Numerical analysis of soil plug behaviour inside open-ended piles during driving

The plugging mechanism of infinitely-long open-ended piles is examined using numerical simulation of the wave propagation inside the soil plug and pile. It is shown that the key parameters for the plugging mechanism are the pile radius, the shape of the impact load, the shear wave velocity of the soil inside the pile, and the friction at the pile–soil interface. Consequently, the tendency of the pile to plug during driving can be assessed prior to the driving process by consideration of these key parameters. Existing one-dimensional models for the shaft response of open-ended piles are discussed and an improved model is presented. The differences between using one-dimensional models and finite element models to simulate the plugging process are examined. The differences are found to vary with the key parameters. Pile-in-pile and lumped-mass one-dimensional models are found to give satisfactory performance for some parameter combinations, while for others an axisymmetric finite element model must be used. © 1998 John Wiley & Sons, Ltd.     

Study on low‐strain integrity testing of pipe‐pile using the elastodynamic finite integration technique

This study focuses on the three‐dimensional (3‐D) characteristics of wave propagation in pipe‐pile using elastodynamic finite integration technique. First, a real 3‐D pile‐soil model in cylindrical coordinate system is presented. Then, the governing equations are established. With the boundary and initial conditions, the numerical solution is obtained. The accuracy and feasibility of the self‐written code are further verified via comparing with the measured data. Velocity histories at different angles of pile top and pile tip are illustrated, and the snapshots reflecting the 3‐D characteristics of wave propagation are given. It shows that the interferences of Rayleigh waves can confuse the result interpretation for pile integrity testing. The increase of hammer contact time can effectively mitigate the interferences, and the interferences of Rayleigh waves are weakest at an angle of 90° from where hammer hits. Besides, surrounding soil can partly mitigate the wave interferences. Copyright © 2012 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.     

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.     

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.     

Semi‐analytical far field model for three‐dimensional finite‐element analysis

A challenging computational problem arises when a discrete structure (e.g. foundation) interacts with an unbounded medium (e.g. deep soil deposit), particularly if general loading conditions and non‐linear material behaviour is assumed. In this paper, a novel method for dealing with such a problem is formulated by combining conventional three‐dimensional finite‐elements with the recently developed scaled boundary finite‐element method. The scaled boundary finite‐element method is a semi‐analytical technique based on finite‐elements that obtains a symmetric stiffness matrix with respect to degrees of freedom on a discretized boundary. The method is particularly well suited to modelling unbounded domains as analytical solutions are found in a radial co‐ordinate direction, but, unlike the boundary‐element method, no complex fundamental solution is required. A technique for coupling the stiffness matrix of bounded three‐dimensional finite‐element domain with the stiffness matrix of the unbounded scaled boundary finite‐element domain, which uses a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co‐ordinate system, is described. The accuracy and computational efficiency of the new formulation is demonstrated through the linear elastic analysis of rigid circular and square footings. Copyright © 2004 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.     

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.     

An analytical solution for wave propagation in a square pile due to transient point load

This paper presents an analytical solution for wave propagation in a square pile due to transient point load. The differential equation of dynamic equilibrium is established considering propagation of waves in both vertical and transverse directions. The soil resistance is simulated by Voigt model. The three-dimensional analytical solution is deduced by using Fourier transform and the separation of variable method. The arithmetical results of the proposed solution show that the velocity responses along the radial direction at the pile top are highly non-uniform. In addition, Young’s modulus and the pile side length exert undisputable influences on the velocity 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.     

砂土中开口管桩沉桩过程的颗粒流模拟研究

基于颗粒流理论,采用PFC2D程序,模拟再现不同型号开口管桩在沉桩过程中土塞的形成演化规律、土颗粒细观结构变化以及桩周土应力场分布情况,并通过分析土体细观变化模式揭示沉桩过程中宏观力学响应的内在机制。计算结果表明,管桩直径对土塞效应影响很大,外径为30 mm的开口管桩,沉桩过程中土塞增量填充率（IFR）值较小,土塞效应明显,土塞高度小,类似闭口桩;随着管桩直径的增大,土塞效应迅速减小,大直径管桩在砂土中沉桩全部闭塞的可能性很小。细观因素（孔隙率和滑动比例）与土体宏观位移表现之间存在着明显的相互对应关系,并依此将桩周土划分3个区域。桩周土体水平应力、竖向应力和剪应力都在桩底附近形成“应力核”,不同型号管桩桩周土应力场分布相近。     

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.     

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 simplified analysis method for piled raft foundations in non‐homogeneous soils

A simplified method of numerical analysis based on elasticity theory has been developed for the analysis of axially and laterally loaded piled raft foundations embedded in non‐homogeneous soils and incorporated into a computer program “PRAB”. In this method, a hybrid model is employed in which the flexible raft is modelled as thin plates and the piles as elastic beams and the soil is treated as springs. The interactions between structural members, pile–soil–pile, pile–soil–raft and raft–soil–raft interactions, are approximated based on Mindlin's solutions for both vertical and lateral forces with consideration of non‐homogeneous soils. The validity of the proposed method is verified through comparisons with some published solutions for single piles, pile groups and capped pile groups in non‐homogeneous soils. Thereafter, the solutions from this approach for the analysis of axially and laterally loaded 4‐pile pile groups and 4‐pile piled rafts embedded in finite homogeneous and non‐homogeneous soil layers are compared with those from three‐dimensional finite element analysis. Good agreement between the present approach and the more rigorous finite element approach is demonstrated. Copyright © 2002 John Wiley & Sons, Ltd.     

Finite element consolidation analysis of soils with vertical drain

This paper presents a finite element procedure for the analysis of consolidation of layered soils with vertical drain using general one‐dimensional (1‐D) constitutive models. In formulating the finite element procedure, a Newton–Cotes‐type integration formula is used to avoid the unsymmetry of the stiffness matrix for a Newton (Modified Newton) iteration scheme. The proposed procedure is then applied for the consolidation analysis of a number of typical problems using both linear and non‐linear soil models. Results from this simplified method are compared with those from a fully coupled consolidation analysis using a well‐known finite element package. The average degree of consolidation, excess porewater pressure and average vertical effective stress are almost the same as those from the fully coupled analysis for both the linear and non‐linear cases studied. The differences in vertical effective stresses are tolerable except for the values near the vertical drain boundaries. The consolidation behaviour of soils below a certain depth of the bottom of vertical drain is actually one‐dimensional for the partially penetrating case. Therefore, there are not much differences in whether one uses a one‐dimensional model or a three‐dimensional model in this region. The average degree of consolidation has good normalized feature with respect to the ratio of well radius to external drainage boundary for the cases of fully penetrating vertical drain using a normalized time even in the non‐linear case. Numerical results clearly demonstrate that the proposed simplified finite element procedure is efficient for the consolidation analysis of soils with vertical drain and it has better numerical stability characteristics. This simplified method can easily account for layered systems, time‐dependent loading, well‐resistance, smear effects and inelastic stress–strain behaviour. This method is also very suitable for the design of vertical drain, since it greatly reduces the unknown variables in the calculation and the 1‐D soil model parameters can be more easily determined. Copyright © 2000 John Wiley & Sons, Ltd.     

Numerical Simulation of 3D Borehole‐to‐Surface Electrical Method

The anomaly response characteristics of the vertical line‐source 3D borehole‐to‐surface model are simulated by an adaptive finite element method. The calculation shows that the anomaly in the radial direction is pressed and the closer to the source, the more pronounced, the anomaly is stretched in the direction perpendicular to the radius. Adding a B pole in the Y direction can offset the effect of stretching to some extent. The anomaly that is closer to the source of the profile is clearer than the anomaly that is far from the source. The research results are of great significance for guiding the practical application of the borehole‐to‐surface electrical method.     

Skin friction features of drilled CIP piles in sand from pile segment analysis

Numerical pile segment analysis is conducted in this study with an advanced soil model to investigate the skin friction behaviour of a drilled Cast‐In‐Place (CIP) pile installed in sand. Although the interface between the sand and pile is considered rough, thin elements adjacent to the pile are used to include effects of localized shear. Unit weights of fluid concrete and accompanied changes in stress are considered as the effects of pile installation. Changes in effective stresses are the most prominent effect due to pile installation with a change in direction of the major principal stress from the vertical to the radial direction. Shear behaviour of the sand at the interface during the early shear stage is related to the contractive tendency of the sand at small strain levels. Changes in the stress field around the pile with little changes in volumetric strain take place during the early shear stage. Stress redistributions during the early shear stage depend on the direction of the major principal stress before shear. Results of the pile segment analyses for drilled CIP piles show good agreement with design methods. Parametric studies are used to characterize the effects of sand density and pile diameter on the skin friction behaviour of drilled CIP piles. Copyright © 2007 John Wiley & Sons, Ltd.     

Rigid cylinder in a transversely isotropic half‐space under lateral loads

A boundary integral equation method is presented for a rigid cylindrical pipe‐pile of finite length embedded in a transversely isotropic half‐space under lateral loads. In the framework of three‐dimensional elastostatics, the complicated soil‐structure interaction problem is shown to be reducible to three coupled Fredholm integral equations. Through an analysis of the associated Cauchy singular kernels, the intrinsic singular characteristics of the radial, angular, and vertical interfacial load transfers are rendered explicit. By means of a complicated numerical procedure, detailed results on the three‐dimensional load–transfer process are provided for benchmark comparison and practical applications. Copyright © 2011 John Wiley & Sons, Ltd.     

现浇混凝土薄壁管桩内摩阻力的数值分析

现浇混凝土薄壁管桩(简称PCC桩)技术是河海大学自主开发研制的用于地基加固处理的新技术,它是一种适合于软土地区的新型高效优质桩型.在全面介绍了PCC桩非线性有限元分析模型的建立过程后,对PCC桩的内摩阻力进行了计算分析.分析结果表明,土塞底部的水平应力在荷载作用过程中有较大的提高,相应位置的内摩阻力达到极限值,内摩阻力沿土塞呈指数曲线分布.同时,对内摩阻力分布规律的主要因素影响也进行了分析,给出了相应的简化计算公式.     

黏土中静压管桩土塞机制研究

针对黏土中管桩土塞形成机制,利用耦合欧拉拉格朗日（CEL）法模拟钢管桩的大变形沉贯过程。在验证网格密度参数对数值计算精度影响的基础上,结合管桩内外土体速度场、应力场、土塞高度和增量充填比的变化分析了土塞演变和土塞形成机制,讨论了摩擦系数以及软硬土夹层对土塞形成的影响,并与离心机试验和理论计算数据验证。结果表明,管桩贯入过程土塞的演变可分为上涌期、过渡期和下滑期3个阶段。随着桩的贯入,桩端下轴线处形成连续的下凹塑性拱,当此处竖向应力增量达到7～8倍不排水抗剪强度时土塞初步形成。同时土塞效应随着桩-土间摩擦系数增大,桩径减小（壁厚相同）而增强;软硬夹层对土塞效应影响显著,上硬下软的土层易形成完全土塞,而上软下硬的土层,硬土挤入管桩不会形成土塞。