Vertical Dynamic Impedance Research Articles

Vertical Dynamic Impedance of Tapered Pile considering Compacting Effect

Based on complex stiffness transfer model, the vertical vibration of tapered pile embedded in layered soil is theoretically investigated by considering the compacting effect of the soil layer surrounding the tapered pile in the piling process. Allowing for the stratification of the surrounding soil and variable crosssection of the tapered pile, the pile-soil system is discretized into finite segments. By virtue of the complex stiffness transfer model to simulate the compacting effect, the complex stiffness of different soil segments surrounding the tapered pile is obtained. Then, substituting the complex stiffness into the vertical dynamic governing equation of tapered pile, the analytical solution of vertical dynamic impedance of tapered pile under vertical exciting force is derived by means of the Laplace technique and impedance function transfer method. Based on the presented solutions, the influence of compacting effect of surrounding soil on vertical dynamic impedance at the pile head is investigated within the low frequency range concerned in the design of dynamic foundation.

A coupled fluid layer–rigid disk–poroelastic half-space vibration problem

This paper proposes a coupled fluid layer–foundation–poroelastic half-space vibration model to study how still water affects foundations operating underwater. As an example, we consider the problem of the vertical vibration of a rigid disk on a poroelastic half-space covered by a fluid layer having a finite depth. The solution of the disk vibration problem is obtained using the boundary conditions at the free surface of the fluid layer and the boundary conditions at the fluid layer–poroelastic medium interface. The solution is expressed in terms of dual integral equations that are converted into Fredholm integral equations of the second kind and solved numerically. Selected numerical results for the vertical dynamic impedance coefficient are examined based on different water depths, poroelastic materials, disk permeabilities and frequencies of excitation. Based on the numerical results, it is proposed that the hydrodynamic pressure caused by the foundation vibration is the intrinsic reason that the existence of a fluid layer has such a great effect on the dynamic characteristics of the foundation. In many cases, the hydrodynamic pressure caused by the foundation vibration cannot be ignored when designing dynamic underwater foundations. These results are helpful in understanding the dynamic response of foundations under still water without water waves, such as foundations in pools, lakes and reservoirs.

Vertical Vibration of Pile Groups in Soil Described by Fractional Derivative Viscoelastic Model

The stress-strain relationship of soil is described by fractional derivative viscoelastic model, and established the vertical governing equations of viscoelastic soil. The stiffness and damping of the soil layer described by fractional viscoelastic model are obtained based on the method of layer. The pile-soil dynamic interaction is modeled by Winkler dynamic elastic-damping model, the pile to pile dynamic interaction and vertical vibration of the pile groups in the soil described by fractional derivative viscoelastic model is solved. The influence of the pile spacing, order of fractional derivative and model parameter of soil on the vertical dynamic impedance of pile groups is also investigated. The result indicated that the curves of the dynamic impedance varying with frequency were more complex with the increase of pile spacing, the influence of the order of fractional derivative on vertical dynamic impedance of pile groups is different at lower frequency and high frequency, and the selection of the constitutive model of viscoelastic soil had great effect on the vertical dynamic impedance of pile groups.

Vertical Vibrations of a Rigid Foundation Embedded in a Poroelastic Half Space

This paper considers the steady-state vertical vibrations of a rigid, cylindrical massive foundation embedded in a poroelastic soil. The foundation is subjected to time-harmonic vertical loading and is perfectly bonded to the surrounding soil. The contact surface between the foundation and the soil is assumed to be smooth and fully permeable. Biot’s poroelastodynamic theory is used in the analysis. The soil underlying the foundation base is assumed to be a homogeneous poroelastic half space while the soil along the side of the foundation is assumed to consist of a series of infinitesimally thin layers. The dynamic interaction problem is solved by a simplified analytical method. The accuracy of the present solution is verified by comparisons with existing solutions for both elastodynamic and poroelastodynamic interaction problems. Selected numerical results for the vertical dynamic impedance and response factor of the rigid foundation are presented to demonstrate the influence of nondimensional frequency of excitation, depth ratio, mass ratio, shear modulus of the backfill, and poroelastic material properties on dynamic interaction between an embedded foundation and a poroelastic half space.

Vertical dynamic response of a rigid foundation embedded in a poroelastic soil layer

AbstractA simplified analytical method is presented for the vertical dynamic analysis of a rigid, massive, cylindrical foundation embedded in a poroelastic soil layer. The foundation is subjected to a time‐harmonic vertical loading and is perfectly bonded to the surrounding soil in the vertical direction. The soil underlying the foundation base is represented by a single‐layered poroelastic soil based on rigid bedrock while the soil at the side of the foundation is modeled as an independent poroelastic layer composed of a series of infinitesimally thin layers. The behavior of the soil is governed by Biot's poroelastodynamic theory and its governing equations are solved by the use of Hankel integral transform. The contact surface between the foundation base and the soil is smooth and fully permeable. The dynamic interaction problem is solved following standard numerical procedures. The accuracy of the present solution is verified by comparisons with the well‐known solutions obtained from other approaches for both the elastodynamic interaction problem and poroelastodynamic interaction problem. Numerical results for the vertical dynamic impedance and response factor of the foundation are presented to demonstrate the influence of nondimensional frequency of excitation, soil layer thickness, poroelastic material parameters, depth ratio and mass ratio on the dynamic response of a rigid foundation embedded in a poroelastic soil layer. Copyright © 2008 John Wiley & Sons, Ltd.

Dynamic impedances of piles and groups of piles in saturated soils

A three-dimensional boundary element model is presented for the computation of time-harmonic dynamic stiffness coefficients of piles and pile groups embedded in two-phase poroelastic soils. Piles are modelled as continuum elastic solids and soil as a fluid-filled poroelastic half-space governed by Biot’s theory. Piles are bonded to the surrounding medium along the contact surface where rigorous pile–soil interaction conditions are imposed. The technique has been applied to the calculation of vertical and horizontal dynamic impedance functions of piles and 2 × 2 pile groups. Selected numerical results are presented to portray the influence of excitation frequency, pile stiffness, porous medium properties and kind of pile–soil contact conditions.