The Vibration of Pile Groups Embedded in a Layered Poroelastic Half Space Subjected to Harmonic Axial Loads by Using Integral Equations Method

2012 ◽  
Vol 204-208 ◽  
pp. 1170-1173
Author(s):  
Chun Bo Cheng ◽  
Man Qing Xu ◽  
Bin Xu
Keyword(s):  
Dynamic Response ◽  
Layer Thickness ◽  
Integral Equations ◽  
Half Space ◽  
Pile Group ◽  
Dynamic Interaction ◽  
Fredholm Integral Equations ◽  
Pile Groups ◽  
Axial Loads ◽  
Layered Half Space

The dynamic response 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 and 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. 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 considerably different influence on the center pile and the corner piles, while for sparsely populated pile group, it has almost the same influence on all the piles.

Dynamic Interaction between the Pile Groups and Layered Poroelastic Half Space to Harmonic Axial Loads

2013 ◽  
Vol 405-408 ◽  
pp. 790-794
Author(s):  
Xue Jia Chen ◽  
Man Qing Xu
Keyword(s):  
Integral Equation ◽  
Half Space ◽  
Significant Influence ◽  
Pile Group ◽  
Dynamic Interaction ◽  
Fredholm Integral Equations ◽  
Pile Groups ◽  
Axial Loads ◽  
Good Agreement ◽  
Layered Half Space

By using Mukis method, the dynamic interaction between the pile group and layered poroelastic half space subjected to axial harmonic loads is investigated in this study. By using Mukis method, the second kind of Fredholm integral equations describing the dynamic interaction between the layered half space and the pile group is constructed. Numerical solution of the integral equation yields the axial force, the displacement of the pile as well as the response of the layered poroelastic half space. Results of this paper are compared with known results, which shows that our solutions is in a good agreement with the known result. The numerical results of this study also demonstrate that the soil inhomogeneity has a significant influence on the response of pile group.

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

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Bin Xu ◽  
Jian-Fei Lu ◽  
Jian-Hua Wang
Keyword(s):  
Half Space ◽  
Middle Layer ◽  
Pile Group ◽  
Dynamic Responses ◽  
Fredholm Integral Equations ◽  
Pile Groups ◽  
Axial Loads ◽  
Reflection Matrix ◽  
Patch Load ◽  
Layered Half Space

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.

Vibration Isolation Using Pile Rows in a Layered Poroelastic Half-Space Against the Vibration Due to Harmonic Loads

2010 ◽  
Author(s):  
Jian-Fei Lu ◽  
Bin Xu ◽  
Jian-Hua Wang
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Vibration Isolation ◽  
Dynamic Interaction ◽  
Isolation Effect ◽  
Fredholm Integral Equations ◽  
Vertical Load ◽  
Large Length ◽  
Patch Load ◽  
Transmission And Reflection

The isolation of the vibration due to a harmonic vertical load using pile rows embedded in a layered poroelastic half-space is investigated in this study. Based on Biot’s theory, the frequency domain fundamental solution for a vertical circular patch load applied in a layered poroelastic half-space is derived via the transmission and reflection matrices (TRM) method. Utilizing Muki and Sternberg’s method, the second kind of Fredholm integral equations describing the dynamic interaction between the pile rows and the layered poroelastic half-space subjected to a harmonic vertical load is constructed. The isolation effect of piles rows for the vibration due to the harmonic vertical load is investigated via numerical solution of the integral equations. Numerical results of this study show that a stiffer upper layer overlying a softer bottom half-space will worsen the vibration isolation effect of pile rows and vice versa. Also, pile rows with large length are preferable for a better vibration isolation effect.

On the Torsion of Elastic Half Spaces With Embedded Penny-Shaped Flaws

1972 ◽  
Vol 39 (3) ◽  
pp. 786-790 ◽  
Author(s):  
R. D. Low
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Rigid Inclusion ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Fredholm Integral Equations ◽  
Graphical Displays ◽  
Penny Shaped Crack ◽  
Shaped Crack

The investigation is concerned with some of the effects of embedded flaws in an elastic half space subjected to torsional deformations. Specifically two types of flaws are considered: (a) a penny-shaped rigid inclusion, and (b) a penny-shaped crack. In each case the problem is reduced to a system of Fredholm integral equations. Graphical displays of the numerical results are included.

Elastic Layer Pressed Against a Half Space

1974 ◽  
Vol 41 (3) ◽  
pp. 703-707 ◽  
Author(s):  
K. C. Tsai ◽  
J. Dundurs ◽  
L. M. Keer
Keyword(s):  
Eigenvalue Problem ◽  
Integral Equations ◽  
Half Space ◽  
Elastic Layer ◽  
Numerical Results ◽  
Fredholm Integral Equations ◽  
Auxiliary Functions ◽  
Receding Contact ◽  
Two Bodies

The paper considers the elastic layer which is pressed against a half space by loads that are not necessarily symmetric about the center of the loaded region. It is shown that the receding contact between the two bodies can be treated by means of superposition, leading to two homogeneous Fredholm integral equations for auxiliary functions that are directly related to the contact tractions. The determination of the extent of contact and the shift between the load and contact intervals can be viewed as an eigenvalue problem of the homogeneous integral equations. Specific numerical results are given for two types of triangular loads, and a comparison is made with certain symmetric loads.

scholarly journals Dynamic Behavior of an Embedded Foundation under Horizontal Vibration in a Poroelastic Half-Space

2019 ◽  
Vol 9 (4) ◽  
pp. 740 ◽  
Author(s):  
Yang Chen ◽  
Wen Zhao ◽  
Pengjiao Jia ◽  
Jianyong Han ◽  
Yongping Guan
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Mixed Boundary ◽  
Fredholm Integral Equations ◽  
Wave Forces ◽  
Dual Integral Equations ◽  
Horizontal Vibration ◽  
Embedded Foundation ◽  
Embedded Foundations ◽  
Caisson Foundations

More and more huge embedded foundations are used in large-span bridges, such as caisson foundations and anchorage open caisson foundations. Most of the embedded foundations are undergoing horizontal vibration forces, that is, wind and wave forces or other types of dynamic forces. The embedded foundations are regarded as rigid due to its high stiffness and small deformation during the forcing process. The performance of a rigid, massive, cylindrical foundation embedded in a poroelastic half-space is investigated by an analytical method developed in this paper. The mixed boundary problem is solved by reducing the dual integral equations to a pair of Fredholm integral equations of the second kind. The numerical results are compared with existing solutions in order to assess the accuracy of the presented method. To further demonstrate the applicability of this method, parametric studies are performed to evaluate the dynamic response of the embedded foundation under horizontal vibration. The horizontal dynamic impedance and response factor of the embedded foundation are examined based on different embedment ratio, foundation mass ratio, relative stiffness, and poroelastic material properties versus nondimensional frequency. The results of this study can be adapted to investigate the horizontal vibration responses of a foundation embedded in poroelastic half-space.

Dynamic Response of a Rigid Footing Bonded to an Elastic Half Space

1972 ◽  
Vol 39 (2) ◽  
pp. 527-534 ◽  
Author(s):  
J. E. Luco ◽  
R. A. Westmann
Keyword(s):  
Dynamic Response ◽  
Integral Equations ◽  
Half Plane ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Elastic Half Space ◽  
Vertical Shear ◽  
Fredholm Integral Equations ◽  
Interface Conditions ◽  
Rigid Footing

The problem of determining the response of a rigid strip footing bonded to an elastic half plane is considered. The footing is subjected to vertical, shear, and moment forces with harmonic time-dependence; the bond to the half plane is complete. Using the theory of singular integral equations the problem is reduced to the numerical solution of two Fredholm integral equations. The results presented permit the evaluation of approximate footing models where assumptions are made about the interface conditions.

Nonlinear vibration of pile groups under lateral loading

1992 ◽  
Vol 29 (4) ◽  
pp. 702-710 ◽  
Author(s):  
Hans H. Vaziri ◽  
Yingcai Han
Keyword(s):  
Dynamic Response ◽  
Nonlinear Vibration ◽  
Damping Ratio ◽  
Pile Group ◽  
Harmonic Excitation ◽  
Pile Groups ◽  
Plane Normal ◽  
Interaction Factors ◽  
Full Scale Tests ◽  
Measured Response

Dynamic response of a pile group, comprising six full-size cast-in-place reinforced concrete piles, is investigated under varying levels of lateral harmonic excitation in two directions: along a plane composed of three piles (X-direction) and along a plane normal to it composed of two piles (Y-direction). The measured response is compared with the theoretical predictions using the dynamic interaction factors approach. To account for the nonlinear response of the pile group using the theoretical model, provisions are made for yielding of soil around the piles by introducing the boundary-zone concept. It is shown that the proposed theory adequately captures the measured response of the pile group under both linear (weak excitation) and nonlinear (strong excitation) conditions. The study performed indicates that although the rocking stiffness of the pile group is strongly influenced by the number of piles along the direction of excitation, the horizontal stiffness remains virtually unaffected. The results obtained show that the stiffness and damping ratio of the pile group reduce as the excitation intensity increases. It is also found that the pile–soil–pile interaction plays a major role in the overall dynamic response of the pile group; this effect is manifested by a reduction in the stiffness and an increase in the damping of the pile group. Key words : dynamics, vibration, piles, pile group, nonlinear vibration, full-scale tests, modelling, resonance, soil separation, soil yielding.

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