Horizontal vibration of a cylindrical rigid foundation embedded in poroelastic half-space

Zheng, Changjie; He, Rui; Kouretzis, George; Ding, Xuanming

doi:10.1016/j.compgeo.2018.11.009

Cited by 20 publications

(16 citation statements)

References 19 publications

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“…To better describe the dynamic characteristics of the partially embedded foundation subjected to horizontal loads, the horizontal dynamic response factor in dimensionless form M h is defined as 14,15,18 :

\begin{equation}{M_h} = \frac{1}{{\sqrt {{{\left( {k - {B_h}a_0^2} \right)}^2} - {c^2}} }}\end{equation}

…”

Section: An Approximate Analytical Methodsmentioning

confidence: 99%

“…The dynamic coupled interaction model of the surrounding soil‐cylindrical rigid foundation system was lucubrated based on the Novak plane strain model, whose precision and accuracy has been verified by many scholars 14,15,18 . At this stage, the potential functions and variable separation method are introduced into solving the vibration equations of saturated soil, so the dimensionless displacements of the surrounding soil in the radial and tangential direction can be easily written:

\begin{equation}{u^{\prime}_r} = \left( { - {F_1}{\Omega _1} - {F_2}{\Omega _2} + {F_3}{\Omega _3}} \right)\cos \theta \end{equation}

\begin{equation}{u^{\prime}_\theta } = \left( { - {F_1}{\Omega _4} - {F_2}{\kern 1pt} {\Omega _5} + {F_3}{\Omega _6}} \right)\sin \theta \end{equation}

\begin{equation}{w^{\prime}_r} = \left( { - {F_1}{\gamma _1}{\Omega _1} - {F_2}{\gamma _2}{\Omega _2} + {F_3}{\gamma _3}{\Omega _3}} \right)\cos \theta \end{equation}

where the constants F 1 , F 2 and F 3 need to be solved by the following boundary conditions; both K 0 (…) and K 2 (…) denote the modified Bessel functions.…”

Section: An Approximate Analytical Methodsmentioning

confidence: 99%

“…[T] is a 8×8 constant matrix determined from Equations ( 12) to (18). Based on the Cramer's rule, the coefficients…”

Section: The Base Resistance Of the Cylindrical Rigid Foundationmentioning

confidence: 99%

“…The dynamic coupled interaction model of the surrounding soil-cylindrical rigid foundation system was lucubrated based on the Novak plane strain model, whose precision and accuracy has been verified by many scholars. 14,15,18 At this stage, the potential functions and variable separation method are introduced into solving the vibration equations of saturated soil, so the dimensionless displacements of the surrounding soil in the radial and tangential direction can be easily written:…”

Section: The Shaft Reactions Of the Cylindrical Rigid Foundationmentioning

confidence: 99%

Section: Dynamic Response Of the Cylindrical Rigid Foundationmentioning

confidence: 99%

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An analytical solution for the horizontal vibration behavior of a cylindrical rigid foundation in poroelastic soil layer

Yang

Zou

2023

Earthq Engng Struct Dyn

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The large size embedded foundation is widely used in the engineering, but the finite thickness of soil layer underlying this foundation is usually neglected in design, which leads to the non‐negligible error of calculation. By virtue of Biot's elastodynamic theory, this paper proposes a simple method to discuss the horizontal dynamic response of the cylindrical rigid foundation partially embedded in a poroelastic soil layer. First, based on the Novak plane strain model, the shaft resistance from the surrounding soil is simulated and solved. Second, the foundation end soil is assumed as a continuous medium of finite thickness, whose initial mechanism is derived from the dynamic interaction between the rigid disk and soil. Finally, the horizontal dynamic response factor is calculated by adopting newton's second law. Several cases are set to verify the rationality of the presented solution and to develop the analysis of key parameters. The numerical results suggest that the soil layer thickness has a significant influence on the dynamic vibration of the embedded foundation, and its effect is consistent with that of poroelastic half‐space when the thickness exceeds certain value.

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\begin{equation}{M_h} = \frac{1}{{\sqrt {{{\left( {k - {B_h}a_0^2} \right)}^2} - {c^2}} }}\end{equation}

…”

Section: An Approximate Analytical Methodsmentioning

confidence: 99%

\begin{equation}{u^{\prime}_r} = \left( { - {F_1}{\Omega _1} - {F_2}{\Omega _2} + {F_3}{\Omega _3}} \right)\cos \theta \end{equation}

\begin{equation}{u^{\prime}_\theta } = \left( { - {F_1}{\Omega _4} - {F_2}{\kern 1pt} {\Omega _5} + {F_3}{\Omega _6}} \right)\sin \theta \end{equation}

\begin{equation}{w^{\prime}_r} = \left( { - {F_1}{\gamma _1}{\Omega _1} - {F_2}{\gamma _2}{\Omega _2} + {F_3}{\gamma _3}{\Omega _3}} \right)\cos \theta \end{equation}

where the constants F 1 , F 2 and F 3 need to be solved by the following boundary conditions; both K 0 (…) and K 2 (…) denote the modified Bessel functions.…”

Section: An Approximate Analytical Methodsmentioning

confidence: 99%

“…[T] is a 8×8 constant matrix determined from Equations ( 12) to (18). Based on the Cramer's rule, the coefficients…”

Section: The Base Resistance Of the Cylindrical Rigid Foundationmentioning

confidence: 99%

Section: The Shaft Reactions Of the Cylindrical Rigid Foundationmentioning

confidence: 99%

Section: Dynamic Response Of the Cylindrical Rigid Foundationmentioning

confidence: 99%

See 3 more Smart Citations

An analytical solution for the horizontal vibration behavior of a cylindrical rigid foundation in poroelastic soil layer

Yang

Zou

2023

Earthq Engng Struct Dyn

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Horizontal vibration of a rigid strip footing on viscoelastic half‐space

Zheng

Cai

Luan

et al. 2020

Num Anal Meth Geomechanics

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This paper presented an analytical method for determining the response of a rigid strip foundation resting on the surface of a viscoelastic half‐space to horizontal dynamic loads, and the associated transient soil displacements resulting from the vibration of the footing. This mixed boundary value problem was solved by means of Jacobi orthogonal polynomials, a more efficient method compared to transforming the dual integral equations resulting from the boundary conditions to Fredholm integral equations. Displacements and stresses of the soil‐footing system were accordingly obtained by applying the inverse Fourier transform. Finally, we used the proposed solution to investigate the effects of material damping and Poisson's ratio of soil on the dynamic response of the strip footing, and the resulting soil displacements.

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Horizontal motions of a rigid disk placed on a poroelastic soil layer of finite thickness

Yang

2023

Num Anal Meth Geomechanics

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In the previous studies of rigid disk-soil dynamics, the soil under the foundation is usually treated as a poroelastic half-space medium. However, the waves due to the vibration of rigid disk can reflect and refract back and forth between the finite soil layer and rigid bedrock, which would significantly influence the soil deformation and flow of the rigid disk-soil system. In order to overcome the shortcoming, this paper presents an analytical solution to determine the response of the rigid disk subjected to harmonic horizontal loads resting on poroelastic soil layer overlying rigid bedrock. The displacements and stresses field of the disk and soil are obtained by virtue of the Hankel transform method, dual integral equations method. Furthermore, the rationality and accuracy of the developed solution are confirmed in comparison with the previous studies. Based on the obtained solutions, numerical examples are performed to the effects of the thickness and permeability of poroelastic soil layer on the dynamic response of the rigid disk-soil system in the physical domain.

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Horizontal vibration of a cylindrical rigid foundation embedded in poroelastic half-space

Cited by 20 publications

References 19 publications

An analytical solution for the horizontal vibration behavior of a cylindrical rigid foundation in poroelastic soil layer

An analytical solution for the horizontal vibration behavior of a cylindrical rigid foundation in poroelastic soil layer

Horizontal vibration of a rigid strip footing on viscoelastic half‐space

Horizontal motions of a rigid disk placed on a poroelastic soil layer of finite thickness

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