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


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.


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



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


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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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