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Research Papers

Impedance Functions for Surface Rigid Rectangular Foundations on Transversely Isotropic Multilayer Half-Spaces

[+] Author and Article Information
Morteza Eskandari-Ghadi

e-mail: ghadi@ut.ac.ir

Amir K. Ghorbani-Tanha

School of Civil Engineering,
College of Engineering,
University of Tehran,
P.O. Box 11165-4563,
Tehran, Iran

1Corresponding author.

Manuscript received July 29, 2012; final manuscript received December 29, 2012; accepted manuscript posted February 11, 2013; published online July 12, 2013. Assoc. Editor: Weinong Chen.

J. Appl. Mech 80(5), 051017 (Jul 12, 2013) (12 pages) Paper No: JAM-12-1354; doi: 10.1115/1.4023626 History: Received July 29, 2012; Revised December 29, 2012; Accepted February 11, 2013

A horizontally multilayered Green elastic transversely isotropic half-space is considered as the domain of the boundary value problem involved in this paper, such that the axes of material symmetry of different layers are parallel to the axis of material symmetry of the lowest half-space, which is depthwise. The domain is assumed to be affected by an arbitrary time-harmonic forced vibration due to a rigid rectangular surface foundation. With the use of a potential function method and the Hankel integral transforms, the displacements and stresses Green's functions are determined in each layer. The unknown functions due to integrations in each layer are transformed to the unknown functions of the surface layer with the use of the concept of propagator matrix and the continuity conditions. The mixed boundary conditions at the surface of the whole domain are numerically satisfied with the assumption of piecewise constant distribution of tractions in the contact area. It is numerically shown that the surface displacement and stress boundary conditions are satisfied very well. The vertical and horizontal impedance functions of the rectangular foundation are determined, which may be used as lumped parameters in time-harmonic soil-structure interaction with transversely isotropic horizontally layered domain as the soil. It is shown that the impedance functions determined in this paper coincide with the same functions for the simpler case of isotropic homogeneous half-space as degenerations of this study.

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Figures

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Fig. 1

Transversely isotropic elastic half-space under arbitrary surface load

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Fig. 2

Description of the model and coordinate system

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Fig. 3

Path of integration for Green's functions

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Fig. 4

Comparison of the real and imaginary parts of the vertical compliance function of a homogeneous half-space containing isotropic material (ν = 0.33¯) affected by a rigid square foundation with the same results reported by Wong and Luco [31]

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Fig. 5

Comparison of the real and imaginary parts of the horizontal compliance function of a homogeneous half-space containing isotropic material (ν = 0.33¯) affected by rigid square foundation with the same results reported by Wong and Luco [31]

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Fig. 6

The distribution of shear stress in between the rigid square foundation and the layered half-space designated as case I for horizontal vibration in terms for different dimensionless frequencies as ω0 = 4.0 and ω0 = 0.5

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Fig. 7

The distribution of shear stress in between a rigid square foundation and the layered half-space denoted as case I in Table 3 due to vertical vibration of the foundation for dimensionless frequencies of ω0 = 4.0 and ω0 = 0.5

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Fig. 8

Horizontal displacement at the surface of the half-space (case I) in terms of horizontal distance due to horizontal vibration of rigid square foundation with dimensionless frequencies of ω0 = 0.5 and ω0 = 3.0

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Fig. 9

Horizontal displacement at the surface of the layered half-space denoted as case I due to vertical vibration of the rigid square foundation with dimensionless frequencies of ω0 = 0.5 and ω0 = 3.0

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Fig. 10

Vertical displacement of layered half-spaces denoted as cases I and III in terms of depth for vertical vibration of the rigid square foundation for dimensionless frequency of ω0 = 3.0

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Fig. 11

The stress σzz in the layered half-spaces denoted as cases I and III in terms of depth due to vertical vibration of the rigid square foundation for dimensionless frequency of ω0 = 3.0

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Fig. 12

Vertical stiffness of square foundation in terms of dimensionless frequency

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Fig. 13

Vertical stiffness of rigid rectangular foundation with aspect ratio of b/a=0.5 in terms of dimensionless frequency

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Fig. 14

Horizontal stiffness of rigid square foundation in terms of dimensionless frequency

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Fig. 15

Horizontal stiffness of rigid rectangular foundation in the x direction according to Fig. 2 with aspect ratio of b/a=0.5 in terms of dimensionless frequency

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Fig. 16

Horizontal stiffness of rigid rectangular foundation in the y direction according to Fig. 2 with aspect ratio of b/a=0.5 in terms of dimensionless frequency

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