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Research Papers

Dynamic Green's Functions and Integral Equations for a Double-Porosity Dual-Permeability Poroelastic Material

[+] Author and Article Information
Pei Zheng, Haolin Li

School of Mechanical Engineering,
University of Shanghai for
Science and Technology,
Shanghai 200093, China

Alexander H.-D. Cheng

School of Engineering,
University of Mississippi,
Oxford, MS 38677-1848

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 23, 2017; final manuscript received March 30, 2017; published online April 27, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(6), 061009 (Apr 27, 2017) Paper No: JAM-17-1049; doi: 10.1115/1.4036439 History: Received January 23, 2017; Revised March 30, 2017

Geomaterials such as sedimentary rocks often contain fissures and cracks. Such secondary porosity will result in the so-called mesoscopic flow in wave propagation. Its presence is increasingly believed to be responsible for the significant wave energy loss in the seismic frequency band. In the present research, the double-porosity dual-permeability model is employed to describe such phenomena. Based on the model, we derive both the three-dimensional (3D) and two-dimensional (2D) dynamic Green's functions for the infinite space. The existence of reciprocity relation is demonstrated, which is used to deduce some interesting relations among Green's functions. These relations can serve as a consistency check on the obtained results. The Somigliana-type integral equations, the basis for the boundary element method (BEM), are also established. The complete list of Green's functions appearing in the integral equations is provided, which enables numerical implementation. Furthermore, the asymptotic behavior of the obtained solutions is discussed.

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Figures

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Fig. 1

Radiation patterns of the P1 and S wave due to a vertical point force with a magnitude fz=109N at r=30   km, ω=0.5   rad  s−1. The numbers on the axes show displacement magnitude in meters.

Grahic Jump Location
Fig. 2

Radiation patterns of the P1 waves for the macroscopic and mesoscopic flow cases, at r=30   km, ω=0.5   rad  s−1

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Fig. 3

Variation of displacement amplitudes of P1 waves versus excitation frequencies at r=30   km, θ=0

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