Seismic Stability Analysis of Square and Rectangular Tunnels in Cohesive-Frictional Soils
Abstract
Seismic activity on a tunnel damages the tunnel support systems. The extent of the tunnel damage depends on the soil type, the magnitude of the earthquake acceleration, and the tunnel cover depth. Hence, analyzing the stress induced by the seismic event from the surrounding ground on the tunnel facilitates a safe tunnel design. Based on the pseudostatic method, this study examined the seismic stability of square and rectangular tunnels placed in cohesive-frictional soil. The tunnel collapse load was found using the lower-bound theorem of limit analysis in combination with the finite-element method. From the distribution of stresses along the periphery, the normal stress at each tunnel node was calculated, and the maximum of stresses was reported as the support pressure. Thus, the systems safeguarding the tunnel against devastating lateral earthquake forces are expected to offer the ultimate resistance equal to the maximum normal stress on the tunnel periphery. With the increase in tunnel cover depth, aspect ratio, seismic acceleration coefficients, and a decrease in soil cohesion and friction angle, the support pressure was noted to enhance. The distribution of normal stresses around the tunnel periphery depends on the tunnel geometry, the soil’s shear strength parameters, and the magnitude of earthquake acceleration. For a square tunnel, the magnitude of stress was maximum on the walls, followed by the roof and base, implying that collapse will be more prone from the side walls. However, the rectangular tunnels are noted to be susceptible to collapse from the roof, followed by walls and base.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
References
Abbo, A. J., D. W. Wilson, S. W. Sloan, and A. V. Lyamin. 2013. “Undrained stability of wide rectangular tunnels.” Comput. Geotech. 53 (Sep): 46–59. https://doi.org/10.1016/j.compgeo.2013.04.005.
ASCE. 2017. Minimum design loads and associated criteria for buildings and other structures. ASCE/SEI 7. Reston, VA: ASCE.
Assadi, A., and S. W. Sloan. 1991. “Undrained stability of shallow square tunnel.” J. Geotech. Eng. 117 (8): 1152–1173. https://doi.org/10.1061/(ASCE)0733-9410(1991)117:8(1152).
BIS (Bureau of Indian Standards). 2019. Criteria for earthquake resistant design of structures: Part 3 bridges and retaining walls. IS 1893: Part 3. New Delhi, India: Bureau of Indian Standards.
Casablanca, O., G. Biondi, E. Cascone, and G. Di Filippo. 2022. “Static and seismic bearing capacity of shallow strip foundations on slopes.” Géotechnique 72 (9): 769–783. https://doi.org/10.1680/jgeot.20.P.044.
CEN (European Committee for Standardization). 2004. Design of structures for earthquake resistance—Part 5: Foundations, retaining structures and geotechnical aspects. Eurocode 8 (EN 1998-5). Brussels, Belgium: CEN.
Chen, F., W. Kang, Z. Yang, and L. Xu. 2022. “Seismic pseudo-static active earth pressure of narrow c-φ soils on gravity walls under translational mode.” In Soil dynamics and earthquake engineering, 161. Amsterdam, Netherlands: Elsevier.
Cilingir, U., and S. P. G. Madabhushi. 2011. “Effect of depth on the seismic response of square tunnels.” Soils Found. 51 (3): 449–457. https://doi.org/10.3208/sandf.51.449.
Davis, E. H., M. J. Gunn, R. J. Mair, and H. N. Seneviratne. 1980. “The stability of shallow tunnels and underground openings in cohesive material.” Géotechnique 30 (4): 397–416. https://doi.org/10.1680/geot.1980.30.4.397.
Dowding, C. H., and A. Rozan. 1978. “Damage to rock tunnels from earthquake shaking.” J. Geotech. Eng. Div. 104 (2): 175–191. https://doi.org/10.1061/AJGEB6.0000580.
FEMA. 2020. NEHRP recommended seismic provisions for new buildings and other structures. Washington, DC: FEMA.
Ganesh, R., and J. P. Sahoo. 2022. “Vertical uplift capacity of rectangular and square plate anchors in granular soil under seismic forces.” J. Earthquake Eng. 26 (14): 7366–7383. https://doi.org/10.1080/13632469.2021.1964641.
Hynes-Griffin, M. E., and A. G. Franklin. 1984. Rationalizing the seismic coefficient method. Washington, DC: USACE.
International Tunnelling Association. 2000. “Guidelines for the design of shield tunnel lining.” Tunnelling Underground Space Technol. 15 (3): 303–331. https://doi.org/10.1016/S0886-7798(00)00058-4.
Konagai, K., J. Johansson, A. Zafeirakos, M. Numada, and A. A. Sadr. 2005. “Damage to tunnels in the October 23, 2004 Chuetsu earthquake.” J. Earthquake Eng. 28: 75.
Koyama, Y. 2003. “Present status and technology of shield tunneling method in Japan.” Tunnelling Underground Space Technol. 18 (2–3): 145–159. https://doi.org/10.1016/S0886-7798(03)00040-3.
Kramer, S. L. 2007. Geotechnical earthquake engineering. New Delhi, India: Pearson Education.
Li, J. 2017. “Key technologies and applications of the design and manufacturing of non-circular TBMs.” Engineering 3 (6): 905–914. https://doi.org/10.1016/j.eng.2017.12.002.
Li, T. 2012. “Damage to mountain tunnels related to the Wenchuan earthquake and some suggestions for aseismic tunnel construction.” Bull. Eng. Geol. Environ. 71 (2): 297–308. https://doi.org/10.1007/s10064-011-0367-6.
Lu, C.-C., and J.-H. Hwang. 2008. “Damage of new Sanyi railway tunnel during the 1999 Chi-Chi earthquake.” In Proc., Geotechnical Earthquake Engineering and Soil Dynamics IV, edited by D. Zeng, M. T. Manzari, and D. R. Hiltunen, Reston, VA: ASCE.
Makrodimopoulos, A., and C. M. Martin. 2006. “Lower bound limit analysis of cohesive-frictional materials using second-order cone programming.” Int. J. Numer. Methods Eng. 66 (4): 604–634. https://doi.org/10.1002/nme.1567.
Marcuson, W. F., and A. G. Franklin. 1983. Seismic design, analysis, and remedial measures to improve stability of existing earth dams. Washington, DC: US Army.
Melo, C., and S. Sharma. 2004. “Seismic coefficients for pseudostatic slope analysis.” In Proc., 13th World Conf. on Earthquake Engineering. Vancouver, BC, Canada: Canadian Association for Earthquake Engineering.
Ngan Vu, M., W. Broere, and J. W. Bosch. 2017. “Structural analysis for shallow tunnels in soft soils.” Int. J. Geomech. 17 (8): 04017038. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000866.
Peng, W., M. Zhao, H. Zhao, and C. Yang. 2022. “Seismic stability of the slope containing a laterally loaded pile by finite-element limit analysis.” Int. J. Geomech. 22 (1): 06021033. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002226.
Roy, N., and R. Sarkar. 2017. “A review of seismic damage of mountain tunnels and probable failure mechanisms.” Geotech. Geol. Eng. 35 (1): 1–28. https://doi.org/10.1007/s10706-016-0091-x.
Sharma, S., and W. R. Judd. 1991. “Underground opening damage from earthquakes.” Eng. Geol. 30 (9): 263–276. https://doi.org/10.1016/0013-7952(91)90063-Q.
Shiau, J., S. Keawsawasvong, and W. Yodsomjai. 2023. “Determination of support pressure for the design of square box culverts.” Int. J. Geomech. 23 (1): 06022035. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002620.
Sloan, S. W. 1988. “Lower bound limit analysis using finite elements and linear programming.” Int. J. Numer. Anal. Methods Geomech. 12 (1): 61–77. https://doi.org/10.1002/nag.1610120105.
Tsinidis, G., K. Pitilakis, and G. Madabhushi. 2016. “On the dynamic response of square tunnels in sand.” Eng. Struct. 125 (Oct): 419–437. https://doi.org/10.1016/j.engstruct.2016.07.014.
Ukritchon, B., and S. Keawsawasvong. 2020. “Undrained stability of unlined square tunnels in clays with linearly increasing anisotropic shear strength.” Geotech. Geol. Eng. 38 (1): 897–915. https://doi.org/10.1007/s10706-019-01023-8.
Wang, J.-N. 1993. Seismic design of tunnels–A simple state-of-the-art design approach. New York: Parsons Brinckerhoff Inc.
Wang, W. L., T. T. Wang, J. J. Su, C. H. Lin, C. R. Seng, and T. H. Hunag. 2001. “Assessment of damage in mountain tunnels due to the Taiwan Chi-Chi earthquake.” Tunnelling Underground Space Technol. 16 (1): 133–150. https://doi.org/10.1016/S0886-7798(01)00047-5.
Wilson, D. W., A. J. Abbo, and S. W. Sloan. 2015. “Undrained stability of tall tunnels.” In Computer methods and recent advances in geomechanics, 447–452. New York: Taylor & Francis.
Wilson, D. W., A. J. Abbo, S. W. Sloan, and K. Yamamotob. 2017. “Undrained stability of rectangular tunnels where shear strength increases linearly with depth.” Canadian Geotech. J. 54 (4): 469–480. https://doi.org/10.1139/cgj-2016-0072.
Wood, M. 1975. “The circular tunnel in elastic ground.” Géotechnique 25 (1): 115–127. https://doi.org/10.1680/geot.1975.25.1.115.
Wu, B. R., and C. J. Lee. 2003. “Ground movements and collapse mechanisms induced by tunneling in clayey soil.” Int. J. Phys. Modell. Geotech. 3 (4): 15–29. https://doi.org/10.1680/ijpmg.2003.030402.
Xu, P., Y. Zhong, K. Hatami, G. Yang, W. Liu, and G. Jiang. 2023. “Influence of reinforcement design on seismic stability of full-height panel MSE walls.” In Soil dynamics and earthquake engineering, 165. New York: Elsevier.
Yang, F., and J. S. Yang. 2010. “Stability of shallow tunnel using rigid blocks and finite-element upper bound solutions.” Int. J. Geomech. 10 (6): 242–247. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000011.
Yu, H., J. Chen, A. Bobet, and Y. Yuan. 2016. “Damage observation and assessment of the Longxi tunnel during the Wenchuan earthquake.” Tunnelling Underground Space Technol. 54 (Feb): 102–116. https://doi.org/10.1016/j.tust.2016.02.008.
Zhao, L. H., X. Cheng, H. C. Dan, Z. P. Tang, and Y. Zhang. 2017. “Effect of the vertical earthquake component on permanent seismic displacement of soil slopes based on the nonlinear Mohr–Coulomb failure criterion.” Soils Found. 57 (2): 237–251. https://doi.org/10.1016/j.sandf.2016.12.002.
Information & Authors
Information
Published In
Natural Hazards Review
Volume 25 • Issue 3 • August 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Jun 9, 2023
Accepted: Feb 23, 2024
Published online: Apr 27, 2024
Published in print: Aug 1, 2024
Discussion open until: Sep 27, 2024
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.