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2023 Vol.24, Issue 2 Preview Page
Development of Modified Flexibility Ratio - Racking Ratio Relationship of Box Tunnels Subjected to Earthquake Loading Considering Rocking
Duhee Park1*
,
Van-Quang Nguyen2
,
Gyuphil Lee3
,
Youngsuk Lee4
1Professor, Department of Civil and Environmental Engineering, Hanyang University
2Post Doctor, Department of Civil and Environmental Engineering, Hanyang University
3Senior Researcher, Korea Institute of Civil Engineering and Building Technology
4Researcher, Seoul Institute of Technology
*Corresponding Author
1 February 2023. pp. 13-24
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Abstract

Tunnels may undergo a larger or a smaller response compared with the free-field soil. In the pseudo-static procedure, the response of the tunnel is most often characterized by a curve that relates the racking ratio (R) with the flexibility ratio (F), where R represents the ratio of the tunnel response with respect to the free-field vibration and F is the relative stiffness of the tunnel and the surrounding soil. A set of analytical and empirical curves that do not account for the depth and the aspect ratio of the tunnel are typically used in practice. In this study, a series of dynamic analyses are conducted to develop a set of F-Rm relations for use in a frame analysis method. Rm is defined as an adjusted R where the rocking mode of deformation is removed and only the racking deformation is extracted. The numerical model is validated against centrifuge test recordings. The influence of aspect ratio, buried depth of tunnel on results is investigated. The results show that Rm increases with the increase of the buried depth and the aspect ratio. The widely used F-R relations are highlighted to be different compared with the obtained results in this study. Therefore, the updated F-Rm relations with proposed equations are recommended to be used in practice design. The rocking response decreases with either the decrease of the difference of stiffness between surrounding soil and tunnel or the larger aspect ratio of the tunnel section.

Keywords
Underground structure
Seismic analysis
Pseudo-static method
Soil-structure interaction
Racking-rocking response
References
1
Abate, G. and Massimino, M.R. (2017), "Parametric analysis of the seismic response of coupled tunnel-soil-aboveground building systems by numerical modelling", Bulletin of Earthquake Engineering, Vol. 15, No. 1, pp. 443~467. 10.1007/s10518-016-9975-7
2
Abate, G., Massimino, M.R. and Maugeri, M. (2015), "Numerical modelling of centrifuge tests on tunnel-soil systems", Bulletin of Earthquake Engineering, Vol. 13, No. 7, pp. 1927~1951. 10.1007/s10518-014-9703-0
3
Abuhajar, O., El Naggar, H. and Newson, T. (2015), "Experimental and numerical investigations of the effect of buried box culverts on earthquake excitation", Soil Dynamics and Earthquake Engineering, Vol. 79, pp. 130~148. 10.1016/j.soildyn.2015.07.015
4
Anderson, D.G. (2008), Seismic analysis and design of retaining walls, buried structures, slopes, and embankments, 0309117658, Transportation Research Board, pp. 105~129.
5
Arango, I. (2008), "Theme paper: Earthquake engineering for tunnels and underground structures. A case history", Geotechnical earthquake engineering and soil dynamics iv, pp. 1~34. 10.1061/40975(318)20518606526
6
Baziar, M.H., Moghadam, M.R., Kim, D.-S. and Choo, Y.W. (2014), "Effect of underground tunnel on the ground surface acceleration", Tunnelling and underground space technology, Vol. 44, pp. 10~22. 10.1016/j.tust.2014.07.004
7
Bobet, A. (2010), "Drained and undrained response of deep tunnels subjected to far-field shear loading", Tunnelling Underground Space Technology, Vol. 25, No. 1, pp. 21~31. 10.1016/j.tust.2009.08.001
8
Bobet, A., Fernandez, G., Huo, H. and Ramirez, J. (2008), "A practical iterative procedure to estimate seismic-induced deformations of shallow rectangular structures", Canadian Geotechnical Journal, Vol. 45, No. 7, pp. 923~938. 10.1139/T08-026
9
Callisto, L. and Ricci, C. (2019), "Interpretation and back-analysis of the damage observed in a deep tunnel after the 2016 norcia earthquake in italy", Tunnelling and underground space technology, Vol. 89, pp. 238~248. 10.1016/j.tust.2019.04.012
10
Chen, C.-H., Wang, T.-T., Jeng, F.-S. and Huang, T.-H. (2012), "Mechanisms causing seismic damage of tunnels at different depths", Tunnelling and underground space technology, Vol. 28, pp. 31~40. 10.1016/j.tust.2011.09.001
11
Chen, Z.-Y., Chen, W. and Zhang, W. (2014), "Seismic performance evaluation of multi-story subway structure based on pushover analysis", Advances in soil dynamics and foundation engineering, pp. 444~454. 10.1061/9780784413425.045
12
Chopra, A. (2001), "Structural dynamics: Theory and applications to earthquake engineering": Prentice Hall, pp. 455~458.
13
Cilingir, U. and Madabhushi, S.G. (2011a), "A model study on the effects of input motion on the seismic behaviour of tunnels", Soil Dynamics and Earthquake Engineering, Vol. 31, No. 3, pp. 452~462. 10.1016/j.soildyn.2010.10.004
14
Cilingir, U. and Madabhushi, S.G. (2011b), "Effect of depth on the seismic response of square tunnels", Soils and foundations, Vol. 51, No. 3, pp. 449~457. 10.3208/sandf.51.449
15
Darendeli, M.B. (2001), Development of a new family of normalized modulus reduction and material damping curves, Ph.D. Thesis, University of Texas at Austin, Texas, USA.
16
Debiasi, E., Gajo, A. and Zonta, D. (2013), "On the seismic response of shallow-buried rectangular structures", Tunnelling and underground space technology, Vol. 38, pp. 99~113. 10.1016/j.tust.2013.04.011
17
Dowding, C.H. and Rozan, A. (1978), "Damage to rock tunnels from earthquake shaking", Journal of the Geotechnical Engineering Division, Vol. 104, No. 2, pp. 175~191. 10.1061/AJGEB6.0000580
18
Ghasemi, H., Cooper, J.D., Imbsen, R., Piskin, H., Inal, F. and Tiras, A. (2000), "The november 1999 duzce earthquake: Post- earthquake investigation of the structures on the tem", Rep. No. FHWA-RD-00, Vol. 146, 00~146.
19
Gillis, K.M. (2015), Seismic response of shallow underground structures in dense urban environments, Ph.D. dissertation, University of Colorado at Boulder.
20
Guoxing, C., Su, C., Xi, Z., Xiuli, D., Chengzhi, Q., Zhihua, W.J.S.D. and Engineering, E. (2015), "Shaking-table tests and numerical simulations on a subway structure in soft soil", Vol. 76, pp. 13~28. 10.1016/j.soildyn.2014.12.012
21
Hashash, Y., Karina, K., Koutsoftas, D. and O'Riordan, N. (2010), "Seismic design considerations for underground box structures", Earth Retention Conference, 3, pp. 620~637. 10.1061/41128(384)64
22
Hashash, Y.M., Hook, J.J., Schmidt, B., John, I. and Yao, C. (2001), "Seismic design and analysis of underground structures", Tunnelling and underground space technology, Vol. 16, No. 4, pp. 247~293. 10.1016/S0886-7798(01)00051-7
23
Hashash, Y.M., Dashti, S., Musgrove, M., Gillis, K., Walker, M., Ellison, K. and Basarah, Y.I. (2018), "Influence of tall buildings on seismic response of shallow underground structures", Journal of Geotechnical and Geoenvironmental Engineering, Vol. 144, No. 12, pp. 04018097. 10.1061/(ASCE)GT.1943-5606.0001963
24
Huo, H., Bobet, A., Fernández, G. and Ramírez, J. (2006), "Analytical solution for deep rectangular structures subjected to far-field shear stresses", Tunnelling and underground space technology, Vol. 21, No. 6, pp. 613~625. 10.1016/j.tust.2005.12.135
25
Iida, H., Hiroto, T., Yoshida, N. and Iwafuji, M. (1996), "Damage to daikai subway station", Soils and foundations, Vol. 36, No. Special, pp. 283~300. 10.3208/sandf.36.Special_283
26
Itasca Consulting Group (2011), Flac - fast lagrange analysis of continua; version7.0. In: User manual.
27
Kuhlemeyer, R.L. and Lysmer, J. (1973), "Finite element method accuracy for wave propagation problems", Journal of Soil Mechanics & Foundations Div, Vol. 99, No. Tech Rpt. 10.1061/JSFEAQ.0001885
28
Kwok, A.O., Stewart, J.P., Hashash, Y.M., Matasovic, N., Pyke, R., Wang, Z. and Yang, Z. (2007), "Use of exact solutions of wave propagation problems to guide implementation of nonlinear seismic ground response analysis procedures", Journal of Geotechnical and Geoenvironmental Engineering, Vol. 133, No. 11, pp. 1385~1398. 10.1061/(ASCE)1090-0241(2007)133:11(1385)
29
Lee, J.-H., Ahn, J.-K. and Park, D. (2015), "Prediction of seismic displacement of dry mountain slopes composed of a soft thin uniform layer", Soil Dynamics and Earthquake Engineering, Vol. 79, pp. 5~16. 10.1016/j.soildyn.2015.08.008
30
Lee, T.-H., Park, D., Nguyen, D.D. and Park, J.-S. (2016), "Damage analysis of cut-and-cover tunnel structures under seismic loading", Bulletin of Earthquake Engineering, Vol. 14, No. 2, pp. 413~431. 10.1007/s10518-015-9835-x
31
Liu, H. and Song, E. (2005), "Seismic response of large underground structures in liquefiable soils subjected to horizontal and vertical earthquake excitations", Computers and Geotechnics, Vol. 32, No. 4, pp. 223~244. 10.1016/j.compgeo.2005.02.002
32
Lu, C.-C. and Hwang, J.-H. (2017), "Implementation of the modified cross-section racking deformation method using explicit fdm program: A critical assessment", Tunnelling and underground space technology, Vol. 68, pp. 58~73. 10.1016/j.tust.2017.05.014
33
Ma, C., Lu, D., Du, X. and Qi, C. (2018), "Effect of buried depth on seismic response of rectangular underground structures considering the influence of ground loss", Soil Dynamics and Earthquake Engineering, Vol. 106, pp. 278~297. 10.1016/j.soildyn.2017.12.021
34
Moghadam, M.R. and Baziar, M.H. (2016), "Seismic ground motion amplification pattern induced by a subway tunnel: Shaking table testing and numerical simulation", Soil Dynamics and Earthquake Engineering, Vol. 83, pp. 81~97. 10.1016/j.soildyn.2016.01.002
35
Nguyen, D.-D., Lee, T.-H., Nguyen, V.-Q. and Park, D. (2019a), "Seismic damage analysis of box metro tunnels accounting for aspect ratio and shear failure", Applied Sciences, Vol. 9, No. 16, pp. 3207. 10.3390/app9163207
36
Nguyen, D.-D., Park, D., Shamsher, S., Nguyen, V.-Q. and Lee, T.-H. (2019b), "Seismic vulnerability assessment of rectangular cut-and-cover subway tunnels", Tunnelling and underground space technology, Vol. 86, pp. 247~261. 10.1016/j.tust.2019.01.021
37
Nguyen, V.-Q., Nizamani, Z.A., Park, D. and Kwon, O.-S. (2020), "Numerical simulation of damage evolution of daikai station during the 1995 kobe earthquake", Engineering Structures, Vol. 206, pp. 110180. 10.1016/j.engstruct.2020.110180
38
Nishioka, T. and Unjoh, S. (2000), "A simplified seismic design method for underground structures based on the shear strain transmitting characteristics", Minamihara Tsukuba: Public works Research Institute.
39
Origin (2016), "Originlab corporation", Northampton, MA, USA.
40
Park, K.-C., Nguyen, V.-Q., Kim, J.-H., Park, D. and Choi, B.-H. (2019), "Estimation of seismically-induced crest settlement of earth core rockfill dams", Applied Sciences, Vol. 9, No. 20, pp. 4343. 10.3390/app9204343
41
Penzien, J. (2000), "Seismically induced racking of tunnel linings", Earthquake Engineering, Vol. 29, No. 5, pp. 683~691. 10.1002/(SICI)1096-9845(200005)29:5<683::AID-EQE932>3.0.CO;2-1
42
Pitilakis, K. and Tsinidis, G. (2014), "Performance and seismic design of underground structures", Earthquake geotechnical engineering design: Springer, pp. 279~340. 10.1007/978-3-319-03182-8_11
43
Sadiq, S., Nguyen, V.Q., Jung, H. and Park, D. (2019), "Effect of flexibility ratio on seismic response of cut-and-cover box tunnel", Advances in Civil Engineering, Vol. 2019. 10.1155/2019/4905329
44
Sanderson, S.T. (2018), Non-linear deformation analysis of an embankment dam, Master thesis, Portland State University. 10.15760/CCEMP.40
45
Sayed, M.A., Kwon, O.-S., Park, D. and Van Nguyen, Q. (2019), "Multi-platform soil-structure interaction simulation of daikai subway tunnel during the 1995 kobe earthquake", Soil Dynamics and Earthquake Engineering, Vol. 125, pp. 105643. 10.1016/j.soildyn.2019.04.017
46
Sharma, S. and Judd, W.R. (1991), "Underground opening damage from earthquakes", Engineering Geology, Vol. 30, No. 3-4, pp. 263~276. 10.1016/0013-7952(91)90063-Q
47
Tsinidis, G. (2017), "Response characteristics of rectangular tunnels in soft soil subjected to transversal ground shaking", Tunnelling Underground Space Technology, Vol. 62, pp. 1~22. 10.1016/j.tust.2016.11.003
48
Tsinidis, G. and Pitilakis, K. (2018), "Improved r-f relations for the transversal seismic analysis of rectangular tunnels", Soil Dynamics and Earthquake Engineering, Vol. 107, pp. 48~65. 10.1016/j.soildyn.2018.01.004
49
Tsinidis, G., Pitilakis, K., Madabhushi, G. and Heron, C. (2015), "Dynamic response of flexible square tunnels: Centrifuge testing and validation of existing design methodologies", Geotechnique, Vol. 65, No. 5, pp. 401~417. 10.1680/gee.61491.071
50
Tsinidis, G., Rovithis, E., Pitilakis, K. and Chazelas, J.L. (2016), "Seismic response of box-type tunnels in soft soil: Experimental and numerical investigation", Tunnelling and underground space technology, Vol. 59, pp. 199~214. 10.1016/j.tust.2016.07.008
51
Wang, G., Yuan, M., Miao, Y., Wu, J. and Wang, Y. (2018), "Experimental study on seismic response of underground tunnel-soil-surface structure interaction system", Tunnelling and underground space technology, Vol. 76, pp. 145~159. 10.1016/j.tust.2018.03.015
52
Wang, J.-N. (1993), Seismic design of tunnels: A simple state-of-the-art design approach, Parsons Brinckerhoff, pp. 147.
53
Wang, J.-N. and Munfakh, G. (2001), Seismic design of tunnels, WIT Press.
54
Wang, W., Wang, T., Su, J., Lin, C., Seng, C. and Huang, T. (2001), "Assessment of damage in mountain tunnels due to the taiwan chi-chi earthquake", Tunnelling and underground space technology, Vol. 16, No. 3, pp. 133~150. 10.1016/S0886-7798(01)00047-5
55
Wang, Y., Shan, S., Zhang, C. and Guo, P. (2019), "Seismic response of tunnel lining structure in a thick expansive soil stratum", Tunnelling Underground Space Technology, Vol. 88, pp. 250~259. 10.1016/j.tust.2019.03.016
56
Xu, H., Li, T., Xia, L., Zhao, J.X. and Wang, D. (2016), "Shaking table tests on seismic measures of a model mountain tunnel", Tunnelling Underground Space Technology, Vol. 60, pp. 197~209. 10.1016/j.tust.2016.09.004
57
Yan, X., Yuan, J., Yu, H., Bobet, A. and Yuan, Y. (2016), "Multi-point shaking table test design for long tunnels under non-uniform seismic loading", Tunnelling and underground space technology, Vol. 59, pp. 114~126. 10.1016/j.tust.2016.07.002
Information
  • Publisher :Korean Geo-Environmental Society
  • Publisher(Ko) :한국지반환경공학회
  • Journal Title :Journal of the Korean Geo-Environmental Society
  • Journal Title(Ko) :한국지반환경공학회 논문집
  • Volume : 24
  • No :2
  • Pages :13-24
  • Received Date : 2022-12-28
  • Revised Date : 2023-01-03
  • Accepted Date : 2023-01-06
  • DOI :https://doi.org/10.14481/jkges.2023.24.2.13
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