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Dynamic 2.5-D Green’s function for a poroelastic half-space. (English) Zbl 1403.74272
Summary: The dynamic two-and-a-half-dimensional (2.5-D) Green’s function for a poroelastic half-space subject to a point load and dilatation source is derived based on Biots theory, with the consideration of both a permeable surface and an impermeable surface. The governing differential equations for the 2.5-D Green’s function are established by applying the Fourier transform to the governing equations of the three-dimensional (3-D) Green’s function. The dynamic 2.5-D Green’s function is derived in a full-space using the potential decomposition and discrete wavenumber methods. The surface terms are introduced to fulfil the free-surface boundary conditions and thereby obtain the dynamic 2.5-D Green’s function for a poroelastic half-space with the permeable and impermeable surfaces. The half-space 2.5-D Green’s function is verified through comparison with the 2.5-D Green’s function regarding an elastodynamic half-space and the 3-D Green’s function for a poroelastic half-space. A numerical case is provided to compare between the full-space solutions and the half-space solutions with two different sets of free-surface boundary conditions. In addition, a case study of efficient calculation of vibration from a tunnel embedded in a poroelastic half-space is presented to show the application of the 2.5-D Green’s function in engineering problems.

##### MSC:
 74S15 Boundary element methods applied to problems in solid mechanics 65M38 Boundary element methods for initial value and initial-boundary value problems involving PDEs 65M80 Fundamental solutions, Green’s function methods, etc. for initial value and initial-boundary value problems involving PDEs 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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