Dynamic Stress Concentrations in Lined Twin Tunnels within Fluid-Saturated Soil
Publication: Journal of Engineering Mechanics
Volume 134, Issue 7
Abstract
An exact analysis for three-dimensional dynamic interaction of monochromatic seismic plane waves with two lined circular parallel tunnels within a boundless fluid-saturated porous elastic medium is presented. The novel features of Biot dynamic theory of poroelasticity along with the appropriate wave field expansions, the pertinent boundary conditions, and the translational addition theorems for cylindrical wave functions are employed to obtain a closed-form solution in the form of infinite series. The analytical results are illustrated with numerical examples in which two identical tunnels, lined with concrete and embedded within water-saturated soils of distinct frame properties (i.e., soft or stiff soils), are insonified by plane fast compressional or shear waves at end-on incidence. The basic dynamic field quantities such as the hoop and axial stress amplitudes are evaluated and discussed for representative values of the parameters characterizing the system. The effects of formation material type, angle of incidence, incident wave frequency, and the proximity of the two tunnels on the liner stresses are examined. Particular attention is paid to the influence of bonding and drainage conditions at the liner/soil interface on the dynamic stress concentrations. Limiting cases are considered and good agreement with the solutions available in the literature is obtained.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abramowitz, M., and Stegun, I. A. (1964). Handbook of mathematical functions, National Bureau of Standards, Washington, D.C.
Achenbach, J. D. (1976). Wave propagation in elastic solids, North-Holland, New York.
Addenbrooke, T. I., and Potts, D. M. (2001). “Twin tunnel interaction: Surface and subsurface effects.” Int. J. Geomech., 1(2), 249–271.
Allard, J. F. (1993). Propagation of sound in porous media, modeling sound absorbing materials, Elsevier Applied Science, London.
Antonio, J., and Tadeu, A. (2001). “3D scattering by multiple cylindrical cavities buried in an elastic formation.” Eur. J. Mech. A/Solids, 20, 367–383.
Balendra, T., Thambiratnam, D. P., Koh, C. G., and Lee, S. L. (1984). “Dynamic response of twin circular tunnels due to incident SH-waves.” Earthquake Eng. Struct. Dyn., 12, 181–201.
Bobet, A. (2001). “Analytical solutions for shallow tunnels in saturated ground.” J. Eng. Mech., 127(12), 1258–1266.
Bobet, A. (2003). “Effect of pore water pressure on tunnel support during static and seismic loading.” Tunn. Undergr. Space Technol., 18, 377–393.
Bourbie, T., Coussy, O., and Zinszner, B. E. (1987). Acoustics of porous media, Gulf Publishing, Houston.
Carcione, J. M., Cavallini, F., Santos, J. E., Ravazzoli, C. L., and Gauzellino, P. M. (2004). “Wave propagation in partially saturated porous media, simulation of a second slow wave.” Wave Motion, 39, 227–240.
Datta, S. K., O’Leary, P. M., and Shah, A. H. (1985). “Three-dimensional dynamic response of buried pipelines to incident longitudinal and shear waves.” J. Appl. Mech., 52, 919–926.
Esmaeili, M., Vahdani, S., and Noorzad, A. (2006). “Dynamic response of lined circular tunnel to plane harmonic waves.” Tunn. Undergr. Space Technol., 21, 511–519.
Fotieva, N. N. (1978). “Calculation of the linings of two closely spaced circular tunnels for seismic effects.” Soil Mech. Found. Eng. (Engl. Transl.), 15, 186–193.
Fotieva, N. N. (1980). “Determination of the minimum seismically safe distance between two parallel tunnels.” Soil Mech. Found. Eng. (Engl. Transl.), 17, 111–116.
Guan, F., and Moore, I. D. (1994). “Three-dimensional dynamic response of twin cavities due to traveling loads.” J. Eng. Mech., 120(3), 637–651.
Gurevich, B., and Schoenberg, M. (1999). “Interface conditions for Biot’s equations of poroelasticity.” J. Acoust. Soc. Am., 105, 2585–2589.
Hashash, Y. M. A., Hook, J. J., Schmidt, B., and Yao, J. I. C. (2001). “Seismic design and analysis of underground structures.” Tunn. Undergr. Space Technol., 16, 247–293.
Hashash, Y. M. A., Park, D., and Yao, J. I. C. (2005). “Ovaling deformations of circular tunnels under seismic loading, an update on seismic design and analysis of underground structures.” Tunn. Undergr. Space Technol., 20, 435–441.
Hasheminejad, S. M., and Avazmohammadi, R. (2007). “Harmonic wave diffraction by two circular cavities in a poroelastic formation.” Soil Dyn. Earthquake Eng., 27, 29–41.
Hasheminejad, S. M., and Badsar, S. A. (2005). “Elastic wave scattering by two spherical inclusions in a poroelastic medium.” J. Eng. Mech., 131(9), 953–965.
Hasheminejad, S. M., 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., 69, 675–683.
Huang, W., Rokhlin, S. I., and Wang, Y. J. (1997). “Analysis of different boundary condition models for study of wave scattering from fiber-matrix interphases.” J. Acoust. Soc. Am., 101, 2031–2042.
Ivanov, Y. A. (1970). Diffraction of electromagnetic waves on two bodies, National Aeronautics and Space Administration, Washington, D.C.
Johnson, D. L., Koplik, J., and Dashen, R. (1987). “Theory of dynamic permeability and tortuosity in fluid-saturated porous media.” J. Fluid Mech., 76, 379–402.
Kattis, S. E., Beskos, D. E., and Cheng, A. H. (2003). “2D dynamic response of unlined and lined tunnels in poroelastic soil to harmonic body wave.” Earthquake Eng. Struct. Dyn., 32, 97–110.
Kim, S. H. (2004). “Interaction behaviors between parallel tunnels in soft ground.” Tunn. Undergr. Space Technol., 19, 448.
Liang, J., Zhang, H., and Lee, V. W. (2003). “A series solution for surface motion amplification due to underground twin tunnels: Incident SV waves.” Earthquake Eng. Eng. Vib., 2(2), 289–298.
Liang, J. W., Zhang, H., and Lee, V. W. (2004). “Series solution for surface motion amplification due to underground group cavities: Incident P waves.” Acta Seismo. Sinica, 17(3), 296–307.
Liu, G. B., Xie, K. H., and Yao, H. I. (2005). “Scattering of elastic wave by a partially sealed cylindrical shell embedded in poroelastic medium.” Int. J. Numer. Analyt. Meth. Geomech., 29, 1109–1126.
Lo, W. C., Sposito, G., and Majer, E. (2006). “Low-frequency dilatational wave propagation through fully-saturated poroelastic media.” Adv. Water Resour., 29(3), 408–416.
Martin, P. A. (1992). “Boundary integral equations for the scattering of elastic waves by elastic inclusions with thin interface layers.” J. Nondestruct. Eval., 11, 167–174.
Moore, I. D., and Guan, F. (1996). “Three-dimensional dynamic response of lined tunnels due to incident seismic waves.” Earthquake Eng. Struct. Dyn., 25, 357–369.
Nam, S. W., and Bobet, A. (2006). “Linear stresses in deep tunnels below the water table.” Tunn. Undergr. Space Technol., 21, 626–635.
No, S. L., Noh, S. H., Lee, S. P., and Seo, J. W. (2006). “Construction of long and large twin tube tunnel in Korea-Sapaesan Tunnel.” Tunn. Undergr. Space Technol., 21, 393–519.
Ohyoshi, T., Kamata, T., and Miura, K. (1986). “Spectral analysis of backscattered elastic waves from two fluid-filled cylindrical cavities.” Nippon Kikai Gakkai Ronbunshu, A Hen, 52, 180–187.
Okumura, T., Takewaki, N., Shimizu, K., and Fukutake, K. (1992). “Dynamic response of twin circular tunnels during earthquakes.” NIST Spec. Publ., 840, 181–191.
Pao, Y. H., and Mow, C. C. (1973). Diffraction of elastic waves and dynamics stress concentration, Crane Russak, New York.
Robert, S., Conoir, J. M., Franklin, H., and Luppe, F. (2004). “Resonant elastic scattering by a finite number of cylindrical cavities in an elastic matrix.” Wave Motion, 40(3), 225–239.
Rokhlin, S. I., and Wang, Y. J. (1991). “Analysis of boundary conditions for elastic wave interaction with an interface between two solids.” J. Acoust. Soc. Am., 89, 503–515.
Roumeliotis, J. A., Ziopoulos, A. P., and Kokkorakis, G. C. (2001). “Acoustic scattering by a circular cylinder parallel with another of small radius.” J. Acoust. Soc. Am., 109(3), 870–877.
Sancar, S., and Pao, Y. H. (1981a). “Spectral analysis of elastic pulses backscattered from two cylindrical cavities in a solid. Part I.” J. Acoust. Soc. Am., 69(6), 1591–1596.
Sancar, S., and Sachse, W. (1981b). “Spectral analysis of elastic pulses backscattered from two cylindrical cavities in a solid. Part II.” J. Acoust. Soc. Am., 69(6), 1597–1609.
Shah, A. H., Wong, K. C., and Datta, S. K. (1983). “Single and multiple scattering of elastic waves in two dimensions.” J. Acoust. Soc. Am., 74, 1033–1043.
Skudrzyc, E. (1971). The foundations of acoustics, basic mathematics, and basic acoustics, Springer, New York.
Stoll, R. D. (1989). Sediment acoustics, Springer. Berlin.
Varadan, V. K., Varadan, V. V., and Pao, Y. H. (1989). “Multiple scattering of elastic waves by cylinders of arbitrary cross section. I: SH waves.” J. Acoust. Soc. Am., 63, 1310–1319.
Vashishth, A. K., and Khurana, P. (2004). “Waves in stratifed anisotropic media: A transfer matrix approach.” J. Sound Vib., 277, 239–275.
Wang, J. H., Zhou, X. L., and Lu, J. F. (2005). “Dynamic stress concentration around elliptic cavities in saturated poroelastic soil under harmonic plane waves.” Int. J. Solids Struct., 42, 4295–4310.
Zeng, X., and Cakmak, A. S. (1985). “Scattering of plane SH-waves by multiple cavities.” Press. Vess. Pip. Div. Pub. PVP, 98, 155–163.
Zhou, X. L., Wang, J. H., and Zhou, G. M. (2006). “Scattering of elastic wave around double elliptic cavities in saturated soil.” Yantu Lixue/Rock Soil Mech., 27(7), 1033–1037.
Zitron, N. R. (1967). “Multiple scattering of elastic waves by two arbitrary cylinders.” J. Acoust. Soc. Am., 42(3).
Zou, Z., and Li, S. (2002). “Stresses in an infinite medium with two similar circular cylindrical inclusion.” Acta Mech., 156, 93–108.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 134 • Issue 7 • July 2008
Pages: 542 - 554
Copyright
© 2008 ASCE.
History
Received: Apr 2, 2007
Accepted: Dec 27, 2007
Published online: Jul 1, 2008
Published in print: Jul 2008
Notes
Note. Associate Editor: Younane N. Abousleiman
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.