedirect.com/science/article/pii/S0267726109000827
[34]	TANAHASHI H. Formulas for an infinitely long bernoulli-Euler beam on the Pasternak model[J]. Soils and Foundations, 2004, 44(5): 109–118. http://www.jstage.jst.go.jp/A_PRedirectJournalInit?sryCd=sandf1995&noVol=44&noIssue=5&kijiCd=44_5_109&screenID=AF06S010
[35]	YU J, ZHANG C R, HUANG M S. Soil-pipe interaction due to tunnelling: assessment of Winkler modulus for underground pipelines[J]. Computers and Geotechnics, 2013, 50: 17–28. http://or.nsfc.gov.cn/bitstream/00001903-5/73948/1/1000004995705.pdf
[36]	LIU X Z, LI X F, SANG Y L, et al. Experimental study on normal fault rupture propagation in loose strata and its impact on mountain tunnels[J]. Tunnelling and Underground Space Technology, 2015, 49: 417–425. http://www.onacademic.com/detail/journal_1000038099248410_d5aa.html

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