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In this paper, an analytical methodology is proposed to study the vibration of an offshore friction pile embedded in multilayered saturated viscoelastic soils by combining Biot's saturated wave propagation theory, Novak's plane-strain model, and the fictitious saturated soil pile model. The corresponding semi-analytical solution for the dynamic response of the pile is developed considering the heterogeneity, porosity, and limited thickness of the soils. The approach and relevant solution presented are validated by comparisons with existing solutions. Furthermore, numerical instances are used to investigate the influences of the porosity and heterogeneity of the saturated soils around and beneath the pile on the vibration of the pile. The findings from this paper provide a theoretical reference for a comprehensive understanding of the wave propagation characteristics of a friction pile embedded in heterogeneous saturated soil with limited thickness. [ABSTRACT FROM AUTHOR]

Taking both pile end stress diffusion effect and pile‐soil interface softening effect into account, a new nonlinear method for the vertical settlement of pile is proposed in this paper. In detail, a new model, namely stress bubble fictitious soil pile model, is proposed to simulate the support from the pile bottom soil. The nonlinear soil softening model is introduced to establish the relationship between unit pile shaft friction and pile‐soil relative displacement. Then, a nonlinear calculation method for load‐settlement analysis in multilayered soil is developed with the integration of these two models. The validity and accuracy of the proposed method are verified through the comparisons against experimental and existing simplified methods. At last, a detailed parametric study is conducted to assess the influence of the parameters related to the proposed model and pile‐soil system on the load‐displacement behavior of single pile. The promotion of this method could hugely boost the prediction of the single pile settlement for the preliminary design of pile foundation in layered soil. [ABSTRACT FROM AUTHOR]

The vertical vibration of a viscoelastic pile immersed in arbitrarily layered soil is investigated by taking the interaction among pile, pile surrounding soil (PSS) and pile end soil (PES) into account. Firstly, considering both the stratification and stress wave effect of soil, a mathematical model of the pile–soil system is established based on the fictitious soil pile (FSP) model. Then, utilizing the impedance function transfer method and Laplace transform technique, the analytical solutions of the vertical dynamic impedance of pile are derived in the frequency domain. The analytical solutions are validated by comparing them with other existing solutions. Finally, a parametric study is put forward to investigate the properties of PES on the vertical dynamic impedance of pile. The results reveal that the properties of PES have a significant effect on the vertical dynamic impedance of pile, but there is a critical influence thickness for this effect. For the cases of the PES thickness exceeding the critical influence thickness, further increase of PES thickness will not affect the dynamic behavior of the pile–soil system. [ABSTRACT FROM AUTHOR]

In this paper, an analytical methodology is proposed to study the vibration of an offshore friction pile embedded in multilayered saturated viscoelastic soils by combining Biot’s saturated wave propagation theory, Novak’s plane-strain model, and the fictitious saturated soil pile model. The corresponding semi-analytical solution for the dynamic response of the pile is developed considering the heterogeneity, porosity, and limited thickness of the soils. The approach and relevant solution presented are validated by comparisons with existing solutions. Furthermore, numerical instances are used to investigate the influences of the porosity and heterogeneity of the saturated soils around and beneath the pile on the vibration of the pile. The findings from this paper provide a theoretical reference for a comprehensive understanding of the wave propagation characteristics of a friction pile embedded in heterogeneous saturated soil with limited thickness.

The vertical vibration of a viscoelastic pile immersed in arbitrarily layered soil is investigated by taking the interaction among pile, pile surrounding soil (PSS) and pile end soil (PES) into account. Firstly, considering both the stratification and stress wave effect of soil, a mathematical model of the pile–soil system is established based on the fictitious soil pile (FSP) model. Then, utilizing the impedance function transfer method and Laplace transform technique, the analytical solutions of the vertical dynamic impedance of pile are derived in the frequency domain. The analytical solutions are validated by comparing them with other existing solutions. Finally, a parametric study is put forward to investigate the properties of PES on the vertical dynamic impedance of pile. The results reveal that the properties of PES have a significant effect on the vertical dynamic impedance of pile, but there is a critical influence thickness for this effect. For the cases of the PES thickness exceeding the critical influence thickness, further increase of PES thickness will not affect the dynamic behavior of the pile–soil system.

The additional mass model is introduced to simulate the dynamic interaction of soil plug and pipe pile under small deformations and strains. In the additional mass model, the inertia and damping effect of soil plug, and the displacement phase difference between soil plug and pipe pile are taken into consideration. Based on the additional mass model, the analytical solutions of the torsional dynamic response of a pipe pile in the frequency domain are derived by utilizing the Laplace transform technique and impedance transfer function. The corresponding quasi-analytical solution in the time domain for a pipe pile subjected to semi-sinusoidal exciting force is obtained by using the inverse Fourier transform. A parameter sensitivity analysis of the additional mass model is conducted to determine the approximate range of the parameter values of the distributed Voigt model. The validity of the presented solutions is also verified by comparing the torsional dynamic behavior of the pipe pile calculated via the additional mass model with those based on the plane strain model. Utilizing the developed solutions, a parametric study is conducted to investigate the influence of the properties of soil-pile system on the torsional vibration characteristics of pipe pile. [ABSTRACT FROM AUTHOR]

The torsional dynamic response of a pile embedded in layered soil is investigated while considering the influence of the pile end soil. The finite soil layers under the end of the pile are modeled as a fictitious soil pile that has the same cross-sectional area as the pile and is in perfect contact with the pile end. To allow for variations of the modulus or cross-sectional area of the pile and soil, the soil surrounding and below the pile is vertically decomposed into finite layers. Using the Laplace transform and impedance function transfer method, the analytical solution for the dynamic response of the pile head in the frequency domain is then obtained, and the relevant semi-analytical solution in the time domain is derived using the inverse Fourier transform and convolution theorem. The rationality and accuracy of the solution is verified by comparing the torsional dynamic behavior of the pile calculated with the fictitious soil pile with those based on a rigid support model and a viscoelastic support model. Finally, a parametric study is conducted to investigate the influence of the properties and thickness of the pile end soil on the torsional dynamic response of the pile. [ABSTRACT FROM AUTHOR]

Based on the dynamic Winkler model and fictitious soil pile model to consider the relative sliding at the pile-soil interface and the propagation effect of soil beneath the pile toe, respectively, a more rigorous analytical model for the vertical vibration problems of a floating pile is established. The general solution for the displacement of soil is derived by combining the Laplace transform and variable separation methods. Then, the vertical dynamic solution of the floating pile is obtained by introducing the pile-soil interface condition and transfer function recursion method. Furthermore, extensive parametric analyses are performed to investigate the effects of the stiffness coefficient for the dynamic Winkler model, the length of the fictitious soil pile, and the inhomogeneity of the soils and pile on the vertical vibration for the floating pile. This indicates that the proposed analytical model provides a wider range and more rigorous application for the vertical vibration problems of floating piles embedded in layered and limited thickness soils. Moreover, the reduced form of the obtained solution can also be applied to investigate the corresponding vibration problems of end-bearing piles. [ABSTRACT FROM AUTHOR]

Based on the fictitious soil pile model, the effect of sediment on the vertical dynamic impedance of rock-socketed pile with large diameter was theoretically studied by means of Laplace transform technique and impedance function transfer method. Firstly, the sediment under rock-socketed pile was assumed to be fictitious soil pile with the same sectional area. The Rayleigh-Love rode model was used to simulate the rock-socketed pile and the fictitious soil pile with the consideration of the lateral inertial effect of large-diameter pile. The layered surrounding soils and bedrock were modeled by the plane strain model. Then, by virtue of the initial conditions and boundary conditions of the soil-pile system, the analytical solution of the vertical dynamic impedance at the head of rock-socketed pile was derived for the arbitrary excitation acting on the pile head. Lastly, based on the presented analytical solution, the effect of sediment properties, bedrock property and lateral inertial effect on the vertical dynamic impedance at rock-socketed pile head were investigated in detail. It is shown that the sediment properties have significant effect on the vertical dynamic impedance at the rock-socketed pile head. The ability of soil-pile system to resist dynamic vertical deformation is weakened with the increase of sediment thickness, but amplified with the increase of shear wave velocity of sediment. The ability of soil-pile system to resist dynamic vertical deformation is amplified with the bedrock property improving, but the ability of soil-pile system to resist vertical vibration is weakened with the improvement of bedrock property. [ABSTRACT FROM AUTHOR]

[Display omitted] The development of settlement at pile heads due to vertical loads is one of the most important factors in pile design. For large-scale pile-supported infrastructure and elevated roads, the cumulative plastic deformation caused by cyclic loads could be so dangerous that only elastic deformation is permitted. However, existing methods rely heavily on measurements from field tests, while only a few analytical approaches have been developed based on the Winkler model or load transfer functions, which are mostly empirical. Moreover, present theories can hardly unify the computation of end-bearing piles and floating piles, since the classification between these two types of piles is often ambiguous. In this study, a new approach based on the fictitious soil pile model is proposed, and a semi-analytical is derived. The efficacy of the solution is demonstrated via comparisons against measured curves in the field and rigorous numerical results. Finally, a parametric study is performed to investigate the influence of pile and soil properties and the existence of a strong or weak soil interlayer on the vertical settlement of a single pile. On this basis, a new pile design factor referred as 'optimal aspect ratio' is proposed to acquire suitable pile dimensions. [ABSTRACT FROM AUTHOR]

Based on Biot's theory of wave propagation in saturated porous media, a new analytical approach for the vertical vibration of a floating pile in saturated viscoelastic soil is proposed, by combining the differential operator method with a fictitious saturated soil pile (FSSP) model. As an extended fictitious soil pile model, the FSSP model can fully consider the wave propagation in saturated soil with limit thickness beneath pile toe. The analytical solution for the velocity admittance of pile head is derived by introducing the completely coupled conditions at the pile-soil interface. The accuracy of the proposed approach and relevant solutions are degenerated and subsequently verified via comparisons with previous solutions. In addition, comparative analyses are further carried out to examine the effects of the porosity and shear modulus of soil as well as the layer thickness of the saturated soil layer beneath pile toe on the dynamic behavior of the floating pile. It is indicated that the presented approach and relevant solutions provide a more wide-ranging application for vertical vibration problems of a floating pile in saturated soil, which can be degenerated for the vertical vibration problems of a floating pile in single-phase soil or an end-bearing pile in saturated soil. [ABSTRACT FROM AUTHOR]

The vertical dynamic response of a pile embedded in radially inhomogeneous soil is investigated while allowing for the vertical wave effect of soil. For most engineering applications, the soil adjacent to pile may be hardened or softened due to the construction disturbance effect of pile, leading to the radial inhomogeneity of soil which has a significant influence on the vibration characteristics of pile. To consider this problem, this paper introduced the vertical shear complex stiffness transfer model to simulate the radial inhomogeneity of the surrounding soil and underlying soil of pile. Then, the governing equations of pile-soil system subjected to vertical dynamic loading are established based on the fictitious soil pile model. By means of Laplace transfer method, vertical shear complex stiffness transfer method and impedance function transfer method, the analytical solution of the vertical dynamic impedance of pile head is derived in the frequency domain. The present solution is verified by comparing it with existing solution. Based on the present solution, a parametric study is conducted to study the influence of the construction disturbance effect of pile surrounding soil and underlying soil on the vertical dynamic response of pile head. The results show that, even if the surrounding soil of pile is hardened or softened within a very small range, the construction disturbance effect still has a remarkable influence on the vertical dynamic response of pile head. • The present solutions can take both the inhomogeneity of pile surrounding soil and pile end soil into account. • The vertical shear complex stiffness transfer method is used to simulate the inhomogeneity of soil in the radial direction. • The disturbance influences the vertical dynamic response of pile head largely even if the surrounding soil deforms a little. [ABSTRACT FROM AUTHOR]