Scattering of harmonic P1 and SV waves by a shallow lined circular tunnel in a poroelastic half-plane. Issue 158 (July 2022)

• Record Type: Journal Article
• Authors: Liu, Qijian; Yue, Cheng; Zhao, Mingjuan
• Is Part Of: Soil dynamics and earthquake engineering. Issue 158(2022)
• Publication Date: 2022-07
• Subjects: Wave scattering -- Poroelastic half-plane -- Lined tunnel -- Complex variable method -- Conformal mapping; Soil dynamics -- Periodicals; Earthquake engineering -- Periodicals; Sols -- Dynamique -- Périodiques; Génie parasismique -- Périodiques; 624.176205
• DOI: 10.1016/j.soildyn.2022.107306
• Languages: English
• ISSNs: 0267-7261

Abstract

Abstract: An analytical solution for the scattering of harmonic P1 and SV waves in a poroelastic half-plane with a shallow lined tunnel is obtained using the plane complex theory in elastodynamics. In light of the wave function expansions, the wave fields of the poroelastic medium and the liner with unknown coefficients are obtained based on Biot's theory and Helmholtz decomposition. Complex-valued expressions of the effective stresses, the fluid stress, and the displacements of the poroelastic medium and the liner are expressed by the complex variable function method and the conformal transformation technique. With the boundary conditions and the continuity of the medium-liner interface, the boundary value problem results in a series of algebraic equations. The unknown coefficients in the infinite set of algebraic equations can be solved numerically by truncating the series number. A parametric study for the incident SV waves is performed to investigate dynamic stress concentrations and fluid stress of the medium and the liner. Numerical results show that the embedment depth of the tunnel, the incident angle of the excitations, and the porosity of the medium have considerable influence on the dynamic responses of the medium and the liner. The shielding effect of the tunnel on the incident SV waves is obvious. For the big embedment depth of the tunnel, the scattered waves contribute little to the displacements and dynamic stress concentration of the medium and the liner. For a high porosity close to the critical value, the response of the medium-liner system to the incident waves is great. Highlights: Scattering of P1 and SV waves in a poroelastic half-plane with a shallow circular lined tunnel is solved analytically. The plane elastic complex theory and conformal mapping are adopted. A parametric study is performed for the responses of the tunnel and ground surface. Porosity has a considerable influence on the dynamic responses of the medium. The shielding effect of the tunnel is obvious to the incident SV waves.