Scattering of plane P,SV or Rayleigh waves by a shallow lined tunnel in an elastic half space |
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| Institution: | 1. Aristotle University of Thessaloniki, Research Unit of Soil Dynamics and Geotechnical Earthquake Engineering, Department of Civil Engineering, PO Box 424, GR-54124 Thessaloniki, Greece;2. University of Catania, Department of Civil and Environmental Engineering, Sicily, Italy;1. Luleå University of Technology, Luleå 971 87, Sweden;2. Rock Mechanics in Hydraulic Structural Engineering, Ministry of Education, China;3. State Key Lab of Water Resources and Hydropower Engineering Science, Wuhan University, China;1. Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;2. School of Foundation, Hebei Institute of Architecture and Civil Engineering, Zhangjiakou 075000, China;1. Department of Civil Engineering, Zanjan Branch, Islamic Azad University, Zanjan, Iran;2. Geotechnical Engineering Research Center, International Institute of Earthquake Engineering and Seismology (IIEES), No. 26, Arghavan Street, North Dibajee, Farmanieh, Tehran, Iran;3. Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran;1. Department of Civil Engineering, Zanjan Branch, Islamic Azad University, Zanjan, Iran;2. Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran |
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| Abstract: | Based on the plane complex variable theory and the image technique, an analytical solution is presented for scattering of plane harmonic P, SV or Rayleigh waves by a shallow lined circular tunnel in an elastic half space. The major contribution of this study is the treatment of the orthogonality of the boundary conditions along the half surface and the cavity wall. In terms of the image technique, the scattered waves by the half surface are simulated as transmitting from the image source of the origin of the tunnel. Using two different conformal mapping functions, we obtained the complex-valued stresses and displacements of the elastic medium and the liner in the image domain, respectively. The boundary value problem results in a set of infinite algebraic equations. The accuracy of the present approach is verified by comparing the present solution results with the available published data. Parametric study indicates that the embedment depth, the shear modulus and the thickness of the liner have significant influences on the dynamic response of the liner and the medium. |
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