Scattering of Plane SH Waves Induced by a Semicylindrical Canyon with a Subsurface Circular Lined Tunnel
Publication: International Journal of Geomechanics
Volume 18, Issue 6
Abstract
An analytical study of multiple scattering of plane shear horizontal (SH) waves induced by a semicylindrical canyon and a nearby buried circular lined tunnel in a homogeneous elastic half-space is presented using the wavefunction expansion method. The wavefields are given in terms of the wavefunction series with unknown complex coefficients in corresponding coordinate systems. Then, when the relative location between the canyon and tunnel is taken into consideration, the two wavefields induced by the tunnel and its mirror are described in the local coordinate system by applying the oblique form of Graf’s addition theorem. Finally, the unknowns are solved by taking advantage of boundary conditions. The effects of the location and size of the tunnel and the frequency of incident waves on surface-displacement amplitudes are illustrated. Based on an analysis of the numerical results, the effects of the location of the tunnel on canyon ground motions are significant. It was found that a pattern of amplification can obviously take place at the left shoulder of the canyon with a subsurface lined tunnel under horizontal incident SH waves.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported by the National Key Basic Research Program of China (973 Program) (Grant 2015CB057901), the National Natural Science Foundation of China (Grants 41630638, 51479050, and 51608172), the National Key Research and Development Program of China (Grant 2016YFC0800205), the Public Service Sector R&D Project of the Ministry of Water Resource of China (Grant 201501035-03), and the 111 Projects (Grant B13024).
References
Abramowitz, M., and I. A. Stegun. 1972. Handbook of mathematical functions with formulas, graphs, and mathematical tables. New York: Dover.
Boore, D. M. 1973. “The effect of simple topography on seismic waves: Implications for accelerations recorded at Pacoima Dam, San Fernando Valley, California.” Bull. Seismol. Soc. Am. 63(5): 1603–1609.
Bouchon, M. 1973. “Effect of topography on surface motion.” Bull. Seismol. Soc. Am. 63(3): 615–632.
Chen, J. T., J. W. Lee, C. F. Wu, and I. L. Chen. 2011. “SH-wave diffraction by a semi-circular hill revisited: A null-field boundary integral equation method using degenerate kernels.” Soil Dyn. Earthquake Eng. 31(5–6): 729–736. https://doi.org/10.1016/j.soildyn.2010.12.001.
England, R., F. J. Sabina, and I. Herrera. 1980. “Scattering of SH waves by surface cavities of arbitrary shape using boundary methods.” Phys. Earth Planet. Inter. 21(2–3): 148–157. https://doi.org/10.1016/0031-9201(80)90066-7.
Gao, Y. F., D. H. Dai, N. Zhang, Y. Wu, and A. H. Mahfouz. 2017. “Scattering of plane and cylindrical SH waves by a horseshoe shaped cavity.” J. Earthquake Tsunami 11(2): 1650011.
Gao, Y. F., N. Zhang, D. Y. Li, Y. Q. Cai, and Y. Wu. 2012. “Effects of topographic amplification induced by a U-shaped canyon on seismic waves.” Bull. Seismol. Soc. Am. 102(4): 1748–1763. https://doi.org/10.1785/0120110306.
Gatmiri, B., and H. Eslami. 2007. “Scattering of harmonic waves by a circular cavity in a porous medium: Complex functions theory approach.” Int. J. Geomech. 7(5): 371–381.
Kara, H. F. 2016. “A note on response of tunnels to incident SH-waves near hillsides.” Soil Dyn. Earthquake. Eng. 90: 138–146. https://doi.org/10.1016/j.soildyn.2016.08.021.
Komatitsch, D., and J. P. Vilotte. 1998. “The spectral element method: An efficient tool to simulate the seismic response of 2D and 3D geological structures.” Bull. Seismol. Soc. Am. 88(2): 368–392.
Lee, V. W., S. Chen, and I. R. Hsu. 1999. “Antiplane diffraction from canyon above subsurface unlined tunnel.” J. Eng. Mech. 125(6): 668–675. https://doi.org/10.1061/(ASCE)0733-9399(1999)125:6(668).
Lee, V. W., J. W. Liang, and H. Luo. 2006. “Antiplane (SH) waves diffraction by a semicircular cylindrical hill revisited: An improved analytic wave series solution.” J. Eng. Mech. 132(10): 1106–1114. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:10(1106).
Lee, V. W., H. Luo, and J. W. Liang. 2004. “Diffraction of anti-plane SH waves by a semi-circular cylindrical hill with an inside concentric semi-circular tunnel.” Earthquake Eng. Eng. Vib. 3(2): 249–262. https://doi.org/10.1007/BF02858239.
Lee, V. W., and M. D. Trifunac. 1979. “Response of tunnels to incident SH waves.” J. Eng. Mech. 105(4): 643–659.
Liang, J. W., M. Ding, and J. J. Du. 2013. “Diffraction of cylindrical SH waves around circular lined cavity: Analytical solution.” [In Chinese.] J. Earthquake Eng. Eng. Vib. 33(1): 1–7.
Liang, J. W., H. Luo, and V. W. Lee. 2004. “Scattering of plane SH waves by a circular-arc hill with a circular tunnel.” [In Chinese.] Acta Seismol. Sin. 26(5): 495–508.
Lin, S. Y., H. H. Hung, J. P. Yang, and Y. B. Yang. 2017. “Seismic analysis of twin tunnels by a finite/infinite element approach.” Int. J. Geomech. 17(9): 04017060. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000940.
Liu, D. K., and G. Q. Wang. 2006. “Antiplane SH-deformation of a semi-cylindrical hill above a subsurface cavity.” [In Chinese.] Chin. J. Theor. Appl. Mech. 38(2): 209–218.
Liu, G., B. Ji, and D. K. Liu. 2008. “Analytical solution for ground motion of a half space with a semi-cylindrical canyon and a beeline crack.” Proc. R. Soc. London, Ser. A 464(2095): 1905–1921. https://doi.org/10.1098/rspa.2007.0382.
Liu, Q. J., C. Zhang, and M. I. Todorovska. 2016. “Scattering of SH waves by a shallow rectangular cavity in an elastic half space.” Soil Dyn. Earthquake. Eng. 90: 147–157. https://doi.org/10.1016/j.soildyn.2016.08.027.
Pao, Y. H., and C. C. Mow. 1973. Diffraction of elastic waves and dynamic stress concentrations. New York: Crane, Russak & Company.
Saha, A., S. Kundu, S. Gupta, and P. K. Vaishnav. 2017. “SH wave propagation in a finite thicker layer of the void pore sandwiched by heterogeneous orthotropic media.” Int. J. Geomech. 17(5): 06016033. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000807.
Sánchez-Sesma, F. J., and E. Rosenblueth. 1979. “Ground motion at canyons of arbitrary shape under incident SH waves.” Earthquake Eng. Struct. Dyn. 7(5): 441–450. https://doi.org/10.1002/eqe.4290070505.
Semblat, J. F. 2011. “Modeling seismic wave propagation and amplification in 1D/2D/3D linear and nonlinear unbounded media.” Int. J. Geomech. 11(6): 440–448.https://doi.org/10.1061/(ASCE)GM.1943-5622.0000023.
Shi, Z. F., Y. G. Wen, and Q. J. Meng. 2017. “Propagation attenuation of plane waves in saturated soil by pile barriers.” Int. J. Geomech. 17(9): 04017053. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000963.
Smerzini, C., J. Avilés, R. Paolucci, and F. J. Sanchez-Sesma. 2009. “Effect of underground cavities on surface earthquake ground motion under SH wave propagation.” Earthquake Eng. Struct. Dyn. 38(12): 1441–1460. https://doi.org/10.1002/eqe.912.
Smith, W. D. 1975. “The application of finite element analysis to body wave propagation problems.” Geophys. J. Int. 42(2): 747–768. https://doi.org/10.1111/j.1365-246X.1975.tb05890.x.
Trifunac, M. D. 1973. “Scattering of plane SH waves by a semi-cylindrical canyon.” Earthquake Eng. Struct. Dyn. 1(3): 267–281. https://doi.org/10.1002/eqe.4290010307.
Watson, G. N. 1958. A treatise on the theory of Bessel functions. 2nd ed. Cambridge, UK: Cambridge University Press.
Wong, H. L., and P. C. Jennings. 1975. “Effects of canyon topography on strong ground motion.” Bull. Seismol. Soc. Am. 65(5): 1239–1257.
Yuan, X. M., and F. L. Men. 1992. “Scattering of plane SH waves by a semi-cylindrical hill.” Earthquake. Eng. Struct. Dyn. 21(12): 1091–1098. https://doi.org/10.1002/eqe.4290211205.
Zhang, C., Q. J. Liu, and P. Deng. 2015. “Antiplane scattering of SH waves by a trapezoidal valley with a circular-arc alluvium in an elastic half space.” J. Earthquake Tsunami 9(3): 1550008. https://doi.org/10.1142/S1793431115500086.
Zhang, C., and C. Zhao. 1988. “Effects of canyon topography and geological conditions on strong ground motion.” Earthquake Eng. Struct. Dyn. 16(1): 81–97. https://doi.org/10.1002/eqe.4290160107.
Zhang, N., Y. F. Gao, Y. Q. Cai, D. Y. Li, and Y. Wu. 2012. “Scattering of SH waves induced by a non-symmetrical V-shaped canyon.” Geophys. J. Int. 191(1): 243–256. https://doi.org/10.1111/j.1365-246X.2012.05604.x.
Zhang, N., Y. F. Gao, and R. Y. S. Pak. 2017. “Soil and topographic effects on ground motion of a surficially inhomogeneous semi-cylindrical canyon under oblique incident SH waves.” Soil Dyn. Earthquake Eng. 95: 17–28. https://doi.org/10.1016/j.soildyn.2017.01.037.
Zheng, P., and B. Y. Ding. 2016. “Potential method for 3D wave propagation in a poroelastic medium and its applications to Lamb’s problem for a poroelastic half-space.” Int. J. Geomech. 16(2): 04015048. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000530.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 18 • Issue 6 • June 2018
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Mar 10, 2017
Accepted: Nov 13, 2017
Published online: Mar 30, 2018
Published in print: Jun 1, 2018
Discussion open until: Aug 30, 2018
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.