Abstract
This paper presents 2.5D scattering of incident plane SH waves by a canyon in layered half-space by the indirect boundary element method (IBEM). The free field response is carried out to give the displacements and stresses on the line which forms boundary of the canyon. The fictitious uniform moving loads are applied to the same line to calculate the Green’s functions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The displacements due to the free field and from the fictitious uniform moving loads have to be added to obtain the whole motion. The numerical results are carried out for the cases of a canyon in homogenous and in one layer over bedrock. The results show that the 2.5D wave scattering problem is essentially different from the 2D case, and there exist distinct differences between the wave amplification by a canyon in layered half-space and that in homogeneous half-space. The reasons for the distinct difference are explored, and the effects of the thickness and stiffness of the layer on the amplification are discussed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ba Z (2008). Green’s Functions for Layered Half-Space and Elastic Wave Scattering by Local Sites. PhD Dissertation, Tianjin University, Tianjin, 72–98 (in Chinese with English abstract).
de Barros F C P and Luco J E (1994). Response of a layered viscoelastic half-space to a moving point load. Wave Motion19: l89–210.
Dravinski M and Mossessian T K (1987). Scattering of plane harmonic P, SV, and Rayleigh waves by dipping layers of arbitrary shape. Bull Seism Soc Amer77: 212–235.
Kawase H (1988). Time-domain response of a semi-circular canyon for incident SV, P, and Rayleigh waves calculated by the discrete wavenumber boundary element method. Bull Seism Soc Amer78: 1 415–1 437.
Liang J and Ba Z (2007). Exact dynamic stiffness matrices of 3-D layered site and its Green’s functions. Earthq Eng Eng Vib27(5): 7–17 (in Chinese with English abstract).
Liang J, Yan L and Lee V W (2002). Scattering of incident plane P waves by a circular-arc canyon with a coving layer. Acta Mechanica Solida Sinica23(4): 397–411.
Liao Z (2002). Introduction to Wave Motion Theories in Engineering. Second edition. Science Press, Beijing, 236–270 (in Chinese).
Luco J E, Wong H L and de Barros F C P (1990). Three dimensional response of a cylindrical canyon in a layered halfspace. Int J Earthq Eng Struct Dynam19: 799–817.
Papageorgiou A and Pei D (1998). A discrete wave number boundary element method for study of 3-D response of 2-D scatterers. Earthq Eng Struct Dynam27(6): 619–638.
Pedersen H, Sanchez-Sesma F J and Campillo M (1994). Three-dimensional scattering by two-dimensional topographies. Bull Seism Soc Amer84: 1 169–1 183.
Sanchez-Sesma F J and Campillo M (1991). Diffraction of P, SV, and Rayleigh waves by topographic features: A boundary integral formulation. Bull Seism Soc Amer81: 2 234–2 253.
Stamps A A and Beskos D E (1996). 3-D seismic response analysis of long lined tunnels in half-space. Soil Dyn Earthq Eng15: 111–118.
Trifunac M D (1973). Scattering of plane SH wave by a semi-cylindrical canyon. Earthq Eng Struct Dynam1: 267–281.
Vogt R F, Wolf J P and Bachmann H (1988). Wave scattering by a canyon of arbitrary shape in a layered half-space. Earthq Eng Struct Dynam16: 803–812.
Wolf J P (1985). Dynamic Soil-Structure Interaction. Englewood Cliffs, Prentice-Hall, 160–164.
Wong H L (1982). Effect of surface topography on the diffraction of P, SV and Rayleigh waves. Bull Seism Soc Amer72(4): 1 167–1 183.
Wong H L and Trifunac M D (1974). Scattering of plane SH-waves by a semi-elliptical canyon. Earthq Eng Struct Dynam3: 157–169.
Yuan X and Liao Z (1995). Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section. Earthq Eng Struct Dynam24: 1 303–1 313.
Zhang L and Chopra A K (1991). Three-dimensional analysis of spatially varying ground motions around a uniform canyon in a homogeneous half-space. Int J Earthq Eng Struct Dynam20: 911–926.
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Ba, Z., Liang, J. 2.5D scattering of incident plane SH waves by a canyon in layered half-space. Earthq Sci 23, 25–33 (2010). https://doi.org/10.1007/s11589-009-0085-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11589-009-0085-3