Dynamic response of a pile embedded in elastic half space subjected to harmonic vertical loading

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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“…Similar method for solving definite integrals and its adaptability are conducted in study of Hayati et al 21 . and Zheng et al 22–24

\begin{equation*}{K_{11}}\left( {r,t} \right) = \sqrt {rt} \int_0^\infty {\xi \left[ {\frac{{{Q_{11}}\left( \xi \right)}}{{{l_1}}} - 1} \right]{J_{ - \frac{1}{2}}}\left( {\xi r} \right){J_{ - \frac{1}{2}}}\left( {\xi t} \right)} d\xi ,\;{K_{12}}\left( {r,t} \right) = \sqrt {rt} \int_0^\infty {\xi \left[ {\frac{{{Q_{12}}\left( \xi \right)}}{{{l_2}}} - 1} \right]{J_{ - \frac{1}{2}}}\left( {\xi r} \right){J_{\frac{3}{2}}}\left( {\xi t} \right)} d\xi ,\end{equation*}

K_{21} ((), r, t) badbreak= \sqrt{r t} \int_{0}^{\infty} ξ [\frac{Q_{21} (ξ)}{l_{3}} - 1] J_{\frac{3}{2}} (ξ r) J_{- \frac{1}{2}} (ξ t) d ξ, K_{22} ((), r, t) goodbreak= \sqrt{r t} \int_{0}^{\infty} ξ [\frac{Q_{22} (ξ)}{l_{4}}]

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Section: An Approximate Analytical Methodsmentioning

confidence: 99%

“…where Φ 1 (r) and Φ 2 (r) can be calculated from the Gauss-Legendre quadrature method. Similar method for solving definite integrals and its adaptability are conducted in study of Hayati et al 21 and Zheng et al [22][23][24] 𝐾 11 (𝑟, 𝑡) =…”

Section: The Base Resistance Of the Cylindrical Rigid Foundationmentioning

confidence: 99%

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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“…e virtual pile model originated by Muki and Sternberg [17][18][19][20][21][22][23][24] and the simplified continuum analytical model proposed by Nogami and Novak [25] are used to investigate the dynamic load transfer problem of a one-dimensional elastic rod in the stratum. In recent years, several key applications such as large diameter piles and pipe piles have been realized via the latter method [26][27][28][29]. Yang and Pan attempted to carry out a three-dimensional analysis based on Saint-Venant's principle, which is likely the analytical solution most similar to that from a three-dimensional analysis [30].…”

Section: Introductionmentioning

confidence: 99%

Vertically Dynamic Response of an End‐Bearing Pile Embedded in a Frozen Saturated Porous Medium under Impact Loading

Cao

Zhou

et al. 2019

Shock and Vibration

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A frozen soil is a multiphase medium composed of solid particles, ice, and water, and the cementation between the solid particles and ice strengthens with a decrease in temperature. Based on the theory of a composite solid-state saturated porous medium, a uniform solution for the vertical vibration of an end-bearing pile in a frozen soil is derived analytically. The axial displacements under impact loading in the time domain are calculated by using the numerical inverse transformation technique. The solution can degenerate into an end-bearing pile in a saturated soil layer as the temperature approaches the freezing point. If the cementation between the solid particles and ice is ignored, the amplitude of the displacement will be overestimated. The numerical results show that temperature has a significant impact on the dynamic responses of the pile due to variation of the ice content and, consequently, of the cementation between solid particles and ice.

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Vertical vibration of piles in viscoelastic non-uniform soil overlying a rigid base

et al. 2019

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Dynamic response of a pile embedded in elastic half space subjected to harmonic vertical loading

Cited by 9 publications

References 14 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

Vertically Dynamic Response of an End‐Bearing Pile Embedded in a Frozen Saturated Porous Medium under Impact Loading

Vertical vibration of piles in viscoelastic non-uniform soil overlying a rigid base

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