Dynamic 2.5-D Green’s function for a poroelastic half-space.

*(English)*Zbl 1403.74272Summary: 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.) |

##### Keywords:

2.5-D Green’s function; poroelastic half-space; Biots theory; boundary element; discrete wavenumber; Fourier transform
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\textit{S. Zhou} et al., Eng. Anal. Bound. Elem. 67, 96--107 (2016; Zbl 1403.74272)

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