Due to the complexity of scattering issues by topographical features above subterranean cavities, few studies have been conducted in this field. In this regard, a 2-D scattering and diffraction of in-plane P and SV waves induced by a U-shaped canyon above underground cavities is proposed herein to account for the topographic effect of such a canyon. To show the interaction between U-shaped canyons and underground cavities or underground holes like natural karstic cavities and their effects on the surface ground motion, a parametric analysis is carried out in the time-domain by BE method. The important parameters considered in this parametric study include: the width of the underground cavities; the cavity depth; the depth and radios of cavity and shape of canyon. The results indicate the following: (1) different incident waves are caused different amplification pattern; (2) the presence of underground cavities may change the surface motion field significantly; (3) the strong ground motion amplitude appears to be very sensitive to the frequency of incoming waves and depends on size and shape of the canyoncavity system, and generally seismic interaction between them.
Lee, V. and Amornwongpaibun, A. (2013) Scattering of anti-plane (SH) waves by a semi-elliptical hill: I- Shallow hill. Soil Dynamics and Earthquake Engineering, 52, 116-125.
Razmkhah, A., Kamalian, M., and Alielahi, H. (2008) Seismic behavior of 2D topographic features subjected to vertically propagating incident SV at high frequency. Proc. of the 4th Decennial Geotechnical Earthquake Engineering and Soil Dynamics Conference (GEESD 5), EESD Committee of ASCEâs Geo-Institute.
Fishman, K.L. and Ahmad, S. (1995) Seismic response for alluvial valleys subjected to SH, P and SV waves. Soil Dynamics and Earthquake Engineering, 14, 249-58.
Alielahi, H., Kamalian, M., and Adampira, M. (2015) Seismic ground amplification by unlined tunnels subjected to vertically propagating SV and P waves using BEM. Soil Dynamics and Earthquake Engineering, 71, 63-79.
Alielahi, H. and Adampira M. (2016) Seismic effects of two-dimensional subsurface cavity on the ground motion by BEM: amplification patterns and engineering applications. International Journal of Civil Engineering, 14(4), 233-251.
Lee, V.W., Chen, S., and Hsu, I.R. (1999) Antiplane diffraction from canyon above a subsurface unlined tunnel. ASCE Journal of Engineering Mechanic, 25(6), 668-675.
Liang, J., Ba, Z., and Lee, V.W. (2007) Scattering of plane P waves around a cavity in poroelastic half space (i): analytical solution. Journal of Earthquake Engineer ing and Engineering Vibration, 27(1), 1-6.
Manoogian, M.E. (2000) Scattering and diffraction of SH waves above an arbitrarily shaped tunnel. SET Journal of Earthquake Technology, 37(1-3), 11-26.
Liu, Q., Zhao, M., andWang, L. (2013) Scattering of plane P, SV or Rayleigh waves by a shallow lined tunnel in an elastic half space. Soil Dynamics and Earthquake Engineering, 49, 52-63.
Crichlow, J.M. (1982) The effect of underground structure on seismic motions of the ground surface. Geophysical Journal of the Royal Astronomical Society, 70, 563-575.
Rodriguez-Castellanos, A., Luzonb, F., and Sanchez-Sesma, F.J. (2005) Diffraction of seismic waves in elastic, Cracked Halfplane Using a Boundary Integral Formulation. Soil Dynamics and Earthquake Engineering, 25, 827-837.
Rodriguez-Castellanos,A., Sanchez-Sesma, F.J., Luzon, F., and Martin, R. (2006) Multiple scattering of elastic waves by subsurface fractures and cavities. Bulletin of the Seismological Society of America, 96(4a), 1359-1374.
Yiouta-Mitra, P., Kouretzis, G., Bouckovalas, G., and Sofianos, A. (2007) Effect of underground structures in earthquake resistant design of surface structures. Dynamic Response and Soil Properties, GSP 160, Geo- Denver: New Peaks in Geotechnics.
Yu, C.W. and Dravinski,M. (2009) Scattering of plane harmonic SH wave by a completely embedded corrugated scattered. International Journal for Numerical Methods in Engineering, 78, 196-214.
Yu, C.W. and Dravinski, M. (2009) Scattering of plane harmonic P, SV or Rayleigh waves by a completely embedded corrugated cavity. Geophysical Journal International, 178(1), 479-487.
Dravinski, M. and Yu, C.H. (2010) Peak surface motion due to scattering of a plane harmonic SH wave by a randomly corrugated scatterer. Journal of Seismology, 14, 653-664.
Dravinski, M. and Yu, C.H. (2011) Peak surface motion due to scattering of plane harmonic P, SV, or Rayleigh waves by rough cavity embedded in an elastic half-space. Journal of Seismology, 15, 131-145.
Parvanova, S.L., Dineva, P.S.,Manolis, G.D., and Wuttke, F. (2014) Seismic response of lined tunnels in the half-plane with surface topography. Bulletin of Earthquake Engineering, 12, 981-1005.
Parvanova, S.L., Dineva, P.S., andManolis, G.D. (2014) Elastic wave fields in a half-plane with free surface relief, tunnels and multiple buried inclusions. Acta Mechanica, 225(7), 1843-1865.
Sica, S., Russo, A.D., Rotili, F., and Simonelli, A.L. (2014) Ground motion amplification due to shallow cavities in nonlinear soils. Natural Hazards, 71, 1913-1935.
Alielahi, H., Kamalian, M., Asgari Marnani, J., Jafari, M.K., and Panji, M. (2013) Applying a time-domain boundary element method for study of seismic ground response in the vicinity of embedded cylindrical cavity. International Journal of Civil Engineering, 11(1), 45-54.
Alielahi, H. and Adampira, M. (2016) Effect of twin-parallel tunnels on seismic ground response due to vertically in-plane waves. International Journal of Rock Mechanics and Mining Sciences, 85, 67-83.
Alielahi, H. and Adampira, M. (2016) Sitespecific response spectra for seismic motions in half-plane with shallow cavities. Soil Dynamics and Earthquake Engineering, 80, 163-167.
Alielahi, H., Kamalian, M., and Adampira, M. (2016) A BEM investigation on the influence of underground cavities on the seismic response of canyons. Acta Geotechnica, 11(2), 391-413.
Trifunac, M.D. (1972) Scattering of plane SH waves by a semi-cylindrical canyon. Earth Eng. and Struc. Dyn., 1, 267-281.
Sanchez-Sesma, F.J. (1985) Diffraction of elastic SH waves by wedges. Bulletin of the Seismological Society of America, 75(5), 1435-1446.
Gao, Y., Zhang, N., Li, D., Liu, H., Cai, Y., and Wu, Y. (2012) Effects of topographic amplification induced by a u-shaped canyon on seismic waves. Bulletin of the Seismological Society of America, 4, 1748-1763.
Yang, Z., Xu, H., Hei, B., and Zhang, J. (2014) Antiplane response of two scalene triangular hills and a semi-cylindrical canyon by incident SH-waves. Ear thquake Engineer ing and Engineering Vibration, 13, 569-581.
Zhao, C. and Valliappan, S. (1993) Incident P and SV wave scattering effects under different canyon topographic and geological conditions. Int. J. Num. Analy. Methods in Geomechanics, 17(2), 73-94.
Kamalian, M., Jafari, M.K., Sohrabi-Bidar, A., Razmkhah, A., and Gatmiri, B. (2006) Timedomain two dimensional site response analysis of non-homogeneous topographic structures by a hybrid FE / BE method. Soil Dynamics and Earthquake Engineering, 26(8), 753-765.
Kamalian, M., Gatmiri, B., Sohrabi-Bidar, A., and Khalaj, A. (2007) Amplification pattern of 2-D semi sine shaped canyons subjected to vertically propagating incident waves. Communications in Numerical Method in Engineering, 23, 871-887.
Harbor, J.M. (1992) Numerical modeling of the development of U-shaped valleys by glacial erosion. Geol. Soc. Am. Bull., 104, 1364-1375.
Chiang, C.S. and Yu, H.S. (2006) Morphotectonics and incision of the Kaoping submarine canyon, SW Taiwan orogenic wedge. Geomorphology, 80, 199-213.
Manolis, G.D. and Beskos, D.E. (1987) Boundary Element Methods in Elasto-dynamics. Allen and Unwin, London.
Israil, A.S.M. and Banerjee, P.K. (1990) Advanced time domain formulation of BEM for two-dimensional transient elasto-dynamics. Int. J. Numer. Methods Eng., 29, 1421-1440.
Brebbia, C.A. and Dominguez, J. (1989) Boundary Elements, an Introductory Course. Southampton: Computational Mechanics Publication.
Katsikadelis J.T. (2002) Boundary Elements: Theory and Applications. Netherland: Elsevier Science Ltd.
Dominguez, J. and Gallego, R. (1991) The timedomain boundary element method for elastodynamic problems. Mathematical and Computer Modeling, 15(3-5), 119-129.
Kamalian,M., Gatmiri, B., and Sohrabi-Bidar, A. (2003) On time-domain two-dimensional site response analysis of topographic structures by BEM. J. Seismol. Earthq. Eng., 5, 35-45.
Luco, J.E. andDeBarros, F.C.P. (1994) Dynamic displacements and stresses in the vicinity of a cylindrical cavity embedded in a halfspace. Earthq. Eng. Struct. Dyn., 23, 321-40.
Kamalian, M., Jafari, M.K., Sohrabi-Bidar, A., and Razmkhah, A. (2008) Seismic response of 2d semi-sine shaped hills to vertically propagating incident waves: amplification patterns and engineering applications. Earthquake Spectra, 24(2), 405-430.
Ricker N. (1960) The formand laws of propagation of seismic wavelets. Geophysics, 18, 40, doi 10.1190/1.1437843.44. Borcherdt, R.D. (1994) Estimates of sitedependent response spectra for design (methodology and justification). Earthquake Spectra, 10, 617-653.
Carrer, J.A.M. and Mansur, W.J. (2004) Alternative time-marching schemes for elastodynamic analysis with the domain boundary element method formulation. Computational Mechanics, 34, 387-399.
Chuhan, Z., Yuntao, R., Pekao, O.A., and Feng, J. (2004) Time-domain boundary element method for underground structures in orthotropic media. Journal of Engineering Mechanics, 130(1), 105-116.
Soares, Jr. D. and Mansur, W.J. (2007) An efficient stabilized boundary element formulation for 2D time-domain acoustics and elastodynamics. Computational Mechanics, 40, 355-365.
Mansur, W.J. (1983) A Time-Stepping Technique to Solve Wave Propagation Problems Using the Boundary Element Method. Ph.D. Dissertation, Southampton University.
Partridge, P.W., Brebbia, C.A., andWrobel, L.C. (1992) The Dual ReciprocityBoundary Element Method. ComputationalMechanics Publications, Southampton and Boston.
Kontoni, D.P.N. and Beskos, D.E. (1993) Transient dynamic elastoplastic analysis by the dual reciprocity BEM. Engineering Analysis with Boundary Element, 12, 1-16.
Marrero, M. and Dominguez, J. (2003) Numerical behavior of time-domain BEM for three dimensional transient elasto-dynamic problems. Engineering Analysis with Boundary Elements, 27, 39-48.
Kawase, H. (1988) Time-domain response of a semi-circular canyon for incident P, SV and Rayleigh waves calculated by the discrete wave number boundary element method. Bulletin of the Seismological Society of America, 78, 1415-1437.
Ohtsuki, A. and Harumi, K. (1983) Effect of topography and subsurface in homogeneities on seismic SV waves. Earthq. Eng. Struct. Dyn., 11, 441-462.
Lee, V.W., Manoogian, M.E., and Chen, S. (2002) Antiplane SH-deformations near a surface rigid foundation above a subsurface rigid circular tunnel. Earthquake Engineering and Engineering Vibration, 1(1), 27-35.
Alielahi, H., & Karimkhani, P. (2016). Studying the Effects of U-Shaped Canyons and Underground Cavities Interaction on the Surface Ground Motion Due to SV and P Waves by BEM. Journal of Seismology and Earthquake Engineering, 18(4), 231-254.
MLA
Hamid Alielahi; Peyman Karimkhani. "Studying the Effects of U-Shaped Canyons and Underground Cavities Interaction on the Surface Ground Motion Due to SV and P Waves by BEM". Journal of Seismology and Earthquake Engineering, 18, 4, 2016, 231-254.
HARVARD
Alielahi, H., Karimkhani, P. (2016). 'Studying the Effects of U-Shaped Canyons and Underground Cavities Interaction on the Surface Ground Motion Due to SV and P Waves by BEM', Journal of Seismology and Earthquake Engineering, 18(4), pp. 231-254.
VANCOUVER
Alielahi, H., Karimkhani, P. Studying the Effects of U-Shaped Canyons and Underground Cavities Interaction on the Surface Ground Motion Due to SV and P Waves by BEM. Journal of Seismology and Earthquake Engineering, 2016; 18(4): 231-254.
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