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Decoupling coefficients of dilatational wave for Biot’s dynamic equation and its Green’s functions in frequency domain

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Abstract

Green’s functions for Biot’s dynamic equation in the frequency domain can be a highly useful tool for the investigation of dynamic responses of a saturated porous medium. Its applications are found in soil dynamics, seismology, earthquake engineering, rock mechanics, geophysics, and acoustics. However, the mathematical work for deriving it can be daunting. Green’s functions have been presented utilizing an analogy between the dynamic thermoelasticity and the dynamic poroelasticity in the frequency domain using the u-p formulation. In this work, a special term “decoupling coefficient” for the decomposition of the fast and slow dilatational waves is proposed and expressed to present a new methodology for deriving the poroelastodynamic Green’s functions. The correctness of the solution is demonstrated by numerically comparing the current solution with Cheng’s previous solution. The separation of the two waves in the present methodology allows the more accurate evaluation of Green’s functions, particularly the solution of the slow dilatational wave. This can be advantageous for the numerical implementation of the boundary element method (BEM) and other applications.

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Author information

Authors and Affiliations

  1. City College, Zhejiang University, Hangzhou, 310012, China

    Boyang Ding

  2. Department of Civil Engineering, Zhejiang University of Technology, Hangzhou, 310014, China

    Boyang Ding & Zhanglong Chen

  3. College of Civil Engineering and Architecture, University of Mississippi, Mississippi, 38677-1848, USA

    A. H. D. Cheng

Authors
  1. Boyang Ding
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  2. A. H. D. Cheng
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  3. Zhanglong Chen
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Correspondence to Boyang Ding.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 51478435, 11402150, and 11172268)

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Ding, B., Cheng, A.H.D. & Chen, Z. Decoupling coefficients of dilatational wave for Biot’s dynamic equation and its Green’s functions in frequency domain. Appl. Math. Mech.-Engl. Ed. 37, 121–136 (2016). https://doi.org/10.1007/s10483-016-2015-9

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  • DOI: https://doi.org/10.1007/s10483-016-2015-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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