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Bulletin of Earthquake Engineering

, Volume 12, Issue 2, pp 981–1005 | Cite as

Seismic response of lined tunnels in the half-plane with surface topography

  • Sonia L. Parvanova
  • Petia S. Dineva
  • George D. ManolisEmail author
  • Frank Wuttke
Original Research Paper

Abstract

In this work, we examine the seismic response of multiple tunnels reinforced with liners and buried within the elastic homogeneous half-plane in the presence of surface relief. The seismic waves are upward propagating, time-harmonic, horizontally polarized shear (SH) waves. More specifically, we examine: (a) the scattered wave fields along the free surface and inside the half-plane with the embedded tunnels; (b) the dynamic stress concentration factors that develop at the soil-liner interfaces; (c) the stresses and displacements that develop inside the tunnel liners. We use a sub-structuring technique that is based on the direct boundary element method to model each constituent part of the problem separately. Then, assembly of the full problem is accomplished through the imposition of compatibility and equilibrium conditions at all interfaces. Next, a detailed verification study is carried out based on comparisons against available analytical and/or numerical results for a series of test examples. Subsequently, detailed numerical simulations are conducted and the results of these parametric studies reveal the influence of the following key parameters on the soil-tunnel system response: (a) the shape of the free-surface relief; (b) the depth of placement of the tunnels and their separation distance; (c) the SH-wavelength to tunnel diameter ratio; (d) the elastic properties of the tunnel lining rings and (e) the dynamic interaction effects between the free-surface relief and the tunnels.

Keywords

Seismic response SH-waves Surface relief Lined tunnels  Boundary elements Dynamic stress concentration 

Notes

Acknowledgments

Authors P.S.D. and F.W. wish to acknowledge support provided through the DFG Grant No. DFG-Wu 496/5-1.

References

  1. Achenbach JD (1973) Wave propagation in elastic solids. North-Holland, AmsterdamGoogle Scholar
  2. Beskos DE (1987) Boundary element methods in dynamic analysis. Appl Mech Rev 40:1–23CrossRefGoogle Scholar
  3. Beskos DE (1997) Boundary element methods in dynamic analysis: Part II (1986–1996). Appl Mech Rev 50(3):149–197CrossRefGoogle Scholar
  4. Cao XR, Song TS, Liu DK (2001) Scattering of plane SH-wave by a cylindrical hill of arbitrary shape. Appl Math Mech 22(9):1082–1089CrossRefGoogle Scholar
  5. Chen JT, Chen PY, Chen CT (2008) Surface motion of multiple alluvial valleys for incident plane SH-waves by using a semi-analytical approach. Soil Dyn Earthq Eng 28:58–72CrossRefGoogle Scholar
  6. Chen JT, Lee JW, Wu CF, Chen IL (2011) SH-wave diffraction by a semi-circular hill revisited: a null-field boundary integral equation method using degenerate kernels. Soil Dyn Earthq Eng 31:729–736CrossRefGoogle Scholar
  7. Chen PY, Chen CT, Chen JT (2005) A semi-analytical approach for dynamic stress concentration factor of Helmholtz problems with circular holes. In: Proceedings of the 29th national conference on theoretical and applied mechanics (NTHU), Hsinchu, Taiwan, Dec 16–17, pp E046–1- E046–8Google Scholar
  8. Chen Z (2007) Effects of shallow buried cavity on anti-plane ground motion. Rock Soil Mech 28(8):1655–1660Google Scholar
  9. Datta SK, El-Akily AH (1978) Diffraction of elastic waves in a half-space I. Integral representation and matched asymptotic expansions. In: Miklowitz J, Achenbach JD (eds) Modern problems in elastic wave propagation. Wiley, New YorkGoogle Scholar
  10. Datta SK, Shah AH (1982) Scattering of SH-waves by embedded cavities. Wave Motion 4:256–283CrossRefGoogle Scholar
  11. Dineva PS, Wuttke F, Manolis GD (2012) Elastic wave scattering and stress concentration effects in non-homogeneous poroelastic geological media with discontinuities. Soil Dyn Earthq Eng 41:102–118CrossRefGoogle Scholar
  12. Dravinski M, Yu MC (2011) Scattering of plane harmonic SH waves by multiple inclusions. Geophys J Int 186:1246–1331CrossRefGoogle Scholar
  13. Fu LY, Bouchon M (2004) Discrete wavenumber solutions to numerical wave propagation in piecewise heterogeneous media-I. Theory of two-dimensional SH-case. Geophys J Int 157:481–498CrossRefGoogle Scholar
  14. Fu LY (2005) Rough surface scattering: comparison of various approximation theories for 2D SH-waves. Bull Seismol Soc Am 95:646–663CrossRefGoogle Scholar
  15. Gatmiri B, Arson C, Nguyen KV (2008) Seismic site effects by an optimized 2D BE/FE method I. Theory, numerical optimization and application to topographical irregularities. Soil Dyn Earthq Eng 28:632–645CrossRefGoogle Scholar
  16. Gatmiri B, Maghoul P, Arson C (2009) Site-specific spectral response of seismic movement due to geometrical and geotechnical characteristics of sites. Soil Dyn Earthq Eng 29:51–70CrossRefGoogle Scholar
  17. Hao L, Lee VW, Liang J (2010) Anti-plane (SH) waves diffraction by an underground semi-circular cavity: analytical solution. Earthq Eng Struct Dyn 9:385–396Google Scholar
  18. Han F, Wang G, Kang C (2011) Scattering of SH-waves on triangular hill joined by semi-cylindrical canyon. Appl Math Mech 32(3):309–326CrossRefGoogle Scholar
  19. Hirai H (1988) Analysis of transient response of SH-wave scattering in a half-space by the boundary element method. Eng Anal 5(4):189–194CrossRefGoogle Scholar
  20. Howard T (1983) Seismic Design of Embankments and Caverns. In: Proceedings ASCE geotechnical division symposium, Philadelphia, Pennsylvania, ASCE Publication, New YorkGoogle Scholar
  21. Kamalian M, Jafari MK, Bidar AS, Razmkhah A (2008) Seismic response of 2-D semi-sine shaped hills to vertically propagating incident waves: amplification patterns and engineering applications. Earthq Spectra 24(2):405–430CrossRefGoogle Scholar
  22. Lee VW (1977) On the deformations near circular underground cavity subjected to incident plane SH-waves. In: Proceedings of the application of computer methods in engineering conference, University of South California, Los Angeles, pp 951–959Google Scholar
  23. Lee VW, Chen S, Hsu IR (1999) Anti-plane diffraction from canyon above subsurface unlined tunnel. J Eng Mech Div ASCE 125(6):668–675CrossRefGoogle Scholar
  24. Lee VW, Manoogian ME, Chen S (2002) Anti-plane SH-deformation near a surface rigid foundation above a subsurface rigid circular tunnel. Earthq Eng Eng Vib 1(1):27–35CrossRefGoogle Scholar
  25. Lee VW, Hao L, Liang J (2004) Diffraction of anti-plane SH-waves by a semi-circular cylindrical hill with an inside concentric semi-circular tunnel. Earthq Eng Eng Vib 3(2):249–262CrossRefGoogle Scholar
  26. Luco JE, Barros CP (1994) Dynamic displacements and stresses in the vicinity of a cylindrical cavity embedded in a half-space. Earthq Eng Struct Dyn 23:321–340CrossRefGoogle Scholar
  27. Liang J, Hao L, Lee VW (2010) Diffraction of plane SH waves by a semi-circular cavity in half-space. Earthq Sci 23:5–12CrossRefGoogle Scholar
  28. MATLAB (2008) The language of technical computing, Version 7.7, The MathWorks Inc., Natick, MassachusettsGoogle Scholar
  29. Manoogian M (2000) Scattering and diffraction of SH-waves above an arbitrarily shaped tunnel. ISET J Earthq Technol 37(1–3):11–26Google Scholar
  30. Manoogian ME, Lee VW (1996) Diffraction of SH-waves by subsurface inclusions of arbitrary shape. J Eng Mech ASCE 122(2):123–129CrossRefGoogle Scholar
  31. Manolis GD, Beskos DE (1987) Boundary element methods in elastodynamics. Allen and Unwin, LondonGoogle Scholar
  32. Manolis GD, Beskos DE (1997) Underground and lifeline structures. In: Beskos DE, Anagnostopoulos SA (eds) Computer analysis and design of earthquake resistant structures: a handbook. Computational Mechanics Publications, Southampton, pp 775–837Google Scholar
  33. Ohtsu M, Uesugi SH (1985) Analysis of SH wave scattering in a half space and its applications to seismic responses of geologic structures. Eng Anal 2(4):198–204CrossRefGoogle Scholar
  34. Oreste PP (2003) A procedure for determining the reaction curve of shotcrete lining considering transient conditions. J Rock Mech Rock Eng 360(30):209–236Google Scholar
  35. Panza G, Paskaleva I, Dineva P, La Mura C (2009) Earthquake site effects modeling by hybrid MS-BIEM: the case study of Sofia Bulgaria. Rendiconti di Scienze Fisiche by the Accademia dei Lincei 20:91–116CrossRefGoogle Scholar
  36. Parvanova S (2010) Modelling and static analysis of two dimensional regions containing multi-phase inclusions by boundary element method. J Theoret Appl Mech Sofia Bulgaria 40(4):101–118Google Scholar
  37. Sanchez-Sesma FJ, Rosenblueth E (1979) Ground motion at canyons of arbitrary shape under incident SH-waves. Earthq Eng Struct Dyn 7:441–450CrossRefGoogle Scholar
  38. Shah AH, Wong KC, Datta SK (1982) Diffraction of SH-waves in a half-space. Earthq Eng Struct Dyn 10:519–528CrossRefGoogle Scholar
  39. Tsaur DH, Chang KH (2012) Multiple scattering of SH waves by an embedded truncated circular cavity. J Marine Sci Technol 20(1):73–81Google Scholar
  40. Tsaur DH, Chang KH (2009) Scattering and focusing of SH waves by convex circular-arc topography. Geophys J Int 177:222–234CrossRefGoogle Scholar
  41. Trifunac MD (1973) Scattering of plane SH-wave by a semi-cylindrical canyon. Earthq Eng Struct Dyn 1:267–281CrossRefGoogle Scholar
  42. Vogt RF, Wolf JP, Bachmann H (1988) Wave scattering by a canyon of arbitrary shape in a layered half-space. Earthq Eng Struct Dyn 16:803–812CrossRefGoogle Scholar
  43. Wang G, Liu D (2002) Scattering of SH-wave by multiple circular cavities in half space. Earthq Eng Eng Vib 1(1):36–44CrossRefGoogle Scholar
  44. Wong HL, Trifunac MD (1974) Scattering of plane SH-wave by a semi-elliptic canyon. Earthq Eng Struct Dyn 3:157–169CrossRefGoogle Scholar
  45. Wuttke F, Dineva P, Schanz T (2011) Seismic wave propagation in laterally inhomogeneous geological region via a new hybrid approach. J Sound Vib 330:664–684CrossRefGoogle Scholar
  46. Yuan X, Liao ZP (1994) Scattering of plane SH waves by a cylindrical canyon of circular-arc-cross-section. Soil Dyn Earthq Eng 13:407–412CrossRefGoogle Scholar
  47. Yuan X, Men FL (1992) Scattering of plane SH waves by a semi-cylindrical hill. Earthq Eng Struct Dyn 21:1091–1098CrossRefGoogle Scholar
  48. Yuan X, Liao ZP (1996) Surface motion of a cylindrical hill of circular-arc cross-section for incident plane SH waves. Soil Dyn Earthq Eng 15:189–199CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Sonia L. Parvanova
    • 1
  • Petia S. Dineva
    • 2
  • George D. Manolis
    • 3
    Email author
  • Frank Wuttke
    • 4
  1. 1.Department of Civil EngineeringUniversity of Architecture, Civil Engineering and GeodesySofiaBulgaria
  2. 2.Institute of MechanicsBulgarian Academy of SciencesSofiaBulgaria
  3. 3.Department of Civil EngineeringAristotle University of ThessalonikiThessalonikiGreece
  4. 4.Chair of Marine and Land Geomechanics and GeotechnicsChristian Albrechts UniversityKielGermany

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