Abstract
The Havriliak-Negami model for dynamic viscoelastic material behavior and Biot’s theory of poroelasticity are employed to develop an exact solution for three-dimensional scattering effect of harmonic plane P-SV waves from a circular cavity lined with a multilayered fluid-filled shell of infinite length containing viscoelastic damping materials and embedded within a fluid-saturated permeable surrounding soil medium. The analytical results are illustrated with numerical examples where the effects of liner/coating structural arrangement, viscoelastic material properties, liner-soil interface bonding condition, seismic excitation frequency, and angle of incidence on the induced dynamic stress concentrations are evaluated and discussed to obtain representative values of the parameters that characterize the system. It is demonstrated that incorporating viscoelastic damping materials with a low shear modulus in the constrained layer configuration is an efficient means of enhancing the overall seismic isolation performance, especially for near-normally incident seismic shear waves where the amplitudes of induced dynamic stresses may be reduced by up to one-third of those without isolation in a relatively wide frequency range. Some additional cases are considered and good agreements with solutions available in the literature are obtained.
Similar content being viewed by others
References
Abramowitz M and Stegun A (1964), Handbook of Mathematical Functions, Washington D.C.: National Bureau of Standards.
Allard JF (1993), Propagation of Sound in Porous Media: Modeling Sound Absorbing Materials, London: Elsevier Applied Science.
Biot MA (1962), “Mechanics of Deformation and Acoustic Propagation in Porous Medium,” J. Appl. Phys. 33(4): 1482–1498.
Bourbie T, Coussy O and Zinszner BE (1987), Acoustics of Porous Media, Houston: Gulf Publishing.
Bulychev NS (1980), “A Seismic Design of Multiple-layer Lining for Round Tunnels,” Proceedings of the Southeast Asian Conference on Soil Engineering, pp.375–382.
Datta SK, Wong KC and Shah AH (1984), “Dynamic Stress and Displacement Around Cylindrical Cavities of Arbitrary Shapes,” J. Appl. Mech., ASME, 51: 798–803.
Esmaeili M, Vahdani S and Noorzad A (2006), “Dynamic Response of Lined Circular Tunnel to Plane Harmonic Waves,” Tunneling, Underground Space Technology, 21: 511–519.
Hartman B, Lee GF and Lee JD (1994), “Loss Factor Height and Width Limits for Polymer Relaxations,” J. Acoust. Soc. Am. 95(1): 226–223.
Hashash YMA, Park D and Yao JIC (2005), “Ovaling Deformations of Circular Tunnels Under Seismic Loading, an Update on Seismic Design and Analysis of Underground Structures,” Tunneling, Underground Space Technology. 20: 435–441.
Hasheminejad SM and Avazmohammadi R (2008), “Dynamic Stress Concentrations in Lined Twin Tunnels Within Fluid-saturated Soil,” J. Eng. Mech., ASCE, 134:542–554.
Hasheminejad SM and Badsar SA (2005), “Elastic Wave Scattering by Two Spherical Inclusions in a Poroelastic Medium,” J. Eng. Mech, ASCE, 131: 953–965.
Hasheminejad SM and Hosseini H (2002), “Radiation Loading of a Cylindrical Source in a Fluid-filled cylindrical Cavity Embedded Within a Fluid Saturated Poroelastic Medium,” J. Appl. Mech., ASME, 69: 675–683.
Hasheminejad SM and Safari N (2005), “Acoustic Scattering from Viscoelastically Coated Spheres and Cylinders in Viscous Fluids,” Journal of Sound and Vibration, 280: 101–125.
Havriliak S and Negami S (1966), “A Complex Plane Analysis of Some Polymer System, Transitions and Relaxations in Polymers,” Journal of Polymer Science, 14: 99–117.
Iida H, Hiroto T, Yoshida N and Iwafuji M (1966), “Damage to Daikai Subway Station,” (Special Issue of Soils and Foundations), The Japanese Geotechnical Society, 283–300.
Jarzynski J (1990), Mechanisms of Sound Attenuation in Materials, in Sound and Vibration Damping with Polymers, Washington D.C.: American Chemical Society
Johnson DL, Koplik J and Dashen R (1987), “Theory of Dynamic Permeability and Tortuosity in Fluid-saturated Porous Media,” J. Fluid Mech. 76: 379–402.
Karinski YS, Shershnev VV and Yankelevsky DZ (2004), “The Effect of an Interface Boundary Layer on the Resonance Properties of a Buried Structure,” Earthq. Eng. Struct. Dyn. 33: 227–247.
Kim DS and Konagai K (2000), “Seismic Isolation Effect of a Tunnel Covered with Coating Material,” Tunneling, Underground Space Technology, 15(4): 437–443.
Kim DS and Konagai K (2001), “Key Parameters Governing the Performance of Soft Tunnel Coating for Seismic Isolation,” Earthquake Eng. Struct. Dyn. 30(9):1333–1343.
Konagai K (1998), “Diagonal Expansion and Contraction of a Circular Tunnel During Earthquakes,” Structural Engineering/Earthquake Engineereing, 15(1): 91s–95s.
Konagai K and Kim DS (2001), “Simple Evaluation of the Effect of Seismic Isolation by Covering a Tunnel with a Thin Flexible Material,” Soil Dyn. Earthquake Eng., 21: 287–295.
Lo WC, Sposito G and Majer E (2006), “Low-frequency Dilatational Wave Propagation Through Fully-saturated Poroelastic Media,” Adv. Water Resources, 29: 408–416.
Murphy JD, Breitenbach ED and Uberall H (1978), “Resonance Scattering of Acoustic Waves from Cylindrical Shells,” J. Acoust. Soc. Am., 64: 677–683.
Pao YH and Mow CC (1973), Diffraction of Elastic Waves and Dynamics Stress Concentration, New York: Crane Russak.
Pierce AD (1981), Acoustics: An Introduction to Its Physical Principles and Applications, New York: McGraw Hill.
Shimada et al. (1998), European Patent: EP 0955335A1.
Shimamura S, Kasai H and Haruumi M (1999), “Seismic Isolation Effect for a Tunnel with a Soft Isolation Layer,” Structural Engineering/Earthquake Engineereing, 16(2): 143s–154s.
Skudrzyk E (1971), The Foundations of Acoustics, New York: Springer-Verlag.
Vollmann J and Dual J (1997), “High-resolution Analysis of the Complex Wave Spectrum in a Cylindrical Shell Containing a Viscoelastic Medium, Part I. Theory and Numerical Results,” J. Acoust. Soc. Am., 102(2): 896–908.
Willis RL, Wu L and Berthelot YH (2001), “Determination of the Complex Young’s and Shear Dynamic Moduli of Viscoelastic Materials,” J. Acoust. Soc. Am. 109(2): 1–11.
Zheng H, Pau GSH and Wang YY (2006), “A Comparative Study on Optimization of Constrained Layer Damping Treatment for Structural Vibration Control,” Thin-walled Structures, 44: 886–896.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hasheminejad, S.M., Miri, A.K. Seismic isolation effect of lined circular tunnels with damping treatments. Earthq. Eng. Eng. Vib. 7, 305–319 (2008). https://doi.org/10.1007/s11803-008-0842-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11803-008-0842-7