Torsional dynamic response of a large‐diameter pipe pile in viscoelastic saturated soil

An analytical solution is developed in this paper to investigate the dynamic response of a large‐diameter end‐bearing pipe pile subjected to torsional loading in viscoelastic saturated soil. The wave propagation in saturated soil and pile are simulated by Biot's two‐phased linear theory and one‐dimensional elastic theory, respectively. The dynamic equilibrium equations of the outer soil, inner soil, and pile are established. The solutions for the outer and inner soils in frequency domain are obtained by Laplace transform technique and the separation of variables method. Then, the dynamic response of the pile is obtained on the basis of the perfect contacts between the pile and the outer soil as well as the inner soil. The results in this paper are compared with that of a solid pile in elastic saturated soil to verify the validity of the solution. Furthermore, the solution in this paper is compared with the classic plane strain solution to verify the solution further and check the accuracy of the plane strain solution. Numerical results are presented to analyze the vibration characteristics and illustrate the effect of the soil parameters and the geometry size of the pile on the complex impedance and velocity admittance of the pile head. Finally, the displacement of the soil at different depth and frequency is analyzed. Copyright © 2014 John Wiley & Sons, Ltd.     

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

This 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.     

非均质土中桩端扩散虚土桩法的桩基纵向振动研究

根据桩端土应力扩散的规律,建立了桩端扩散虚土桩模型。基于该模型对非均质土中桩-土纵向耦合振动进行研究。利用复刚度传递多圈层平面应变模型,得到桩与虚土桩桩侧土的剪切复刚度。结合边界条件、初始条件和连续条件,对扩散虚土桩和实体桩动力方程从底层往顶层逐层进行求解,得到桩顶动力响应的频域解析解和时域半解析解。通过对桩端扩散虚土桩扩散角、扩散层厚度、桩侧土非均质性和桩长的影响进行计算分析,得到基于扩散虚土桩法桩-土纵向振动响应特性。研究结论可为桩基础动力设计和动态检测提供理论依据。     

Vertical dynamic response of an inhomogeneous viscoelastic pile

The vertical dynamic response of an inhomogeneous viscoelastic pile embedded in layered soil subjected to axial loading has been investigated. The interaction between pile and soil is simulated by a general Voigt model, one that has been demonstrated by earlier investigators to be capable of representing the plane strain case of soil adequately. The analytical solutions of pile responses in the frequency domain are obtained by using the (two-sided) Laplace transform. The corresponding semi-analytical solutions in the time domain for the case of a pile subjected to an instantaneous half-sine exciting force applied at the pile top are obtained via Fourier transform inversion. Using these solutions, a parametric study of the influence of the pile and soil properties on the vertical dynamic responses has been undertaken. It is shown that an abrupt variation of the soil properties with depth cannot yield evident reflection signal that may lead geotechnical engineers to assess the pile integrity wrongly from the velocity curve of the pile top, and the influence of viscosity of the pile material on the response is different from that of the damping of the soil surrounding the pile. The theoretical model developed in the present paper has also been validated in field studies, where it is shown by means of three examples that the solution developed in this study has been adequately verified by comparison of the theoretical pile model and field measurements of the dynamic responses.     

On vertical dynamic stability and cross‐section optimization of closed‐ended hollow pile by considering soil compaction effects

This paper conducts a comprehensive study on the effects of expansion force after pile driving on the vertical vibration of the hollow pile. The initial radially inhomogeneous strain field of soil in disturbed soil region and dynamic shear modulus of remolded soil are constructed by applying the cylindrical cavity expansion method. The equation governing the incremental motion of the soil is consequently deduced on the basis of incremental deformations superposed on an underlying finite deformation. The longitudinal impedance of the top of the pile and the velocity response in frequency and time domains are also numerically studied. The relations between the expansion force after pile driving and the velocity response of the pile with different wall thickness are discussed accordingly. The results suggest that a pile has a better dynamical stability when the characteristics of the section are optimized and interacting force with soil medium gets smaller.     

Three‐dimensional finite element analyses of passive pile behaviour

Piles may be subjected to lateral soil pressures as a result of lateral soil movements from nearby construction‐related activities such as embankment construction or excavation operations. Three‐dimensional finite element analyses have been carried out to investigate the response of a single pile when subjected to lateral soil movements. The pile and the soil were modelled using 20‐node quadrilateral brick elements with reduced integration. For compatibility between the soil–pile interface elements, 27‐node quadrilateral brick elements with reduced integration were used to model the soil around the pile adjacent to the soil–pile interface. A Mohr–Coulomb elastic–plastic constitutive model with large‐strain mode was assumed for the soil. The analyses indicate that the behaviour of the pile was significantly influenced by the pile flexibility, the magnitude of soil movement, the pile head boundary conditions, the shape of the soil movement profile and the thickness of the moving soil mass. Reasonable agreement is found between some existing published solutions and those developed herein. Copyright © 2005 John Wiley & Sons, Ltd.     

Vertical impedance of an end‐bearing pile in viscoelastic soil

This paper presents a new method to derive the analytical solution for the vertical impedance of an end‐bearing pile in viscoelastic soil. The soil is assumed as a homogeneous and isotropic layer, and the pile is considered as a one‐dimensional Euler rod. Considering both the vertical and radial displacements of soil and soil–pile coupled vibration, the governing equations of the soil and pile are established. The volumetric strain of soil is obtained by transformation on the equations of soil and variable separation method. Then the vertical and radial displacements of soil are obtained accordingly. The displacement response and impedance function of pile are derived based on the continuity assumption of the displacement and stress between the pile and soil. The solution is verified by being compared with an existing solution obtained by introducing potential functions. Furthermore, a comparison with two other simplified solutions is conducted. Numerical examples are presented to analyze the vibration characteristics of the pile. Copyright © 2014 John Wiley & Sons, Ltd.     

A non‐linear coupled finite element–boundary element model for the prediction of vibrations due to vibratory and impact pile driving

This paper presents a non‐linear coupled finite element–boundary element approach for the prediction of free field vibrations due to vibratory and impact pile driving. Both the non‐linear constitutive behavior of the soil in the vicinity of the pile and the dynamic interaction between the pile and the soil are accounted for. A subdomain approach is used, defining a generalized structure consisting of the pile and a bounded region of soil around the pile, and an unbounded exterior linear soil domain. The soil around the pile may exhibit non‐linear constitutive behavior and is modelled with a time‐domain finite element method. The dynamic stiffness matrix of the exterior unbounded soil domain is calculated using a boundary element formulation in the frequency domain based on a limited number of modes defined on the interface between the generalized structure and the unbounded soil. The soil–structure interaction forces are evaluated as a convolution of the displacement history and the soil flexibility matrices, which are obtained by an inverse Fourier transformation from the frequency to the time domain. This results in a hybrid frequency–time domain formulation of the non‐linear dynamic soil–structure interaction problem, which is solved in the time domain using Newmark's time integration method; the interaction force time history is evaluated using the θ‐scheme in order to obtain stable solutions. The proposed hybrid formulation is validated for linear problems of vibratory and impact pile driving, showing very good agreement with the results obtained with a frequency‐domain solution. Linear predictions, however, overestimate the free field peak particle velocities as observed in reported field experiments during vibratory and impact pile driving at comparable levels of the transferred energy. This is mainly due to energy dissipation related to plastic deformations in the soil around the pile. Ground vibrations due to vibratory and impact pile driving are, therefore, also computed with a non‐linear model where the soil is modelled as an isotropic elastic, perfectly plastic solid, which yields according to the Drucker–Prager failure criterion. This results in lower predicted free field vibrations with respect to linear predictions, which are also in much better agreement with experimental results recorded during vibratory and impact pile driving. Copyright © 2008 John Wiley & Sons, Ltd.     

Vertical response of pile raft foundations subjected to tunneling‐induced ground movements in layered soil

A simplified analysis method has been developed to estimate the vertical movement and load distribution of pile raft foundations subjected to ground movements induced by tunneling based on a two‐stage method. In this method, the Loganathan–Polous analytical solution is used to estimate the free soil movement induced by tunneling in the first stage. In the second stage, composing the soil movement to the pile, the governing equilibrium equations of piles are solved by the finite difference method. The interactions between structural members (such as pile–soil, pile–raft, raft–soil, and pile–pile) are modeled based on the elastic theory method of a layered half‐space. The validity of the proposed method is verified through comparisons with some published solutions for single piles, pile groups, and pile rafts subjected to ground movements induced by tunneling. Good agreements between these solutions are demonstrated. The method is also used for a parametric study to develop a better understanding of the behavior of pile rafts influenced by tunneling operation in layered soil foundations. Copyright © 2011 John Wiley & Sons, Ltd.     

Vertical dynamic response of pile in a radially heterogeneous soil layer

An analysis of a pile vertical response considering soil inhomogeneity in the radial direction under dynamic loads is presented. The solution technique is based on a three‐dimensional axisymmetric model, which includes the consideration of the vertical displacement of the soil. The soil domain is subdivided into a number of annular vertical zones, and the continuity of the displacements and stresses are imposed at both the interface of pile–soil and the interfaces of adjacent soil zones to establish the dynamic equilibrium equations of the pile–soil interaction. Then, the equations of each soil zone and of the pile are solved one by one to obtain the analytical and semi‐analytical dynamic responses at the top of the pile in the frequency domain and time domain. Parametric studies have been performed to examine the influence of soil parameters' variations in the radial direction caused by the construction effect on the dynamic responses of pile. The results of the studies have been summarized and presented in figures to illustrate the influences of the soil parameters as they change radially. The effect of the radius of the disturbed soil zone caused by construction is also studied in this paper. Copyright © 2008 John Wiley & Sons, Ltd.     

Dynamic responses of a pile embedded in a layered poroelastic half‐space to harmonic lateral loads

A single pile embedded in a layered poroelastic half‐space subjected to a harmonic lateral load is investigated in this study. Based on Biot's theory, the frequency domain fundamental solution for a horizontal circular patch load applied in the layered poroelastic half‐space is derived via the transmission and reflection matrices method. Utilizing Muki and Sternberg's method, the second kind of Fredholm integral equation describing the dynamic interaction between the layered half‐space and the pile subjected to a top harmonic lateral load is constructed. The proposed methodology is validated by comparing results of this paper with some existing results. Numerical results show that for a two‐layered half‐space, the thickness of the upper softer layer has pronounced influences on the dynamic response of the pile and the half‐space. For a three‐layered half‐space, the presence of a softer middle layer in the layered half‐space will enhance the compliance for the pile significantly, while a stiffer middle layer will diminish the dynamic compliance of the pile considerably. Copyright © 2009 John Wiley & Sons, Ltd.     

Poroelastic model for pile–soil interaction in a half‐space porous medium due to seismic waves

In this paper, frequency domain dynamic response of a pile embedded in a half‐space porous medium and subjected to P, SV seismic waves is investigated. According to the fictitious pile methodology, the problem is decomposed into an extended poroelastic half‐space and a fictitious pile. The extended porous half‐space is described by Biot's theory, while the fictitious pile is treated as a bar and a beam and described by the conventional 1‐D structure vibration theory. Using the Hankel transformation method, the fundamental solutions for a half‐space porous medium subjected to a vertical or a horizontal circular patch load are established. Based on the obtained fundamental solutions and free wave fields, the second kind of Fredholm integral equations describing the vertical and the horizontal interaction between the pile and the poroelastic half‐space are established. Solution of the integral equations yields the dynamic response of the pile to plane P, SV waves. Numerical results show the parameters of the porous medium, the pile and incident waves have direct influences on the dynamic response of the pile–half‐space system. Significant differences between conventional single‐phase elastic model and the poroelastic model for the surrounding medium of the pile are found. Copyright © 2007 John Wiley & Sons, Ltd.     

Dynamic characteristics of a large‐diameter pile in saturated soil and its application

This study theoretically investigates the dynamic response of an end‐bearing pile embedded in saturated soil considering the transverse inertial effect of the pile. The saturated soil surrounding the pile is described by Biot poroelastic theory, and the pile is represented by a Rayleigh‐Love rod because both the vertical and radial displacements at the soil‐pile interface are considered. The potential function decomposition method and variable separation method are introduced to solve the governing equations of the soil, in which the vertical and radial displacement components are coupled. The governing equation of the pile is solved using the continuity conditions at the pile‐soil interface. Next, the velocity admittance in the frequency domain and the velocity response in the time domain at the pile top are presented based on the Laplace transform and inverse Fourier transform, respectively. Subsequently, the reduced solution is compared with a 1‐dimensional model solution to verify the validity, and the influences of the slenderness ratio of the pile on the transverse inertial effect of the pile are analyzed. Moreover, Poisson ratio, the slenderness ratio of the pile, and the pile‐soil modulus ratio are studied. Finally, the theoretical and measured curves in the engineering project are compared, and the results demonstrate the good application prospects of the solution presented in this article.     

Analysis of pile subjected to torsion in multi‐layered soil

A new method of analysis of piles in multi‐layered elastic soil subjected to a torque at the head is developed. The differential equation governing the angle of twist in the pile is derived using the variational principles of mechanics. The method of initial parameters is used to obtain closed‐form solutions of the angle of twist and torque in the pile as a function of depth. The inputs required for the analysis are shear moduli of pile and soil, pile geometry and thickness of soil layers. Copyright © 2013 John Wiley & Sons, Ltd.     

Longitudinal vibration of a pile embedded in layered soil considering the transverse inertia effect of pile

The dynamic response of a viscoelastic bearing pile embedded in multilayered soil is theoretically investigated considering the transverse inertia effect of the pile. The soil layers surrounding the pile are modeled as a set of viscoelastic continuous media in three-dimensional axisymmetric space, and a simplified model, i.e., the distributed Voigt model, is proposed to simulate the dynamic interactions of the adjacent soil layers. Meanwhile, the pile is assumed to be a Rayleigh–Love rod with material damping and can be divided into several pile segments allowing for soil layers and pile defects. Both the vertical and radial displacement continuity conditions at the soil–pile interface are taken into account. The potential function decomposition method and the variable separation method are introduced to solve the governing equations of soil vibration in which the vertical and radial displacement components are coupled. On this basis, the impedance function at the top of the pile segment is derived by invoking the force and displacement continuity conditions at the soil–pile interface as well as the bottom of pile segment. The impedance function at the pile head is then obtained by means of the impedance function transfer method. 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 soil-layer interactions have been verified by comparing the present solutions with two published solutions and a set of well-documented measured pile test data. A parametric analysis is then conducted using the present solutions to investigate the influence of the transverse inertia effect on the dynamic response of an intact pile and a defective pile for different design parameters of the soil–pile system.     

Expanded superposition method for impedance functions of inclined‐pile groups

This paper presents a superposition method expanded for computing impedance functions (IFs) of inclined‐pile groups. Closed‐form solutions for obtaining horizontal, vertical, and rocking IFs, estimated by using pile‐to‐pile interaction factors, are proposed. IFs of solitary inclined piles, crossed IFs, and explicit incorporation of compatibility conditions for pile‐head movements are also appropriately taken into consideration. All of these factors should be known in advance and will be computed and shown for the most relevant cases. The accuracy of the proposed closed‐form solutions is verified for 2 × 2 and 3 × 3 square inclined‐pile groups embedded in an isotropic viscoelastic homogeneous half‐space soil medium, with hysteretic damping. The pile‐to‐pile interaction factors are computed by means of a three‐dimensional time‐harmonic boundary elements–finite elements coupling formulation. The results indicate that the IFs obtained from the proposed method are in good agreement with those obtained from the coupling formulation. Furthermore, crossed vertical‐rocking IFs of solitary piles need to be appropriately considered for obtaining rocking IFs when the number of piles is small. Copyright © 2015 John Wiley & Sons, Ltd.     

饱和黏弹性地基土中管桩纵向振动研究

用解析方法在频率域内研究考虑质量耦合效应的饱和黏弹性地基土中管桩的纵向振动特性。基于Biot理论,采用薄层法,推导得到饱和黏弹性地基土的位移、应力等的表达式。将管桩等效为一维弹性杆件处理。根据界面连续性条件,给出饱和黏弹性地基土中管桩的纵向振动一般分析方法和桩顶动力复刚度的表达式。在该基础上,对比分析饱和地基土中实心桩和管桩纵向振动特性。通过算例分析,考察桩周土和桩芯土的力学参数对桩顶刚度因子和等效阻尼的影响。研究表明,饱和黏弹性地基土中实心桩和管桩的纵向振动有明显的差异。     

Analysis of piled raft with nodular pile subjected to vertical load using a Winkler model approach

An investigation is made to present analytical solutions provided by a Winkler model approach for analysis of piled rafts with nodular pile subjected to vertical loads in nonhomogeneous soils. The vertical stiffness coefficient along a piled raft with the nodular pile in nonhomogeneous soils is derived from the displacement given by the Mindlin solution for elastic continuum analysis. The vertical stiffness coefficients for the bases of the raft and the nodular part in the nodular pile in a soil are expressed by the Muki solution for the 3‐D elastic analysis. The relationship between settlement and vertical load on the pile base is presented considering the Mindlin solution and the equivalent thickness in the equivalent elastic method. The interaction factor between the shaft of the nodular pile and the soil is expressed taking into account the Mindlin solution and the equivalent elastic modulus. The relationship between settlement and vertical load for a piled raft with the nodular pile in nonhomogeneous soils is obtained by using the recurrence equation of influence factors of the pile for each layer. The percentage of each load carried by both nodular pile and raft subjected to vertical load is represented through the vertical influence factors proposed here. Comparison of the results calculated by the present method for piled rafts with nodular piles in nonhomogeneous soils has shown good agreement with those obtained from the finite element method and a field test. Copyright © 2016 John Wiley & Sons, Ltd.     

Simplified three-dimensional analysis of horizontally vibrating floating and fixed-end pile groups

This note presents an approximate analytical solution for estimating the time-harmonic impedance of pile groups subjected to horizontal dynamic loads, for different boundary conditions at pile tip (free and fixed). The derived solution considers waves due to pile vibrations propagating in both horizontal and vertical directions, unlike earlier solutions based on the plane-strain model, which ignores vertically propagating waves. This allows accounting for pile boundary conditions on the soil attenuation function, as well as modeling the response of the pipe group-soil system near the first natural frequency of the soil layer, where solutions based on the plane-strain model fail to account for resonance phenomena.     

Analysis of pile‐raft foundations under complex loads in layered soils

Considering there is hardly any concerted effort to analyze the pile‐raft foundations under complex loads (combined with vertical loads, horizontal loads and moments), an analysis method is proposed in this paper to estimate the responses of pile‐raft foundations which are subjected to vertical loads, horizontal loads and moments in layered soils based on solutions for stresses and displacements in layered elastic half space. Pile to pile, pile to soil surface, soil surface to pile and soil surface to soil surface interactions are key ingredients for calculating the responses of pile‐raft foundations accurately. Those interactions are fully taken into account to estimate the responses of pile‐raft foundations subject to vertical loads, horizontal loads and moments in layered soils. The constraints of the raft on vertical movements, horizontal movements and rotations of the piles as well as the constraints of the raft on vertical movements and horizontal movements of the soils are considered to reflect the coupled effect on the raft. The method is verified through comparisons with the published methods and FEM. Then, the method is adopted to investigate the influence of soil stratigraphy on pile responses. The study shows that it is necessary to consider the soil non‐homogeneity when estimating the responses of pile‐raft foundations in layered soils, especially when estimating the horizontal responses of pile‐raft foundations. The horizontal loads and the moments have a significant impact on vertical responses of piles in pile‐raft foundations, while vertical loads have little influence on horizontal responses of piles in pile‐raft foundations in the cases of small deformations. The proposed method can provide a simple and useful tool for engineering design. Copyright © 2013 John Wiley & Sons, Ltd.