Numerical modelling of the driving response of thin‐walled open‐ended piles

The driving response of thin‐walled open‐ended piles is studied using numerical simulation of the wave propagation inside the soil plug and the pile. An elastic finite element analysis is carried out to identify the stress wave propagation in the vicinity of the pile toe. It is found that the shear stress wave has the highest magnitude above the bottom of the soil plug. Below the bottom of the soil plug, the vertical stress wave has the highest magnitude. Although the shear stress wave propagating in the radial direction is similar in magnitude to the vertical stress wave at the bottom of the soil plug, it decays rapidly while travelling downwards. The highest vertical stress at the bottom of the soil plug appears after the vertical stress wave interacts with the shear stress wave travelling in the radial direction. Initially, the vertical stress wave propagates with the dilation wave velocity in both the radial and vertical directions. After it interacts with the shear stress wave, the vertical stress wave starts to propagate with the shear wave velocity in the radial direction and with the axial wave velocity downwards. It is concluded that at the bottom of the soil plug, the interaction between the waves travelling in radial and vertical directions is important. The capabilities of several one‐dimensional pile‐in‐pile models to reproduce the driving response given by a two‐dimensional axisymmetric finite element model is studied. It is seen that when the base of the soil plug fails, a one‐dimensional pile‐in‐pile model can be used to achieve results in agreement with the finite element model. However, when the pile is unplugged, where the base of the soil plug does not fail, a reduced finite element mesh that permits the radial wave propagation inside the soil plug must be used. Copyright © 2001 John Wiley & Sons, Ltd.     

Vertical amplitude reduction of Rayleigh waves by a row of piles in a poroelastic half‐space

A row of rigid piles is addressed as the countermeasures for isolating Rayleigh waves in a poroelastic half‐space. The complex characteristic equations for Rayleigh waves are derived via Biot's theory and their existence conditions are given. The piles are modeled as Euler–Bernoulli beams with longitudinal displacements and the diffracted field by each pile is constructed only with Rayleigh waves. Six infinite linear systems of algebraic equations are obtained in terms of the equilibrium of forces and continuity of displacements at the pile–soil interfaces. The systems are subsequently solved in the complex least‐squares sense. The influence of certain pile and soil characteristics such as the permeability of poroelastic soil, spacing between the piles and length of the piles on the isolating performance of a pile barrier is investigated. Computed results show that the permeability of poroelastic soil displays a significant effect on the vertical amplitude reduction of Rayleigh waves. Copyright © 2009 John Wiley & Sons, Ltd.     

Propagation of Rayleigh waves in fluid‐saturated non‐homogeneous soils with the graded solid skeleton distribution

The propagation characteristic of Rayleigh waves in a fluid‐saturated non‐homogeneous poroelastic half‐plane is addressed. Based on Biot's theory for fluid‐saturated media, which takes the inertia, fluid viscosity, mechanical coupling, compressibility of solid grains, and fluid into account, the dispersion equations of Rayleigh waves in fluid‐saturated non‐homogeneous soils/rocks are established. By considering the shear modulus of solid skeleton variation with depth exponentially, a small parameter, which reflects the relative change of shear modulus, is introduced. The asymptotic solution of the dispersion equation expressing the relationship between the phase velocity and wave number is obtained by using the perturbation method. In order to analyze the effects of non‐homogeneity on the propagation characteristic of Rayleigh waves, the variation of the phase velocity with the wave number is presented graphically and discussed through numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Noise Reduction Technique Applied to the Multichannel Analysis of Surface Waves

This paper shows the presence of noises and technique to reduce these noises during the surface wave analysis. The frequency-dependent properties of Rayleigh-type surface waves can be used for imaging and characterizing the shallow subsurface. Interference by coherent source-generated noise inhibits the reliability of shear-wave velocities determined through inversion of the phase velocities of Rayleigh waves. Among these interferences by non-planar, non-fundamental mode Rayleigh waves (noise) are body waves, scattered and non-source-generated surface waves, and higher-mode surface waves. For the reduction of noise, the filtering technique is implemented in this paper for the multichannel analysis of surface wave method (MASW). With the de-noising technique during the MASW method, more robust and reliable outcome is achieved. The significance of this paper is to obtain pre-awareness about noises during surface wave analysis and take better outcomes with de-noising performance in near surface soil investigations.     

A modulus‐multiplier approach for non‐linear analysis of laterally loaded pile groups

A modulus‐multiplier approach, which applies a reduction factor to the modulus of single pile p–y curves to account for the group effect, is presented for analysing the response of each individual pile in a laterally loaded pile group with any geometric arrangement based on non‐linear pile–soil–pile interaction. The pile–soil–pile interaction is conducted using a 3D non‐linear finite element approach. The interaction effect between piles under various loading directions is investigated in this paper. Group effects can be neglected at a pile spacing of 9 times the pile diameter for piles along the direction of the lateral load and at a pile spacing of 6 times the pile diameter for piles normal to the direction of loading. The modulus multipliers for a pair of piles are developed as a function of pile spacing for departure angle of 0, 90, and 180sup>/sup> with respect to the loading direction. The procedure proposed for computing the response of any individual pile within a pile group is verified using two well‐documented full‐scale pile load tests. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical modelling of large deformations associated with driving of open‐ended piles

This paper presents a ‘Eulerian‐like’ finite element technique to simulate the large accumulated displacements of piles subjected to multiple hammer blows. For each hammer blow, results are obtained using a standard small strain finite element model and, at the end of each hammer blow, material flow is taken into account with reference to a fixed finite element mesh. Residual stresses calculated at the Gauss integration points of the deformed finite element mesh are mapped on to the fixed finite element mesh, and these stresses are used as initial stresses for the next hammer blow. At the end of each hammer blow, stiffness and mass matrices are recalculated for the volume of material remaining inside the fixed finite element mesh. Results obtained with and without allowing material to flow through the fixed mesh are compared for several hammer blows. Build up of residual stresses, soil flow and yielded points around the pile are presented for plugged, partially‐plugged and unplugged piles. Using the new finite element technique, the driving of a pile from the soil surface is studied. The ability to analyse this and other large deformation problems is the main advantage of the new finite element technique. Copyright © 2000 John Wiley & Sons, Ltd.     

A revised solution for the horizontal vibration of an end‐bearing pile in viscoelastic soil

This note presents a new method to derive closed‐form expressions describing the horizontal response of an end‐bearing pile in viscoelastic soil subjected to harmonic loads at its head. The soil surrounding the pile is assumed as a linearly viscoelastic layer. The propagation of waves in the soil and pile is treated mathematically by three‐dimensional and one‐dimensional theories, respectively. Unlike previous studies of the problem, the formulation presented allows the governing equations of the soil to be solved directly, eliminating the need to introduce potential functions. Accordingly, the dynamic response of the pile is obtained by means of the initial parameter method, invoking the requirement for continuity at the pile–soil interface. It is demonstrated that the derived compact solution matches exactly an existing solution that utilises potential functions to formulate the problem. Copyright © 2016 John Wiley & Sons, Ltd.     

Soil‐pile interaction in the pile vertical vibration considering true three‐dimensional wave effect of soil

The dynamic response of an end bearing pile embedded in a linear visco‐elastic soil layer with hysteretic type damping is theoretically investigated when the pile is subjected to a time‐harmonic vertical loading at the pile top. The soil is modeled as a three‐dimensional axisymmetric continuum in which both its radial and vertical displacements are taken into account. The pile is assumed to be vertical, elastic and of uniform circular cross section. By using two potential functions to decompose the displacements of the soil layer and utilizing the separation of variables technique, the dynamic equilibrium equation is uncoupled and solved. At the interface of soil‐pile system, the boundary conditions of displacement continuity and force equilibrium are invoked to derive a closed‐form solution of the vertical dynamic response of the pile in frequency domain. The corresponding inverted solutions in time domain for the velocity response of a pile subjected to a semi‐sine excitation force applied at the pile top are obtained by means of inverse Fourier transform and the convolution theorem. A comparison with two other simplified solutions has been performed to verify the more rigorous solutions presented in this paper. Using the developed solutions, a parametric study has also been conducted to investigate the influence of the major parameters of the soil‐pile system on the vertical vibration characteristics of the pile. Copyright © 2013 John Wiley & Sons, Ltd.     

Torsional wave propagation in non‐homogeneous layer between non‐homogeneous half‐spaces

The study of surface wave in a layered medium has their possible application in geophysical prospecting. In the present work, dispersion equation for torsional wave in an inhomogeneous isotropic layer between inhomogeneous isotropic half‐spaces has been derived. Two cases are discussed separately for torsional wave propagation in inhomogeneous layer between homogeneous and non‐homogeneous half‐spaces, respectively. Further, two possible modes for torsional wave propagation are obtained in case of inhomogeneous layer sandwiched between non‐homogeneous half‐spaces. Closed form solutions for displacement in the layer and half‐spaces are obtained in each case. The study reveals that the layer width, layer inhomogeneity, frequency of inhomogeneity, as well as inhomogeneity in the half‐space has significant effect on the propagation of torsional surface waves. Displacement and implicit dispersion equation for torsional wave velocities are expressed in terms of Heun functions and their derivatives. Effects of inhomogeneity on torsional wave velocity are also discussed graphically by plotting the dimensionless phase velocity against dimensionless and scaled wave number for different values of inhomogeneity parameter. Copyright © 2012 John Wiley & Sons, Ltd.     

采用Laplace变换分析桩基应力波传播问题

将土体中的混凝土桩基简化为黏滞介质中的一维黏弹性杆,桩顶部受锤头冲击产生内部应力波。根据杆内微元应力平衡条件建立杆中一维黏弹性应力波传播的控制方程,结合桩顶锤头冲击条件和桩底弹-黏性约束条件给出桩基两端的耦合边界条件。对控制方程和定解条件作Laplace变换并求解变换后的常微分方程,得到变换域的应力像函数解析解。采用数值反变换技术将像函数转变为时间域的应力波形。应用此方法可以较方便地分析桩基中应力波的产生、传播、反射及相互作用过程。     

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.     

Time-domain analysis of velocity waves in a pipe pile due to a transient point load

The propagation of stress waves in a pipe pile subjected to a transient point load cannot be expressed using traditional one-dimensional (1D) wave theory. This paper presents an analytical solution used to investigate the wave propagation in a pipe pile under an axial point load. The soil resistance is simulated using the Winkler model, and the excitation force is simulated with a semi-sinusoidal impulse. A time-domain analytical solution for the three-dimensional wave equation is derived using the separation of variables and variation of constants methods. The solution is verified with a frequency domain analytical solution in which the time-domain response is calculated by numerical Fourier inverse transformation. Furthermore, the solution proposed in this paper is compared with the results of model testing and 3D FEM analysis. The comparisons show that the analytical solution proposed in this study agrees well with the results of previous studies. The proposed solution is subsequently applied in case studies. The vertical velocity responses in the circumferential and axial directions are analyzed to reveal the propagation characteristics of transient waves in the pipe pile. Moreover, the effects of the location and period of the excitation force, the side and tip resistances and high-order modes are studied in detail.     

A study of the effect of driving on pre‐bored piles

A finite element model for pile‐driving analysis is developed and used to investigate the behaviour of pre‐bored piles, which are then driven the last 1.25 or 2.25 m to their final design depth. The study was conducted for the case of saturated clays. The model traces the penetration of the pile into the soil and accommodates for large deformations. The non‐linear behaviour of the clay in this study is predicted using the bounding‐surface‐plasticity model, as applied to isotropic cohesive soils. The details of the 3‐D numerical modelling and computational schemes are presented. A significant difference was observed in the pile displacement during driving, and in the computed soil resistance at the pile tip, particularly at the earliest driving stages. No difference in soil resistance at the soil pile interface along the pile shaft was detected between the pre‐bored piles whether driven 1.25 or 2.25 m. Copyright © 2002 John Wiley & Sons, Ltd.     

Source signature and elastic waves in a half‐space under a sustainable line‐concentrated impulsive normal force

First, the response of an ideal elastic half‐space to a line‐concentrated impulsive normal load applied to its surface is obtained by a computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. Then, the geometry is determined of the obtained waves and the source signature—the latter is the imprint of the spatiotemporal configuration of the excitation source in the resultant response. Behind the dilatational precursor wave, there exists a pencil of three plane waves extending from the vertex at the impingement point of the precursor wave on the stress‐free surface of the half‐space to three points located on the other two boundaries of the solution domain. These four wave‐arresting points (end points) of the three plane waves constitute the source signature. One wave is an inhibitor front in the behaviour of the normal stress components and the particle velocity, while in the behaviour of the shear stress component, it is a surface‐axis wave. The second is a surface wave in the behaviour of the horizontal components of the dependent variables, while the third is an inhibitor wave in the behaviour of the shear stress component. An inhibitor wave is so named, since beyond it, the material motion is dying or becomes uniform. A surface‐axis wave is so named, since upon its arrival, like a surface wave, the dependent variable in question features an extreme value, but unlike a surface wave, it exists in the entire depth of the solution domain. It is evident from this work that Saint‐Venant's principle for wave propagation problems cannot be formulated; therefore, the above results are a consequence of the particular model proposed here for the line‐concentrated normal load. Copyright © 2002 John Wiley & Sons, Ltd.     

Three‐dimensional nonlinear finite element analysis of pile groups in saturated porous media using a new transmitting boundary

The dynamic behaviour of pile groups subjected to an earthquake base shaking is analysed. An analysis is formulated in the time domain and the effects of material nonlinearity of soil, pile–soil–pile kinematic interaction and the superstructure–foundation inertial interaction on seismic response are investigated. Prediction of response of pile group–soil system during a large earthquake requires consideration of various aspects such as the nonlinear and elasto‐plastic behaviour of soil, pore water pressure generation in soil, radiation of energy away from the pile, etc. A fully explicit dynamic finite element scheme is developed for saturated porous media, based on the extension of the original formulation by Biot having solid displacement (u) and relative fluid displacement (w) as primary variables (u–w formulation). All linear relative fluid acceleration terms are included in this formulation. A new three‐dimensional transmitting boundary that was developed in cartesian co‐ordinate system for dynamic response analysis of fluid‐saturated porous media is implemented to avoid wave reflections towards the structure. In contrast to traditional methods, this boundary is able to absorb surface waves as well as body waves. The pile–soil interaction problem is analysed and it is shown that the results from the fully coupled procedure, using the advanced transmitting boundary, compare reasonably well with centrifuge data. Copyright © 2007 John Wiley & Sons, Ltd.     

Axial kinematic response of end‐bearing piles to P waves

Kinematic pile–soil interaction under vertically impinging seismic P waves is revisited through a novel continuum elastodynamic solution of the Tajimi type. The proposed model simulates the steady‐state kinematic response of a cylindrical end‐bearing pile embedded in a homogeneous viscoelastic soil stratum over a rigid base, subjected to vertically propagating harmonic compressional waves. Closed‐form solutions are obtained for the following: (i) the displacement field in the soil and along the pile; (ii) the kinematic Winkler moduli (i.e., distributed springs and dashpots) along the pile; (iii) equivalent, depth‐independent, Winkler moduli to match the motion at the pile head. The solution for displacements is expressed in terms of dimensionless transfer functions relating the motion of the pile head to the free‐field surface motion and the rock motion. It is shown that (i) a pile foundation may significantly alter (possibly amplify) the vertical seismic excitation transmitted to the base of a structure and (ii) Winkler moduli pertaining to kinematic loading differ from those for inertial loading. Simple approximate expressions for kinematic Winkler moduli are derived for use in applications. Copyright © 2013 John Wiley & Sons, Ltd.     

Analysis of soil–pile–structure interaction in a two‐layer ground during earthquakes considering liquefaction

This study is conducted with a numerical method to investigate the seismic behaviour among certain soils, single piles, and a structure. A series of numerical simulations of the seismic behaviour of a single‐pile foundation constructed in a two‐layer ground is carried out. Various sandy soils, namely, dense sand, medium dense sand, reclaimed soil, and loose sand, are employed for the upper layer, while one type of clayey soil is used for the lower layer. The results reveal that when a structure is built in a non‐liquefiable ground, an amplification of the seismic waves is seen on the ground surface and in the upper structure, and large bending moments are generated at the pile heads. When a structure is built in a liquefiable ground, a de‐amplification of the seismic waves is seen on the ground surface and in the upper structure, and large bending moments are generated firstly at the pile heads and then in the lower segment at the boundary between the soil layers when liquefaction takes place. Copyright © 2007 John Wiley & Sons, Ltd.     

Analysis of piles subjected to lateral soil movements using a three‐dimensional displacement approach

An analytical approach using the three‐dimensional displacement of a soil is investigated to provide analytical solutions of the horizontal response of a circular pile subjected to lateral soil movements in nonhomogeneous soil. The lateral stiffness coefficient of the pile shaft in nonhomogeneous soil is derived from the rocking stiffness coefficient that is obtained from the analytical solution, taking into account the three‐dimensional displacement represented in terms of scalar potentials in the elastic three‐dimensional analysis. The relationship between horizontal displacement, rotation, moment, and shear force of a pile subjected to lateral soil movements in nonhomogeneous soil is obtainable in the form of the recurrence equation. For the relationship between the lateral pressure and the horizontal displacement, it is assumed that the behavior is linear elastic up to lateral soil yield, and the lateral pressure is constant under the lateral soil yield. The interaction factors between piles subjected to both lateral load and moment are calculated, taking into account the lateral soil movement. The formulation of the lateral displacement and rotation of the pile base subjected to lateral loads in nonhomogeneous soils is presented by taking into account the Mindlin equation and the equivalent thickness for soil layers in the equivalent elastic method. For lateral movement, lateral pressure, bending moment, and interaction factors, there are small differences between results obtained from the 1‐D and the 3‐D displacement methods except a very flexible pile. Copyright © 2015 John Wiley & Sons, Ltd.     

Lateral load distributions on grouped piles from dynamic pile‐to‐pile interaction factors

The load distributions of the grouped piles under lateral loads acting from one side of the pile cap could be approximately modeled using the elasticity equations with the assumptions that the underground structure is rigid enough to sustain the loads, and only small deformations of the soils are yielded. Variations of the soil–pile interactions along the depths are therefore negligible for simplicity. This paper presents the analytical modeling using the dynamic pile‐to‐pile interaction factors for 2 × 2 and 2 × 3 grouped piles. The results were found comparative with the experimental and numerical results of other studies. Similar to others' findings, it was shown that the leading pile could carry more static loads than the trailing pile does. For the piles in the perpendicular direction with the static load, the loads would distribute symmetrically with the centerline whereas the middle pile always sustains the smallest load. For steady‐state loads with operating frequencies up to 30 Hz, the pile load distributions would vary significantly with the frequencies. It is interesting to know that designing the pile foundation needs to be cautioned for steady‐state vibrations as they are a problem of machine foundation. However, for transient loads or any harmonic loads acting upon relatively higher frequencies, the pile loads could be regarded as uniformly distributed. It is hoped that the numerical results of this paper will be helpful in the design practice of pile foundation. Copyright © 2008 John Wiley & Sons, Ltd.