Impedance Function Transfer Method Research Articles

Dynamic response of bored piles with gradient defects during low strain integrity test

With the proposal of the gradient ring-soil pile model, the possibility of utilizing the low strain integrity test for identifying gradient defects of the bored piles embedded in unsaturated soil is confirmed. The gradient ring-soil pile model realizes the simulation of soil-pile interaction at the soil-pile interfaces with arbitrary shapes in the horizontal projection. Compared to existing theoretical answers, this paper extends the low strain test theory to the identification of gradient defects. With the adoption of the Laplace transform, differential operator decomposition theory, variable separation method, and impedance function transfer method, a semi-analytical solution is derived. Taking advantage of the semi-analytical solution, a parametric study is conducted to analyze the variation of the defect shapes on the test signal of the bored pile. Based on the findings, a series of methods for identifying gradient defects in engineering applications are summarized. The main findings can be summarized as follows: 1. The soil filled in the gradient necking defects would significantly decrease the magnitudes of reflected signals at these defects, making them more challenging to be identified; 2. If simply modeling the gradient defects as sudden defects, the severity of defects can be underestimated, resulting in the overestimation of pile capacity; 3. The shape of the gradient defect, as well as the length of the gradient defect, has a significant influence on the reflected signal.

Torsional vibration of tapered pile including circumferential support of surrounding soil

The tapered pile is usually divided into finite segments along the vertical direction due to its variable cross-section when investigating its torsional dynamic characteristics. However, an annular projection would be formed at the contact surface of the adjacent pile segments due to the difference in radius, through which the surrounding soil will apply the circumferential support on the pile segment. In this study, the Voigt model is adopted to model the circumferential support of the surrounding soil acting on the annular projection. On this basis, an amended impedance function transfer method is established combined with the circumferential stress equilibrium equations and circumferential displacement continuity conditions at the contact surface of the adjacent pile segments. The shear complex stiffness transfer method is employed to consider the construction disturbance during pile installation. Then, an improved analytical solution for the torsional vibration of the tapered pile considering the circumferential support of the surrounding soil is established by solving the equations for the soil and pile. Based on the solution, the torsional vibration of the tapered pile is investigated and the influence of the circumferential support of the surrounding soil is revealed under different pile parameters and construction disturbance conditions.

Vertical dynamic response of a floating pile in unsaturated poroelastic media based on the fictitious unsaturated soil pile model

Decades of high-speed railways operation around the world have revealed an increasing number of maintenance issues of pile-supported embankments subjected to long-term dynamic train loads in typical unsaturated soft soil areas. As the physical explanation of vibration characteristics of unsaturated soil piles is a theoretical basis for pile foundation design and pile integrity detection, a developed analytical solution of the vertical dynamic response of a floating pile in homogeneous unsaturated soils is proposed in this work. Based on the fictitious unsaturated soil pile (FUSP) model, the influence of saturation degree on soil shear modulus is considered in governing equations, uncoupled by using potential function and operator decomposition methods. The vertical dynamic response of a floating pile in a frequency domain is derived by employing the pile–soil compatibility conditions and the impedance function transfer method. Time-domain results are obtained by utilizing inverse Fourier transform and the convolution theorem. The correctness of the proposed model is verified by degradation to compare with the two existing solutions. Finally, a parameter study is undertaken to find the most sensitive parameters to the dynamic response of the floating pile in unsaturated soils.

Vertical Dynamic Impedance of a Viscoelastic Pile in Arbitrarily Layered Soil Based on the Fictitious Soil Pile Model

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.

Longitudinal dynamic characteristics of a defective tapered pile with exposed cap in layered soil

The longitudinal dynamic characteristics of a defective tapered pile embedded in layered soil is investigated considering that an exposed cap is connected with the pile top rigidly. According to the layered condition of the surrounding soil and the variable cross-section of the tapered pile, the pile-soil system is discretized into multiple segments. By employing the complex stiffness transfer mechanism (CSTM) to simulate the construction disturbance, the complex stiffness of the surrounding soil was solved. The vertical reaction of the surrounding soil on the annular projections at the interfaces of adjacent pile segments is generalized as a Voigt model, while the exposed cap is regarded as an expanding segment of the pile. The analytical solution to the dynamic impedance of a defective tapered pile with exposed cap subjected to a vertical excitation is then derived by means of the Laplace transformation and the amended impedance function transfer method (AIFTM). Based on the presented solution, the influences of the pile-soil system parameters on the velocity response at the cap top are investigated in detail. Some conclusions derived from this study could provide practical guidance for the engineering practice of tapered pile.

Vertical dynamic response of a pile embedded in radially inhomogeneous soil based on fictitious soil pile model

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.

New interaction model for the annular zone of stepped piles with respect to their vertical dynamic characteristics

Stepped piles with a larger section at the top have been increasingly used as foundations for bridge abutment in China. In this paper, numerical modelling using ABAQUS is firstly carried out to investigate the behavior of a annular zone below the top larger section. Then, a new interaction model with a wedge-shaped soil below the annular zone is proposed for pile–soil system. In the model, the soil wedge and normal pile segment were treated as a generalized pile segment. By combining the Novak plane strain model and Rayleigh-Love rod theory, the dynamic characteristics of a stepped pile subject to a vertical harmonic excitation at the pile head are theoretically investigated. The analytical solutions are deduced using Laplace transform and impedance function transfer method. The proposed model is verified by the sensitivity analysis of the soil wedge dimension and comparison with FEM results. Compared with the conventional Voigt model, the present solution shows a flatter oscillation in complex impedance curves, indicating that the Voigt model may overestimate the dynamic response of stepped piles. Finally, selected results are presented to examine the influence of pile geometry on the vertical dynamic responses.

Dynamic response of a large-diameter pile with variable section in layered saturated soil considering construction disturbance effect

ABSTRACTAn analytical solution is developed in this paper to investigate the vertical time-harmonic response of a large-diameter variable-section pile, and it considers the radial inhomogeneity of the surrounding soil caused by construction disturbance. First, the saturated soil surrounding the pile is described by Biot’s poroelastic theory and a series of infinitesimally thin independent layers along the shaft of the pile, and the pile is represented by a variable-section Rayleigh–Love rod. Then, the dynamic equilibrium equations of the soil and pile are solved to obtain an analytical solution for the impedance function at the pile top using the complex stiffness transfer method and impedance function transfer method. Finally, the proposed solution is compared with previous solutions to verify its reliability, and a parameter study is conducted to provide insights into the sensitivity of the vertical dynamic impedance of the pile and velocity response in low-strain integrity testing on defective piles.

Longitudinal dynamic impedance of a static drill rooted nodular pile embedded in layered soil

ABSTRACTThe static drill rooted nodular (SDRN) pile is a new type of precast pipe pile with equally spaced nodes distributed along the shaft and wrapped by the surrounding cemented soil. In this paper, the longitudinal dynamic response of the SDRN pile embedded in layered soil is investigated with respect to the complexity of the pile body structure and the pile–soil contact condition. First, the shear complex stiffness transfer model is used to simulate the radial inhomogeneity of the surrounding soil. Then, the governing Equations of the pile–soil system subjected to longitudinal dynamic loading are established. The analytical solution for the dynamic response at the pile head is obtained by the shear complex stiffness transfer method and the impedance function transfer method. The degenerate case of the present solution is compared with the published solution to verify its reliability, and the complex impedance of the SDRN pile is compared with that of the precast pipe pile and the bored pile. Finally, a parametric study is conducted to investigate the influence of pile–soil parameters on the complex impedance at the pile head within the low frequency range concerned in the design of the dynamic foundation.

Vertical impedance of tapered piles considering the vertical reaction of surrounding soil and construction disturbance

ABSTRACTThe pile–soil system is divided into layers of sufficient number such that the shear stiffness at the pile–soil interface can be determined based on the complex stiffness transfer method. The vertical reaction of surrounding soil on the annular projections at the interface of adjacent pile segments is simplified using Voigt model, whose spring and damping coefficients are derived afterward, allowing an amended impedance function transfer method to be proposed. Using the amended impedance function transfer method, the dynamic equilibrium equation of the pile is solved to give an analytical solution for the impedance function at the pile top. By comparing the solution proposed in this paper with other solutions, the superiority of the bearing capacity of a tapered pile is further confirmed. A parameter study is then conducted to give insight into the coupled interaction of the vertical reaction of the surrounding soil with construction disturbance in the low-frequency range concerned in the seismic design of the pile foundations.

Analytical solution for the dynamic response of a pile with a variable-section interface in low-strain integrity testing

Considering the displacement and stress continuity conditions at the pile-soil interface, ring-soil pile theory (RSPT) and an amended impedance function transfer method (AIFTM) are proposed as models of rigid pile-soil interaction that consider the interaction at the variable-section interface of a pile with the surrounding soil. The interactions between adjacent three-dimensional soil layers are simplified as uniformly distributed Voigt models to derive the impedance function at the pile top. An inverse Fourier transform is applied to derive the velocity response at the top of the pile under transient excitation. An engineering example is described to confirm the rationality of the proposed solution. The solution simplifies into other previously proposed solutions for specific geometric parameters of the pile shaft. The proposed solution is compared with one that neglects the interaction at the variable-section interface of the pile with the surrounding soil; additionally, the coupled effects of the related pile-soil parameters and the interaction at the variable-section interface with the surrounding soil are analyzed.

Dynamic response of a pile considering the interaction of pile variable cross section with the surrounding layered soil

SummaryAssuming that the pile variable cross section interacts with the surrounding soil in the same way as the pile toe does with the bearing stratus, the interaction of pile variable cross section with the surrounding soil is represented by a Voigt model, which consists of a spring and a damper connected in parallel, and the spring constant and damper coefficient are derived. Thus, a more rigid pile–soil interaction model is proposed. The surrounding soil layers are modeled as axisymmetric continuum in which its vertical displacements are taken into account and the pile is assumed to be a Rayleigh–Love rod with material damping. Allowing for soil properties and pile defects, the pile–soil system is divided into several layers. By means of Laplace transform, the governing equations of soil layers are solved in frequency domain, and a new relationship linking the impedance functions at the variable‐section interface between the adjacent pile segments is derived using a Heaviside step function, which is called amended impedance function transfer method. On this basis, the impedance function at pile top is derived by amended impedance function transfer method proposed in this paper. Then, the velocity response at pile top can be obtained by means of inverse Fourier transform and convolution theorem. The effects of pile–soil system parameters are studied, and some conclusions are proposed. Then, an engineering example is given to confirm the rationality of the solution proposed in this paper. Copyright © 2017 John Wiley & Sons, Ltd.

A new analytical model to study the influence of weld on the vertical dynamic response of prestressed pipe pile

SummaryThis investigation is concerned with the mathematical analysis of a viscoelastic prestressed pipe pile embedded in multilayered soil under vertical dynamic excitation. The pile surrounding soil is governed by the plane strain model, and the soil plug is assumed to be an additional mass connected to the pipe pile shaft by applying the distributed Voigt model. Meanwhile, the prestressed pipe pile is assumed to be a vertical, viscoelastic, and hollow cylinder governed by the one‐dimensional wave equation. Then, analytical solutions of the dynamic response of the pipe pile in the frequency domain are derived by means of the Laplace transform and impedance function transfer method. Subsequently, the corresponding quasi‐analytical solution in the time domain for the case of the prestressed pipe pile undergoing a vertical semi‐sinusoidal exciting force applied at the pile top is obtained by employing the inverse Fourier transform. Utilizing these solutions, selected results for the velocity admittance curve and the reflected wave curve are presented for different heights of the soil plug to examine the influence of weld properties on the vertical dynamic response of prestressed pipe pile. The reasonableness of the theoretical model is verified by comparing the calculated results based on the presented solutions with measured results. Copyright © 2017 John Wiley & Sons, Ltd.

Vertical Vibration Characteristics of a Variable Impedance Pile Embedded in Layered Soil

In engineering applications, various defects such as bulging, necking, slurry crappy, and weak concrete are always observed during pile integrity testing. To provide more reasonable basis for assessing the above defects, this paper proposed simple and computationally efficient solutions to investigate the vertical vibration characteristics of a variable impedance pile embedded in layered soil. The governing equations of pile-soil system undergoing a vertical dynamic loading are built based on the plane strain model and fictitious soil pile model. By employing the Laplace transform method and impedance function transfer method, the analytical solution of the velocity response at the pile head is derived in the frequency domain. Then, the corresponding semianalytical solution in the time domain for the velocity response of a pile subjected to a semisinusoidal force applied at the pile head is obtained by adopting inverse Fourier transform and convolution theorem. Based on the presented solutions, a parametric study is conducted to study the vertical vibration characteristics of variable cross-section pile and variable modulus pile. The study gives an important insight into the evaluation of the construction quality of pile.

Vertical vibration of a large-diameter pipe pile considering the radial inhomogeneity of soil caused by the construction disturbance effect

This paper presents an analytical solution for the vertical vibration of a large-diameter pipe pile considering the radial inhomogeneity of both the outer and inner soil caused by the construction disturbance effect. The radial inhomogeneity of the soil is simulated by gradually varying the soil parameters in the radial direction. The complex impedance at the pile head is obtained by introducing the variable separation method and impedance function transfer method. The proposed solution is compared with existing solutions to verify its reliability. Parametric studies are conducted to investigate the vertical vibration characteristics of the pile.

Torsional dynamic response of a pile embedded in layered soil based on the fictitious soil pile model

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.

Vertical dynamic impedance of pile considering the dynamic stress diffusion effect of pile end soil

ABSTRACTA new analytical model is presented to analyze the dynamic stress diffusion effect of pile end soil on the vertical dynamic impedance of the pile. The surrounding soil of the pile is modeled by using the plane strain model and the pile is simulated by using one-dimensional elastic theory. Finite soil layers below the pile end are modeled as conical fictitious soil pile with stress diffusion angle which reflects the dynamic stress diffusion effect of pile end soil. By means of the Laplace transform and impedance function transfer method, the analytical solution of the vertical dynamic impedance at the pile head in frequency domain is yielded. Then, a comparison with other models is performed to verify the conical fictitious soil pile model. Finally, based on the proposed solution, the selected numerical results are compared to analyze the influence of dynamic stress diffusion effect for different design parameters of the soil-pile system on the vertical dynamic impedance at the pile head.

Vertical dynamic impedance of large-diameter pile considering its transverse inertia effect and construction disturbance effect

ABSTRACTThe vertical dynamic impedance of the large-diameter pile is theoretically investigated considering the construction disturbance effect. First, the Rayleigh–Love rode model is introduced to simulate the large-diameter pile with the consideration of its transverse inertia effect. The shear complex stiffness transfer model is proposed to simulate the radial inhomogeneity of the pile surrounding soil caused by the construction disturbance effect. Then, the pile–soil system is divided into finite segments, and the governing equation of the pile–soil system subjected to vertical dynamic loading is established. Following this, the analytical solution of vertical dynamic impedance at the pile head is obtained by means of the shear complex stiffness transfer method and the impedance function transfer method. Based on the present solution, a parametric analysis is conducted to investigate the influence of the transverse inertia effect on the vertical dynamic impedance at the pile head and its relationship with the pile–soil parameters. Finally, comparisons with published solutions are carried out to verify the reliability of the present solution.

Vertical dynamic impedance of the support plate of the Rod-less drilling rig in layered soil

The vertical dynamic response of the support plate of the Rod-less drilling rig in layered soil is theoretically investigated. The soil layers are modeled as a set of viscoelastic continuous media, and the distributed Voigt model is proposed to simulate the dynamic interactions of the adjacent soil layers. Meanwhile, the support plate is regarded as an annular friction pile with a certain radian and can be divided into several plate segments allowing for soil layers. The governing equation of soil vibration is solved by virtue of the Laplace transform and the separation of variables method. Then the vertical dynamic impedance at the bottom of the support plate is derived by means of the impedance function transfer method as well as the force and displacement continuity conditions at the soil–plate interface. By means of the inverse Fourier transform and convolution theorem, the velocity response in the time domain can also be obtained. The reasonableness of the assumptions of the support plate and soil–layer interactions has been verified by comparing the present solutions with dynamic experiments on a full-scale plate in the field. It is shown that the solution derived in this study agrees better with the experimental one than the more limited solution of Novak. An extensive parametric study has been conducted to investigate the effects of major parameters.

Torsional Dynamic Impedance of a Tapered Pile Considering its Construction Disturbance Effect

The dynamic response of a tapered pile (considering its construction disturbance effect) is investigated when the tapered pile is subjected to a time-harmonic torsional loading. For most engineering conditions, the surrounding soil may be weakened or strengthened owing to the construction disturbance effect of the tapered pile, resulting in the soil becoming radially inhomogeneous. In order to consider this problem, the circumferential shear complex stiffness transfer model is proposed to simulate the radial inhomogeneity of soil. Then, the governing equations of a tapered pile-soil system subjected to torsional dynamic loading are established. By virtue of the circumferential shear complex stiffness transfer method and the impedance function transfer method, the analytical solution of torsional dynamic impedance at the head of the tapered pile is derived. Based on the presented solution, the influence of the construction disturbance effect of the surrounding soil on the torsional dynamic impedance at the pile head is investigated within the low-frequency range concerned in the design of a dynamic foundation. The results show that, even if the hardening range and softening range of the surrounding soil vary within a smaller scale, the hardening effect and softening effect also have a notable influence on the torsional dynamic impedance at the pile head.