Abstract
The failure mechanism of tunnels crossing faults is a critical issue for tunnels located in seismically active regions. This study aims to investigate the nonlinear response of rock tunnels crossing inactive faults under obliquely incident seismic P waves. Based on the equivalent nodal force method together with the viscous-spring boundary, an incident method for the site, which contains fault and is subjected to obliquely incident seismic P waves, is developed first. Then, based on the proposed incident method, the nonlinear response and the failure process of the tunnel crossing inactive fault are numerically studied. The numerical results show that the failure mechanism of the tunnel crossing inactive fault can be attributed to the combined action of the seismic waves and its associated fault slippage. Finally, parameter studies are conducted to investigate the effects of the wave impedance ratio of the fault to the surrounding rock and the incident angle of P waves. By the parameter analysis, it can be concluded that: (1) with decreasing the wave impedance ratio of the fault to the surrounding rock, the seismic response of the tunnel increases significantly; (2) the seismic response of the tunnel increases first and then decreases with the increasing of the incident angle of P waves. This study offers the insight for further research on the seismic stability of tunnels crossing inactive faults.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References Cited
Abdoun, T. H., Ha, D., O’Rourke, M. J., et al., 2009. Factors Influencing the Behavior of Buried Pipelines Subjected to Earthquake Faulting. Soil Dynamics and Earthquake Engineering, 29(3): 415–427. https://doi.org/10.1016/j.soildyn.2008.04.006
Anastasopoulos, I., Gerolymos, N., Drosos, V., et al., 2008. Behaviour of Deep Immersed Tunnel under Combined Normal Fault Rupture Deformation and Subsequent Seismic Shaking. Bulletin of Earthquake Engineering, 6(2): 213–239. https://doi.org/10.1007/s10518-007-9055-0
Aydan, Ö., Ohta, Y., Geniş, M., et al., 2010. Response and Stability of Underground Structures in Rock Mass during Earthquakes. Rock Mechanics and Rock Engineering, 43(6): 857–875. https://doi.org/10.1007/s00603-010-0105-6
Baziar, M. H., Nabizadeh, A., Lee, C. J., et al., 2014. Centrifuge Modeling of Interaction between Reverse Faulting and Tunnel. Soil Dynamics and Earthquake Engineering, 65: 151–164. https://doi.org/10.1016/j.soildyn.2014.04.008
Baziar, M. H., Nabizadeh, A., Mehrabi, R., et al., 2016. Evaluation of Underground Tunnel Response to Reverse Fault Rupture Using Numerical Approach. Soil Dynamics and Earthquake Engineering, 83: 1–17. https://doi.org/10.1016/j.soildyn.2015.11.005
Birtel, V., Mark, P., 2006. Parameterised Finite Element Modelling of RC Beam Shear Failure. ABAQUS Users’ Conference, Oxford
Cividini, A., Gioda, G., Petrini, V., 2010. Finite Element Evaluation of the Effects of Faulting on a Shallow Tunnel in Alluvial Soil. Acta Geotechnica, 5(2): 113–120. https://doi.org/10.1007/s11440-010-0116-1
Du, X. L., Zhao, M., 2010. A Local Time-Domain Transmitting Boundary for Simulating Cylindrical Elastic Wave Propagation in Infinite Media. Soil Dynamics and Earthquake Engineering, 30(10): 937–946. https://doi.org/10.1016/j.soildyn.2010.04.004
Du, X. L., Zhao, M., Wang, J. T., 2006. A Stress Artificial Boundary in FEA for near-Field Wave Problem. Chinese Journal of Theoretical and Applied Mechanics, 38(1): 49–56 (in Chinese with English Abstract)
Gharizade, V. M., Golshani, A., Majidian, S., 2017. Analysis of Cylindrical Tunnels under Combined Primary Near-Fault Seismic Excitations and Subsequent Reverse Fault Rupture. Acta Geodynamica et Geomaterialia, 14(1): 5–26. https://doi.org/10.13168/agg.2016.0024
Huang, J. Q., Du, X. L., Jin, L., et al., 2016. Impact of Incident Angles of P Waves on the Dynamic Responses of Long Lined Tunnels. Earthquake Engineering & Structural Dynamics, 45(15): 2435–2454. https://doi.org/10.1002/eqe.2772
Huang, J. Q., Zhao, M., Du, X. L., 2017. Non-Linear Seismic Responses of Tunnels within Normal Fault Ground under Obliquely Incident P Waves. Tunnelling and Underground Space Technology, 61: 26–39. https://doi.org/10.1016/j.tust.2016.09.006
Huang, J. Q., Zhao, X., Zhao, M., et al., 2020. Effect of Peak Ground Parameters on the Nonlinear Seismic Response of Long Lined Tunnels. Tunnelling and Underground Space Technology, 95: 103175. https://doi.org/10.1016/j.tust.2019.103175
Jalali, H. H., Rofooei, F. R., Attari, N. K. A., et al., 2016. Experimental and Finite Element Study of the Reverse Faulting Effects on Buried Continuous Steel Gas Pipelines. Soil Dynamics and Earthquake Engineering, 86: 1–14. https://doi.org/10.1016/j.soildyn.2016.04.006
Jaramillo, C. A., 2017. Impact of Seismic Design on Tunnels in Rock—Case Histories. Underground Space, 2(2): 106–114. https://doi.org/10.1016/j.undsp.2017.03.004
Johansson, J., Konagai, K., 2006. Fault Induced Permanent Ground Deformations—An Experimental Comparison of Wet and Dry Soil and Implications for Buried Structures. Soil Dynamics and Earthquake Engineering, 26(1): 45–53. https://doi.org/10.1016/j.soildyn.2005.08.003
Karamitros, D. K., Bouckovalas, G. D., Kouretzis, G. P., 2007. Stress Analysis of Buried Steel Pipelines at Strike-Slip Fault Crossings. Soil Dynamics and Earthquake Engineering, 27(3): 200–211. https://doi.org/10.1016/j.soildyn.2006.08.001
Kontogianni, V. A., Stiros, S. C., 2003. Earthquakes and Seismic Faulting: Effects on Tunnels. Turkish Journal of Earth Sciences, 12(1): 153–156
Lee, J., Fenves, G. L., 1998. Plastic-Damage Model for Cyclic Loading of Concrete Structures. Journal of Engineering Mechanics, 124(8): 892–900. https://doi.org/10.1061/(asce)0733-9399(1998)124:8(892)
Li, H. F., Zhao, M., Du, X. L., 2020. Accurate H-Shaped Absorbing Boundary Condition in Frequency Domain for Scalar Wave Propagation in Layered Half-Space. International Journal for Numerical Methods in Engineering, 121(19): 4268–4291. https://doi.org/10.1002/nme.6424
Li, T. B., 2012. Damage to Mountain Tunnels Related to the Wenchuan Earthquake and some Suggestions for Aseismic Tunnel Construction. Bulletin of Engineering Geology and the Environment, 71(2): 297–308. https://doi.org/10.1007/s10064-011-0367-6
Liao, Z. P., Huang, K. L., Yang, B. P., et al., 1984. A Transmitting Boundary for Transient Wave Analyses. Science in China Series A-Mathematics, Physics, Astronomy and Technological Science, 27(10): 1063–1076 (in Chinese with English Abstract)
Lin, M. L., Chung, C. F., Jeng, F. S., et al., 2007. The Deformation of Overburden Soil Induced by Thrust Faulting and Its Impact on Underground Tunnels. Engineering Geology, 92(3/4): 110–132. https://doi.org/10.1016/j.enggeo.2007.03.008
Liu, N. N., Huang, Q. B., Ma, Y. J., et al., 2017. Experimental Study of a Segmented Metro Tunnel in a Ground Fissure Area. Soil Dynamics and Earthquake Engineering, 100: 410–416. https://doi.org/10.1016/j.soildyn.2017.06.018
Liu, X. Z., Li, X. F., Sang, Y. L., et al., 2015. Experimental Study on Normal Fault Rupture Propagation in Loose Strata and Its Impact on Mountain Tunnels. Tunnelling and Underground Space Technology, 49: 417–425. https://doi.org/10.1016/j.tust.2015.05.010
Lubliner, J., Oliver, J., Oller, S., et al., 1989. A Plastic-Damage Model for Concrete. International Journal of Solids and Structures, 25(3): 299–326. https://doi.org/10.1016/0020-7683(89)90050-4
Lysmer, J., Kuhlemeyer, R. L., 1969. Finite Dynamic Model for Infinite Media. Journal of the Engineering Mechanics Division, 95(4): 859–877. https://doi.org/10.1061/jmcea3.0001144
Moradi, M., Rojhani, M., Galandarzadeh, A., et al., 2013. Centrifuge Modeling of Buried Continuous Pipelines Subjected to Normal Faulting. Earthquake Engineering and Engineering Vibration, 12(1): 155–164. https://doi.org/10.1007/s11803-013-0159-z
Newmark, N. M., Hall, W. J., 1975. Pipeline Design to Resist Large Fault Displacement. Proceedings of U. S. NCEE. Ann Arbor: University of Michigan, 416–425
Shahidi, A. R., Vafaeian, M., 2005. Analysis of Longitudinal Profile of the Tunnels in the Active Faulted Zone and Designing the Flexible Lining (for Koohrang-III Tunnel). Tunnelling and Underground Space Technology, 20(3): 213–221. https://doi.org/10.1016/j.tust.2004.08.003
Sim, W. W., Towhata, I., Yamada, S., et al., 2012. Shaking Table Tests Modelling Small Diameter Pipes Crossing a Vertical Fault. Soil Dynamics and Earthquake Engineering, 35: 59–71. https://doi.org/10.1016/j.soildyn.2011.11.005
Tian, Z. M., Zhao, M., Du, X. L., et al., 2014. Earthquake Damage Mechanism and Earthquake-Resistant Characteristics of Special Underground Structures in Mountainous Region Rock. Earthquake Engineering and Engineering Dynamics, 34(S1): 926–935 (in Chinese with English Abstract)
Trifonov, O. V., Cherniy, V. P., 2010. A Semi-Analytical Approach to a Nonlinear Stress-Strain Analysis of Buried Steel Pipelines Crossing Active Faults. Soil Dynamics and Earthquake Engineering, 30(11): 1298–1308. https://doi.org/10.1016/j.soildyn.2010.06.002
Trifonov, O. V., Cherniy, V. P., 2012. Elastoplastic Stress-Strain Analysis of Buried Steel Pipelines Subjected to Fault Displacements with Account for Service Loads. Soil Dynamics and Earthquake Engineering, 33(1): 54–62. https://doi.org/10.1016/j.soildyn.2011.10.001
Vazouras, P., Dakoulas, P., Karamanos, S. A., 2015. Pipe-Soil Interaction and Pipeline Performance under Strike-Slip Fault Movements. Soil Dynamics and Earthquake Engineering, 72: 48–65. https://doi.org/10.1016/j.soildyn.2015.01.014
Vazouras, P., Karamanos, S. A., Dakoulas, P., 2012. Mechanical Behavior of Buried Steel Pipes Crossing Active Strike-Slip Faults. Soil Dynamics and Earthquake Engineering, 41: 164–180. https://doi.org/10.1016/j.soildyn.2012.05.012
Wang, L. R. L., Yeh, Y. H., 1985. A Refined Seismic Analysis and Design of Buried Pipeline for Fault Movement. Earthquake Engineering & Structural Dynamics, 13(1): 75–96. https://doi.org/10.1002/eqe.4290130109
Wang, Z. Z., Zhang, Z., Gao, B., 2012. The Seismic Behavior of the Tunnel across Active Fault. Proceedings 15th World Conference on Earthquake Engineering, Lisbon
Wolf, J. P., Song, C., 1996. Finite Element Modelling of Unbounded Media. John Wiley and Sons, West Sussex
Xu, L. G., Lin, M., 2017. Analysis of Buried Pipelines Subjected to Reverse Fault Motion Using the Vector Form Intrinsic Finite Element Method. Soil Dynamics and Earthquake Engineering, 93: 61–83. https://doi.org/10.1016/j.soildyn.2016.12.004
Yang, S., Mavroeidis, G. P., 2018. Bridges Crossing Fault Rupture Zones: A Review. Soil Dynamics and Earthquake Engineering, 113: 545–571. https://doi.org/10.1016/j.soildyn.2018.03.027
Yang, Y. S., Yu, H. T., Yuan, Y., et al., 2020. Analytical Solution for Longitudinal Seismic Response of Long Tunnels Subjected to Rayleigh Waves. International Journal for Numerical and Analytical Methods in Geomechanics, 44(10): 1371–1385. https://doi.org/10.1002/nag.3066
Yang, Z. H., Lan, H. X., Zhang, Y. S., et al., 2013. Nonlinear Dynamic Failure Process of Tunnel-Fault System in Response to Strong Seismic Event. Journal of Asian Earth Sciences, 64: 125–135. https://doi.org/10.1016/j.jseaes.2012.12.006
Yu, H. T., Chen, J. T., Bobet, A., et al., 2016a. Damage Observation and Assessment of the Longxi Tunnel during the Wenchuan Earthquake. Tunnelling and Underground Space Technology, 54: 102–116. https://doi.org/10.1016/j.tust.2016.02.008
Yu, H. T., Chen, J. T., Yuan, Y., et al., 2016b. Seismic Damage of Mountain Tunnels during the 5.12 Wenchuan Earthquake. Journal of Mountain Science, 13(11): 1958–1972. https://doi.org/10.1007/s11629-016-3878-6
Yu, H. T., Sun, Y. Q., Li, P., et al., 2020. Analytical Solution for Dynamic Response of Underground Rectangular Fluid Tank Subjected to Arbitrary Dynamic Loads. Journal of Engineering Mechanics, 146(8): 04020077. https://doi.org/10.1061/(asce)em.1943-7889.0001817
Yu, H. T., Yuan, Y., Bobet, A., 2017. Seismic Analysis of Long Tunnels: A Review of Simplified and Unified Methods. Underground Space, 2(2): 73–87. https://doi.org/10.1016/j.undsp.2017.05.003
Zhang, C. H., Pan, J. W., Wang, J. T., 2009. Influence of Seismic Input Mechanisms and Radiation Damping on Arch Dam Response. Soil Dynamics and Earthquake Engineering, 29(9): 1282–1293. https://doi.org/10.1016/j.soildyn.2009.03.003
Zhang, L. S., Zhao, X. B., Yan, X. Z., et al., 2016. A New Finite Element Model of Buried Steel Pipelines Crossing Strike-Slip Faults Considering Equivalent Boundary Springs. Engineering Structures, 123: 30–44. https://doi.org/10.1016/j.engstruct.2016.05.042
Zhao, M., Du, X. L., Liu, J. B., et al., 2011. Explicit Finite Element Artificial Boundary Scheme for Transient Scalar Waves in Two-Dimensional Unbounded Waveguide. International Journal for Numerical Methods in Engineering, 87(11): 1074–1104. https://doi.org/10.1002/nme.3147
Zhao, M., Gao, Z. D., Du, X. L., et al., 2019a. Response Spectrum Method for Seismic Soil-Structure Interaction Analysis of Underground Structure. Bulletin of Earthquake Engineering, 17(9): 5339–5363. https://doi.org/10.1007/s10518-019-00673-6
Zhao, M., Li, H. F., Du, X. L., et al., 2019b. Time-Domain Stability of Artificial Boundary Condition Coupled with Finite Element for Dynamic and Wave Problems in Unbounded Media. International Journal of Computational Methods, 16(4): 1850099. https://doi.org/10.1142/s0219876218500998
Zhao, M., Wu, L. H., Du, X. L., et al., 2018. Stable High-Order Absorbing Boundary Condition Based on New Continued Fraction for Scalar Wave Propagation in Unbounded Multilayer Media. Computer Methods in Applied Mechanics and Engineering, 334: 111–137. https://doi.org/10.1016/j.cma.2018.01.018
Acknowledgments
This research was supported by the Beijing Natural Science Foundation Program (No. JQ19029), the National Natural Science Foundation of China (No. 51421005), the Ministry of Education Innovation Team of China (No. IRT_17R03). The final publication is available at Springer via https://doi.org/10.1007/s12583-021-1483-2.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jiao, H., Du, X., Zhao, M. et al. Nonlinear Seismic Response of Rock Tunnels Crossing Inactive Fault under Obliquely Incident Seismic P Waves. J. Earth Sci. 32, 1174–1189 (2021). https://doi.org/10.1007/s12583-021-1483-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12583-021-1483-2