Geomechanics and Engineering

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Viscous damping effects on the seismic elastic response of tunnels in three sites

  • Received : 2017.12.18
  • Accepted : 2019.08.22
  • Published : 2019.08.30
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Abstract

Time-domain commercial codes are widely used to evaluate the seismic behavior of tunnels. Those tools offer a good insight into the performance and the failure mechanism of tunnels under earthquake loading. Viscous damping is generally employed in the dynamic analysis to consider damping at very small strains in some cases, and the Rayleigh damping is commonly used one. Many procedures to obtain the damping parameters have been proposed but they are seldom discussed. This paper illustrates the influence of the Rayleigh damping formulation on the tunnel visco-elastic behavior under earthquake. Four Rayleigh damping determination procedures and three soil shear velocity profiles are accounted for. The results show significant differences in the free-field and in the tunnel response caused by different procedures. The difference is somewhat decreased when the soil site fundamental frequency is increased. The conventional method which consists of using solely the first soil natural mode to determine the viscous damping parameters may lead to an unsafe seismic design of the tunnel. In general, using five times site fundamental frequency to obtain the damping formulation can provide relatively conservative results.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

References

  1. Amorosi, A., Boldini, D. and Elia, G. (2010), "Parametric study on seismic ground response by finite element modeling", Comput. Geotech., 37(4), 515-528. https://doi.org/10.1016/j.compgeo.2010.02.005.
  2. Amorosi, A., Boldini, D. and Falcone G. (2014), "Numerical predication of tunnel performance during centrifuge dynamic tests", Acta Geotechnica, 9(4), 581-596. https://doi.org/10.1007/s11440-013-0295-7.
  3. Badsar, B.A., Schevenels, M., Haegeman, W. and Degrande, G. (2010), "Determination of the material damping ratio in the soil from SASW tests using the half-power bandwidth method", Geophys. J. Int., 182(3), 1493-1508. https://doi.org/10.1111/j.1365-246X.2010.04690.x.
  4. Bilotta, E., Lanzano, G., Madabhushi, S.P.G. and Silvestri, F. (2014), "A numerical round robin on tunnels under seismic actions", Acta Geotechnica, 9(4), 563-579. https://doi.org/10.1007/s11440-014-0330-3.
  5. Bobet, A. (2010), "Drained and undrained response of deep tunnels subjected to farfield shear loading", Tunn. Undergr. Sp. Technol., 25(1), 21-31. https://doi.org/10.1016/j.tust.2009.08.001.
  6. Brennan, A.J., Thusyanthan, N.I. and Madabhushi, S.P.G. (2005), "Evaluation of shear modulus and damping in dynamic centrifuge tests", J. Geotech. Geoenviron. Eng., 131(12), 1488-1497. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:12(1488).
  7. Carlton, B.D. and Pestana, J.M. (2016), "A unified model for estimating the in-situ small strain modulus of clays, silts, sands, and gravels", Soil Dyn. Earthq. Eng., 88, 345-355. https://doi.org/10.1016/j.soildyn.2016.01.019.
  8. Chen, D.H., Du, C.B., Yuan, J.W. and Hong, Y.W. (2012), "An investigation into the influence of damping on the earthquake response analysis of a high arch dam", J. Earthq. Eng., 16(3), 329-349. https://doi.org/10.1080/13632469.2011.638697.
  9. Cilingir, U. and Madabhushi, S.P.G. (2011), "A model study on the effects of input motion on the seismic behavior of tunnels", Soil Dyn. Earthq. Eng., 31(3), 452-462. https://doi.org/10.1016/j.soildyn.2010.10.004.
  10. Conti, R., Viggiani, G.M.B. and Perugini, F. (2014), "Numerical modelling of centrifuge dynamic tests of circular tunnels in dry sand", Acta Geotechnica, 9(4), 597-612. https://doi.org/10.1007/s11440-013-0286-8.
  11. Dinesh, S.V., Sitharam, T.G. and Vinod, J.S. (2004), "Dynamic properties and liquefaction behavior of granular materials using discrete element method", Current Sci., 87(10), 1379-1387.
  12. Gomes, R.C. (2014), "Numerical simulation of the seismic response of tunnels in sand with an elastoplastic model", Acta Geotechnica, 9(4), 613-629. https://doi.org/10.1007/s11440-013-0287-7.
  13. Guo, X., Wong, Y.L. and Yuan, Y.F. (2002), "Estimation of damping ratio of soil sites using microtremor", Earthq. Eng. Eng. Vib., 1(1), 45-49. https://doi.org/10.1007/s11803-002-0006-0.
  14. Groholski, D.R. and Hashash Y.M.A. (2013), "Development of an inverse analysis framework for extracting dynamic soil behavior and pore pressure response from downhole array measurements", Int. J. Numer. Anal. Meth. Geomech., 37(12), 1867-1890. https://doi.org/10.1002/nag.2172.
  15. Groholski, D.R., Hashash, Y.M.A. and Matasovic, N. (2014), "Learning of pore pressure response and dynamic soil behavior from downhole array measurements", Soil Dyn. Earthq. Eng., 61, 40-56. https://doi.org/10.1016/j.soildyn.2014.01.018.
  16. Hardyniec, A. and Charney, F. (2015), "An investigation into effects of damping and nonlinear geometry models in earthquake engineering analysis", Earthq. Eng. Struct. Dyn., 44, 2695-2715. https://doi.org/10.1002/eqe.2604.
  17. Hashash, Y.M.A. and Park, D. (2001), "Non-linear onedimensional seismic ground motion propagation in the Mississippi embayment", Eng. Geol., 62(1-3), 185-206. https://doi.org/10.1016/S0013-7952(01)00061-8.
  18. Hashash, Y.M.A. and Park, D. (2002), "Viscous damping formulation and high frequency motion propagation in nonlinear site response analysis", Soil Dyn. Earthq. Eng., 22(7), 611-624. https://doi.org/10.1016/S0267-7261(02)00042-8.
  19. Hatzigeorgiou, G.D. and Beskos, D.E. (2010), "Soil-structure interaction effects on seismic inelastic analysis of 3-D tunnels", Soil Dyn. Earthq. Eng., 30(9), 851-861. https://doi.org/10.1016/j.soildyn.2010.03.010.
  20. Hleibieh, J., Wegener, D. and Herle, I. (2014), "Numerical simulation of a tunnel surrounded by sand under earthquake using a hypoplastic model", Acta Geotechnica, 9(4), 631-640. https://doi.org/10.1007/s11440-013-0294-8.
  21. Hudson, M., Idriss, M. and Beikae, M. (1994), "User manual for QUAD4M: A computer program to evaluate the seismic response of soil structures using finite element procedures and incorporating a compliant base," University of California, Berkeley, California, U.S.A.
  22. Hu, Y.X. (2006), Earthquake Engineering, Seismological Press, Beijing, China.
  23. Idriss, I.M., Lysmer, J. and Hwang, R. (1973), "QUAD4: A computer program for evaluating the seismic response of soil structures by variable finite element procedures," University of California, Berkeley, California, U.S.A.
  24. Itasca. (2005), Software Manual of FLAC Version5.0, Itasca Consulting Group.
  25. Kontoe, S., Zdravkovic, L., Potts, D.M. and Menkiti, C.O. (2011), "On the relative merits of simple and advanced constitutive models in dynamic analysis of tunnels", Geotechnique, 61(10), 815-829. http://dx.doi.org/10.1680/geot.9.P.141.
  26. Kokusho, T. (1980), "Cyclic triaxial test of dynamic soil properties for wide strain range", Soil. Found., 20(2), 45-60. https://doi.org/10.3208/sandf1972.20.2_45.
  27. Kramer, S.L. (1996), Geotechnical Earthquake Engineering, Prentice-Hall, Upper Saddle River, New Jersey.
  28. Kwok, A.O.L., Stewart, J.P., Hashash, Y.M.A., Matasovic, N., Pyke, R., Wang, Z.Z. and Yang, Z.H. (2007), "Use of exact solution of wave propagation problems to guide implementation of nonlinear seismic ground response analysis procedures", J. Geotech. Geoenviron. Eng., 133(11), 1385-1398. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:11(1385).
  29. Li, Z., Escoffier, S. and Kotronis, P. (2013), "Using centrifuge tests data to identify the dynamic soil properties: Application to Fontainebleau sand", Soil Dyn. Earthq. Eng., 52, 77-87. https://doi.org/10.1016/j.soildyn.2013.05.004.
  30. Lings, M.L. and Greening, P.D. (2001), "A novel bender/extender element for soil testing", Geotechnique, 51(8), 713-717. https://doi.org/10.1680/geot.2001.51.8.713
  31. Liu, X.R., Li, D.L., Wang, J.B. and Wang, Z. (2015), "Surrounding rock pressure of shallow-buried bias tunnels under earthquake", Geomech. Eng., 9(4), 427-445. https://doi.org/10.12989/gae.2015.9.4.427.
  32. Lysmer, J. and Kuhlemeyer, R.L. (1969), "Finite dynamic model for infinite media", J. Eng. Div., 95(4), 859-877.
  33. Manica, N., Ovando, E. and Botero, B. (2014), "Assessment of damping models in FLAC", Comput. Geotech., 59, 12-20. https://doi.org/10.1016/j.compgeo.2014.02.007.
  34. Ni, B. (2007), "Implementation of a bubble model in Flac and its application in dynamic analysis," Ph.D. Thesis, University of Auckland, Auckland, New Zealand.
  35. Park, D. and Hashash, Y.M.A. (2004), "Soil damping formulation in nonlinear time domain site response analysis", J. Earthq. Eng., 8(2), 249-274. https://doi.org/10.1080/13632460409350489
  36. Park, K.H., Tantayopin, K., Tontavanich, B. and Owatsiwong, A. (2009), "Analytical solution for seismic-induced ovaling of circular tunnel lining under no-slip interface conditions: A revisit", Tunn. Undergr. Sp. Technol., 24(2), 231-235. https://doi.org/10.1016/j.tust.2008.07.001.
  37. Peck, R.B., Hendron, A.J. and Mohraz, B. (1972), "State of the art of soft ground tunnelling", Proceedings of the Rapid Excavation and Tunnelling Conference, Chicago, Illinois, U.S.A., June.
  38. Penzien, J. (2000), "Seismically induced racking of tunnel linings", Earthq. Eng. Struct. Dyn., 29(5), 689-691. https://doi.org/10.1002/(SICI)1096-9845(200005)29:5%3C683::AID-EQE932%3E3.0.CO;2-1.
  39. Phillips, C. and Hashash, Y.M.A. (2009), "Damping formulation for nonlinear 1D site response analyses", Soil Dyn. Earthq. Eng., 29(7), 1143-1158. https://doi.org/10.1016/j.soildyn.2009.01.004.
  40. Priestley, M.J.N. and Grant, D.N. (2005), "Viscous damping in seismic design and analysis", J. Earthq. Eng., 9(Spec2), 229-255. https://doi.org/10.1142/S1363246905002365
  41. Rayhani, M.H.T. and Naggar, M.H.E. (2008), "Dynamic properties of soft clay and loose sand from seismic centrifuge tests", Geotech. Geol. Eng., 26(5), 593-602. https://doi.org/10.1007/s10706-008-9192-5.
  42. Sedarat, H., Kozak, A., Hashash, Y.M.A., Shamsabadi, A. and Krimotat, A. (2009), "Contact interface in seismic analysis of circular tunnels", Tunn. Undergr. Sp. Technol., 24(4), 482-490. https://doi.org/10.1016/j.tust.2008.11.002.
  43. Senetakis, K., Anastasiadis, A. and Pitilakis, K. (2015), "A comparison of material damping measurements in resonant column using the steady-state and free-vibration decay method", Soil Dyn. Earthq. Eng., 74, 10-13. https://doi.org/10.1016/j.soildyn.2015.03.009.
  44. Sevim, B. (2013), "Assessment of 3D earthquake response of the Arhavi Highway tunnel considering soil-structure interaction", Comput. Concrete, 11(1), 51-61. https://doi.org/10.12989/cac.2013.11.1.051.
  45. Shih, J.Y., Thompson, D.J. and Zervos, A. (2016), "The effect of boundary conditions, model size and damping models in the finite element modeling of a moving load on track/ground system", Soil Dyn. Earthq. Eng., 89, 12-27. https://doi.org/10.1016/j.soildyn.2016.07.004.
  46. Sun, Q.Q., Bo, J.S., Sun, Y.W. and Zhang, Z.P. (2016a), "A stateof-the-art review of seismic response analysis of tunnels", World Earthq. Eng., 32, 159-169.
  47. Sun, Q.Q., Bo, J.S., Li, X.B. and Wang, X. (2016b), "Comparative study of viscous damping formulation in time-domain site response analysis", Earthq. Eng. Eng. Dyn., 36, 171-179.
  48. Sun, Q.Q. and Bo, J.S. (2017), "Effect of Rayleigh damping matrix on seismic response analysis of deep soft site", Chin. Earthq. Eng., 39, 506-510.
  49. Sun, Q.Q. and Dias, D. (2019a), "Assessment of stress relief during excavation on the seismic tunnel response by the pseudostatic method", Soil Dyn. Earthq. Eng., 117, 384-397. https://doi.org/10.1016/j.soildyn.2018.09.019.
  50. Sun, Q.Q. and Dias, D. (2019b), "Seismic behavior of circular tunnels: Influence of the initial stress state", Soil Dyn. Earthq. Eng., 126, 105808. https://doi.org/10.1016/j.soildyn.2019.105808.
  51. Sun, Q.Q., Dias, D. and Sousa, L.R. (2019), "Impact of an underlying soft soil layer on tunnel lining in seismic conditions", Tunn. Undergr. Sp. Technol., 90, 293-308. https://doi.org/10.1016/j.tust.2019.05.011.
  52. Tong, L. and Wang, Y.H. (2015), "DEM simulation of shear modulus an damping ratio of sand with emphasis on the effects of particle number, particle shape, and aging", Acta Geotechnica, 10(1), 117-130. https://doi.org/10.1007/s11440-014-0331-2.
  53. Tsai, C.C. and Hashash, Y.M.A. (2008), "A novel framework integrating downhole array data and site analysis to extract dynamic soil behavior", Soil Dyn. Earthq. Eng., 28(3), 181-197. https://doi.org/10.1016/j.soildyn.2007.06.008.
  54. Tsai, C.C., Park, D. and Chen, C.W. (2014), "Selection of the optimal frequencies of viscous damping formulation in nonlinear time-domain site response analysis", Soil Dyn. Earthq. Eng., 67, 353-358. https://doi.org/10.1016/j.soildyn.2014.10.026.
  55. Tsinidis, G., Pitilankis, K. and Trikalioti, A. D. (2014), "Numerical simulation of round robin numerical test on tunnels using a simplified kinematic hardening model", Acta Geotechnica, 9, 641-659. https://doi.org/10.1007/s11440-013-0293-9.
  56. Visone, C., Bilotta, E. and Magistris, F.S.D. (2010), "Onedimensional ground response as a preliminary tool for dynamic analyses in geotechnical earthquake engineering", J. Earthq. Eng., 14(1), 131-162. https://doi.org/10.1080/13632460902988950.
  57. Vucetic, M., Lanzo, G. and Doroudian, M. (1998), "Damping at small strains in cyclic simple shear test", J. Geotech. Geoenviron. Eng., 124(7), 585-594. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:7(585).
  58. Wang, J.N. (1993), Seismic Design of Tunnels: A State-of-the-Art Approach, Parsons, Brinckerhoff, Quade and Douglas Inc., New York, U.S.A.
  59. Wang, J.T. (2011), "Investigation of damping in arch dam-waterfoundation rock system of Mauvoisin arch dam", Soil Dyn. Earthq. Eng., 31, 33-44. https://doi.org/10.1016/j.soildyn.2010.08.002
  60. Wang, Z.Z. and Zhang, Z. (2013), "Seismic damage classification and risk assessment of mountain tunnels with a validation for the 2008 Wenchuan earthquake", Soil Dyn. Earthq. Eng., 45, 45-55. https://doi.org/10.1016/j.soildyn.2012.11.002.
  61. Yu, H.T., Chen, J.T., Bobet, A. and Yuan, Y. (2016), "Damage observation and assessment of the Longxi tunnel during the Wenchuan earthquake", Tunn. Undergr. Sp. Technol., 54, 102-116. https://doi.org/10.1016/j.tust.2016.02.008.
  62. Zhang, C.H., Pan, J.W. and Wang, J.T. (2009), "Influence of seismic input mechanisms and radiation damping on arch dam response", Soil Dyn. Earthq. Eng., 29(9), 1282-1293. https://doi.org/10.1016/j.soildyn.2009.03.003.
  63. Zhang, B., Wang, X., Zhang, J.S. and Meng, F. (2017), "Threedimensional limit analysis of seismic stability of tunnel face with quasi-static method", Geomech. Eng., 13(2), 301-318. https://doi.org/10.12989/gae.2017.13.2.301.

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