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Research Papers

Dynamic Responses of Pile Groups Embedded in a Layered Poroelastic Half-Space to Harmonic Axial Loads

[+] Author and Article Information
Bin Xu

Department of Civil Engineering, Nanchang Institute of Technology, Nanchang, Jiangxi 330029, Chinaxubin1@sjtu.edu.cn

Jian-Fei Lu1

Department of Civil Engineering, Jiangsu University, Zhenjiang, Jiangsu 212013, Chinaljfdoctor@yahoo.com

Jian-Hua Wang

Department of Civil Engineering, Shanghai Jiao Tong University, Shanghai 200030, Chinawjh417@sjtu.edu.cn

1

Corresponding author.

J. Vib. Acoust 133(2), 021003 (Mar 01, 2011) (10 pages) doi:10.1115/1.4002123 History: Received July 20, 2008; Revised June 01, 2010; Published March 01, 2011; Online March 01, 2011

The dynamic responses of a pile group embedded in a layered poroelastic half-space subjected to axial harmonic loads is investigated in this study. Based on Biot’s theory, the frequency domain fundamental solution for a vertical circular patch load applied in the layered poroelastic half-space is derived via the transmission and reflection matrix (TRM) method. Utilizing Muki’s method, the second kind of Fredholm integral equations describing the dynamic interaction between the layered half-space and the pile group is constructed. The proposed methodology was validated by comparing the results of this paper with a known result. Numerical results show that in a two-layered half-space, for the closely populated pile group with a rigid cap, the upper softer layer thickness has different influences on the central pile and the corner piles, while for the sparse pile group, it has almost the same influence on all the piles. For a three-layer half-space, the presence of a stiffer middle layer in the layered half-space will enhance the impedance of the pile group significantly, while a softer middle layer will reduce the impedance of the pile group.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

A pile group embedded in a layered poroelastic half space and subjected to a time harmonic vertical load on the cap of the pile group

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Figure 2

Decomposition of the pile-half-space system into fictitious piles and an extended layered poroelastic half-space

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Figure 3

Comparison of the impedances KV(G∗)=KVG/(9KV0S) of the 3×3 pile group embedded in a homogeneous poroelastic half-space for spacing diameter ratio s/d=2.0,5.0,10.0 with those of Wang (11): (a) the real part of the normalized impedances KV(G∗) and (b) the imaginary part of the normalized impedances KV(G∗)

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Figure 4

The normalized impedances KV(G∗)=KV(G)/(9KV0(S)) for the 3×3 pile group versus normalized frequency ω∗=0.0–1.0 with h=0.0, 5.0, and 7.0 m for spacing diameter ratio s/d=2.0,10.0, respectively: (a) the real part of the normalized impedances KV(G∗) and (b) the imaginary part of the normalized impedances KV(G∗)

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Figure 5

Dimensionless axial force N¯∗(z)=N¯(z)/Qa for the corner pile (pile1) when the normalized frequency ω∗=0.5 and h=0.0, 5.0, and 7.0 m for the cases of spacing diameter ratio s/d=2.0,10.0, respectively: (a) the real part of the dimensionless axial force Re(N¯∗(z)) and (b) the imaginary part of the dimensionless axial force Im(N¯∗(z))

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Figure 6

Dimensionless axial force N¯∗(z)=N¯(z)/Qa for the central pile (pile3) when the normalized frequency ω∗=0.5 and h=0.0, 5.0, and 7.0 m for the cases of the spacing diameter ratio s/d=2.0,10.0, respectively: (a) the real part of the dimensionless axial force Re(N¯∗(z)) and (b) the imaginary part of the dimensionless axial force Im(N¯∗(z))

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Figure 7

Dimensionless pore pressure p¯f∗(z)=πR2p¯f(z)/Qa for the corner pile (pile 1) when the normalized frequency ω∗=0.5 and h=0.0, 5.0, and 7.0 m for the cases of the spacing diameter ratio s/d=2.0,10.0, respectively: (a) the real part of the dimensionless pore pressure Re(p¯f∗(z)) and (b) the imaginary part of the dimensionless pore pressure Im(p¯f∗(z))

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Figure 8

Dimensionless pore pressure p¯f∗(z)=πR2p¯f(z)/Qa for the central pile (pile 3) when the normalized frequency ω∗=0.5 and h=0.0 m, 5.0 m and 7.0 m for the cases of spacing diameter ratio s/d=2.0,10.0, respectively: (a) the real part of the dimensionless pore pressure Re(p¯f∗(z)); (b) the imaginary part of the dimensionless pore pressure Im(p¯f∗(z))

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Figure 9

Normalized vertical impedances KV(G∗)=KV(G)/(9KV0(S)) for the 3×3 pile group embedded in a three-layered poroelastic half space with μ(1):μ(2):μ(3)=1:1:1, μ(1):μ(2):μ(3)=1:10:1, and μ(1):μ(2):μ(3)=1:0.1:1 (cases A–C) versus the normalized frequency ω∗=0–1.0 for spacing diameter ratio s/d=2.0: (a) the normalized real part of the impedances KV(G∗) and (b) the normalized imaginary part of the impedances KV(G∗)

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Figure 10

Normalized vertical impedances KV(G∗)=KV(G)/(9KV0(S)) for the 3×3 pile group embedded in a three-layered poroelastic half space with μ(1):μ(2):μ(3)=1:1:1, μ(1):μ(2):μ(3)=1:10:1, and μ(1):μ(2):μ(3)=1:0.1:1 (cases A–C) versus the normalized frequency ω∗=0–1.0 for spacing diameter ratio s/d=10.0: (a) the normalized real part of the impedances KV(G∗) and (b) the normalized imaginary part of the impedances KV(G∗)

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