Applied Mathematics and Mechanics

, Volume 28, Issue 9, pp 1199–1207 | Cite as

Vertical vibrations of elastic foundation resting on saturated half-space

  • Wang Guo-cai  (王国才)Email author
  • Wang Zhe  (王哲)
  • Meng Fan-li  (孟凡丽)


This paper is mainly concerned with the dynamic response of an elastic foundation of finite height bounded to the surface of a saturated half-space. The foundation is subjected to time-harmonic vertical loadings. First, the transform solutions for the governing equations of the saturated media are obtained. Then, based on the assumption that the contact between the foundation and the half-space is fully relaxed and the half-space is completely pervious or impervious, this dynamic mixed boundary-value problem can lead to dual integral equations, which can be further reduced to the Fredholm integral equations of the second kind and solved by numerical procedures. In the numerical examples, the dynamic compliances, displacements and pore pressure are developed for a wide range of frequencies and material/geometrical properties of the saturated soil-foundation system. In most of the cases, the dynamic behavior of an elastic foundation resting on the saturated media significantly differs from that of a rigid disc on the saturated half-space. The solutions obtained can be used to study a variety of wave propagation problems and dynamic soil-structure interactions.

Key words

saturated media elastic foundation vertical vibration dynamic compliance dual integral equations 

Chinese Library Classification

O357.3 TU476 

2000 Mathematics Subject Classification

44A05 45B05 74L10 74S30 


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Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Wang Guo-cai  (王国才)
    • 1
    Email author
  • Wang Zhe  (王哲)
    • 1
  • Meng Fan-li  (孟凡丽)
    • 1
  1. 1.School of Civil Engineering and ArchitectureZhejiang University of TechnologyHangzhouP. R. China

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