Effect of non-linear soil deformation on the interaction among energy piles

This study investigates the effect of non-linear soil deformation on the displacement interaction among energy piles. The work is based on interaction factor analyses of full-scale pile group tests, whose results are compared with experimental evidence. The results presented highlight the tendency of interaction factor analyses that ignore non-linear soil deformation to overestimate the interaction and the displacement of energy pile groups. This outcome, in accordance with previous studies for conventional pile groups subjected to mechanical loads, may be considered in the analysis and design of energy pile groups subjected to thermal (and mechanical) loads through the interaction factor method.     

Displacement interaction among energy piles bearing on stiff soil strata

This study presents an analysis of the displacement interaction among general configurations of energy piles bearing on stiff soil strata that are subjected to thermal loads. This work integrates recent analyses investigating the displacement interaction among predominantly floating energy piles subjected to thermal loads in deep uniform soil deposits. To address this challenge, design charts for energy piles resting on either infinitely or finitely rigid soil strata are presented, applied and validated for the analysis of the vertical displacement of predominantly end-bearing energy pile groups subjected to thermal loads using the interaction factor method.     

能量桩群桩工作特性简化分析方法研究

采用双曲线模型模拟桩土界面上的力学行为,利用剪切位移法反映剪应力在土层中的传递,考虑群桩之间的相互作用,建立了热?力耦合作用下能量桩群桩基础工作特性的简化分析方法。该方法能反映桩土界面上的非线性、桩顶的约束条件和能量桩位置的影响,可直接计算所有桩的位移和轴力。与现有方法相比,计算得到的双桩相互作用因子更加合理。通过与文献中试验数据的对比表明,若只有局部桩经历温度变化,能量桩运行过程中各桩之间存在差异变形,基础出现倾斜,桩顶荷载发生重分布。所建立方法计算方便,能合理模拟能量桩群桩基础的主要工作特性,可用于大规模能量桩群桩基础的设计计算。     

一种确定导管架平台群桩p-y数据的方法

导管架海洋平台群桩基础的桩头约束是一种弹性约束。针对具有弹性约束桩头的群桩,提出了一种利用非线性地基梁群桩模型,通过迭代计算确定导管架平台群桩p-y数据的方法。该方法首先依据单桩p-y曲线,利用具有弹性约束桩头的群桩模型,计算桩头在总荷载作用下的水平位移;再利用Poulos相互作用系数确定由于群桩相互作用引起的桩头附加水平位移,将总荷载作用下的桩头水平位移与桩头附加水平位移叠加后的结果作为迭代计算的初始桩头水平位移。然后,依据桩头荷载与初始桩头水平位移,通过对单桩p-y数据的标定,确定其修正系数Ym,进而得到与第1次计算对应的群桩p-y数据。在接下来的迭代计算中,利用每次更新后的Ym确定该次计算使用的群桩p-y数据,并据此由群桩计算模型计算桩头位移,通过对单桩p-y数据标定确定相应的Ym,直到第i次与第i-1次计算出的Ym(i)和Ym(i-1)之间相对误差小于允许误差为止。由于该方法考虑群桩效应的p-y数据,且借助具有弹性约束桩头的群桩模型进行分析,从而使计算结果能客观反映具有弹性约束桩头群桩之间的相互作用与变形特性。     

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.     

Study on interaction between dissimilar piles in layered soils

This paper, under the assumption that the pile–pile interaction showed elasticity, analyzed the pile–pile interaction between two dissimilar piles in layered soils using the shear displacement method and taking the sheltering effect into account to modify the conventional interaction factor between two dissimilar piles. The linear stiffness of single pile was adopted herein to analyze the influence of the pile stiffness factor, the pile length factor, and the diameter of shorter pile on the pile–pile interaction factor between two dissimilar piles. The interaction factor between two dissimilar piles drew from the present method was generally in good agreement with the interaction factor computed by Wong and Poulos. However, this paper intends to provide a different but more convenient means of estimating the interaction factor between piles that have dissimilar diameters, lengths and pile tip conditions, and the settlement of dissimilar piles in pile groups. Copyright © 2010 John Wiley & Sons, Ltd.     

大规模群桩基础相互作用近似解耦方法

针对传统弹性理论法过高地估计了桩-桩相互作用效应,基于杆件有限单元法建立了半无限土体中群桩基础的桩侧剪应力求解方程,通过简化桩-桩的相互作用效应,将群桩基础桩侧摩阻力的求解方程近似解耦,实现了群桩基础桩身剪应力和位移的快速求解目标。通过两桩相互作用系数以及柔性承台下群桩基础差异沉降的对比分析,验证了该简化方法的合理性。参数分析结果表明,该简化方法计算得到的相互作用系数与严格的边界积分方程法解答较为接近,稍小于Poulos弹性理论法的计算结果;柔性承台下群桩的差异沉降在桩间距较小时与经典解答较为接近,而在桩间距较大时则存在一定的差别。该简化方法大幅减少了群桩计算工作量,适用于大规模群桩基础的快速计算要求。     

Three dimensional elasto‐plastic interface for embedded beam elements with interaction surface for the analysis of lateral loading of piles

This paper presents a numerical formulation for a three dimensional elasto‐plastic interface, which can be coupled with an embedded beam element in order to model its non‐linear interaction with the surrounding solid medium. The formulation is herein implemented for lateral loading of piles but is able to represent soil‐pile interaction phenomena in a general manner for different types of loading conditions or ground movements. The interface is formulated in order to capture localized material plasticity in the soil surrounding the pile within the range of small to moderate lateral displacements. The interface is formulated following two different approaches: (i) in terms of beam degrees of freedoms; and (ii) considering the displacement field of the solid domain. Each of these alternatives has its own advantages and shortcomings, which are discussed in this paper. The paper presents a comparison of the results obtained by means of the present formulation and by other well‐established analysis methods and test results published in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

非均质地基中群桩竖向荷载沉降关系分析

运用剪切位移法计算了桩轴向荷载传递因子。对于桩端采用线性的荷载传递函数,推导了基于弹塑性模型的单桩竖向荷载沉降的解析解。分析过程中考虑了土体强度沿深度线性变化的特性和桩土间的滑移现象,因此更符合大部分土体的实际性状。在此基础上,建立了考虑桩土滑移的桩-桩相互作用系数的计算公式,并将上述方法应用于群桩的分析,获得了群桩的荷载沉降特性。该分析方法克服了目前应用较多的弹性理论方法夸大桩土相互作用的缺点,单桩和群桩的荷载沉降曲线的分析结果和实测数据吻合,证明了该方法的合理性。     

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.     

基于能量法的轴横向荷载作用下单桩受力变形分析

轴向和横向荷载作用下单桩的受力变形分析是桩基研究的重点内容之一。单桩在水平荷载作用下会产生一定的水平位移与弯矩,而此时作用轴向荷载会使得桩体出现一定的压曲与附加弯矩,以致轴横向荷载作用下的单桩受力变形与单独作用水平荷载或轴向荷载的单桩存在较大的区别。故本文基于能量法,首先分别建立轴横向荷载作用下单桩的受力变形能量方程以及桩周土体能量方程,然后考虑桩土变形协调与一定的桩土相互作用,基于最小势能原理得到单桩变形控制微分方程,并采用幂级数法进行求解,最终得到轴横向荷载作用下单桩受力变形分析的幂级数解答。通过编程计算,将本文方法计算结果与试验结果、数值分析结果、规范法计算结果进行对比分析,验证了本文方法的合理性和可行性。在此基础上,基于本文解答进行了影响参数分析,结果表明:桩体长径比、桩土弹性模量比、桩周土模量深度变化系数均对轴横向受荷单桩的桩身水平位移与最大弯矩值有一定的影响,其中桩周土模量深度变化系数以不小于0.6为宜。     

Group interaction on vertically loaded piles in saturated poroelastic soil

The pile-to-pile interaction was obtained for vertically loaded piles embedded in homogeneous poroelastic saturated soil. Deduced from Biot’s theory, the fundamental functions of the quasi-static development for the force, displacement and pore pressure were acquired in cylindrical coordinates. The pile–soil system was decomposed into extended soil and fictitious piles, and the compatibility condition was set up between the axial strain of the fictitious piles and the corresponding average strain over the extended soil. This approach results in the governing equations, which consist of the Fredholm integral equations of the second kind and the basic unknowns of the axial forces along the fictitious pile shaft. The axial force and settlement along the pile shaft were calculated based on the axial forces of the fictitious piles. The interaction between the piles was investigated under different consolidation conditions through a two-pile model, and two pile interaction factors were obtained. Stemming from the two-pile analysis, numerical analyses on the settlement of the pile groups were conducted to probe pile interaction with consolidation. The conventional solutions for the single-phase soil-pile problem seem to underestimate the interaction factor if the consolidation effect is taken into account as pile settlement continues. The pile-to-pile interaction can also aggravate the percentage of consolidation settlement (PCS), and as the pile number increases, the value of the PCS will also increase. Several key factors, such as the pile stiffness, pile slenderness ratio and pile spacing, are investigated to better understand the impact of consolidation on pile analysis.     

Centrifuge shaking table tests on 4 × 4 pile groups in liquefiable ground

A series of centrifuge shaking table model tests are conducted on 4?×?4 pile groups in liquefiable ground in this study, achieving horizontal–vertical bidirectional shaking in centrifuge tests on piles for the first time. The dynamic distribution of forces on piles within the pile groups is analysed, showing the internal piles to be subjected to greater bending moment compared with external piles, the mechanism of which is discussed. The roles of superstructure–pile inertial interaction and soil–pile kinematic interaction in the seismic response of the piles within the pile groups are investigated through cross-correlation analysis between pile bending moment, soil displacement, and structure acceleration time histories and by comparing the test results on pile groups with and without superstructures. Soil–pile kinematic interaction is shown to have a dominant effect on the seismic response of pile groups in liquefiable ground. Comparison of the pile response in two tests with and without vertical input ground motion shows that the vertical ground motion does not significantly influence the pile bending moment in liquefiable ground, as the dynamic vertical total stress increment is mainly carried by the excess pore water pressure. The influence of previous liquefaction history during a sequence of seismic events is also analysed, suggesting that liquefaction history could in certain cases lead to an increase in liquefaction susceptibility of sand and also an increase in dynamic forces on the piles.     

液化场地桩-土-桥梁结构地震相互作用简化分析方法

液化场地桩-土-桥梁结构地震相互作用分析属于桩基桥梁抗震设计中的一个关键科学问题,而目前尚缺乏合理的简化分析方法。鉴于此,直接针对振动台试验,基于Penzien模型,建立了液化场地桩-土-桥梁结构地震相互作用的数值分析模型与相应的简化分析方法。通过振动台试验验证了数值建模途径与简化计算分析方法的正确性,可用于液化场地桩基桥梁结构地震反应的分析,并且特别考虑砂层中孔压升高引起的砂土承载力衰减效应,推荐了计算参数的合理选取方法;据此进行了桩径、桩土初始模量比、砂土内摩擦角、上部桥梁结构质量等重要参数对液化场地桩-土地震相互作用影响的敏感性分析。研究表明：在液化场地条件下,随桩径和桩土初始模量比的增大,桩的峰值加速度、峰值位移减小,而桩的峰值弯矩则增大;随砂土内摩擦角增大,桩的峰值加速度、峰值弯矩、峰值应力均增大,而桩的峰值位移则减小;随上部结构配重增大,桩的峰值位移、峰值弯矩均增大。     

深厚软土中抗滑桩的修正悬臂桩计算方法

大面积堆填或开挖时深厚软土地层内部常产生较大滑移,这为该类地层中考虑桩土作用的抗滑桩分析带来较大困难。考虑深厚软土的滑移性状,针对既有悬臂桩法计算存在的问题进行修正,滑动面上部桩身受荷段的桩身荷载采用等腰三角形分布且极值点为极限侧土压力,设滑动面下部桩身锚固段上侧桩周软土为理想弹塑性以考虑软土大位移条件,下侧为弹性状态,并通过位移叠加原理对传统方法求解产生滑动面不连续的缺陷进行修正。通过现场桩侧堆载试验验证,修正悬臂桩法的弯矩和位移计算结果较好,桩顶位移误差小于3%,桩身最大弯矩误差小于10%。所提方法有助于深厚软土地层抗滑桩的设计和计算。     

On the response prediction of horizontally loaded fixed-head pile groups in sands

The aim of this paper is to investigate the behavior of laterally loaded pile groups in sands with a rigid head and correlate the response of a pile group it to that of a single pile. For this purpose, a computationally intensive study using 3-D nonlinear numerical analysis was carried out for different pile group arrangements in sandy soils. The responses of the pile groups were compared to that of the single pile and the variation of the displacement amplification factor R_a was then quantified. The influence of the number of piles, the spacing, and the deflection level on the group response is discussed. A relationship for predicting the response of a pile group, based on its configuration and the response of a single pile, has been formulated allowing also for soil shear strength which was found to affect the group response. The relationship provides a reasonable prediction for various group configurations in sandy soils.     

考虑桩-土-结构相互作用的桥梁桩基地震反应有限元分析

地震荷载作用下桩-土-结构相互作用问题在桥梁抗震研究中越来越受到重视。本文结合工程实例,利用有限元仿真软件ADINA,建立桩-土-结构相互作用的有限元实体分析模型。选取三种时程波作为地震荷载,对在地震作用下桩-土-结构相互作用对桩的沉降位移,桩侧摩阻力和有效应力的影响进行了分析研究,对桩基设计提出了较为合理的建议。     

Uncoupled analysis of stabilizing piles in weathered slopes

This paper describes a simplified numerical approach for analyzing the slope/pile system subjected to lateral soil movements. The lateral one-row pile response above and below the critical surface is computed by using load transfer approach. The response of groups was analyzed by developing interaction factors obtained from a three-dimensional nonlinear finite element study. An uncoupled analysis was performed for stabilizing piles in slope in which the pile response and slope stability are considered separately. The non-linear characteristics of the soil–pile interaction in the stabilizing piles are modeled by hyperbolic load transfer curves. The Bishop's simplified method of slope stability analysis is extended to incorporate the soil-pile interaction and evaluate the safety factor of the reinforced slope. Numerical study is performed to illustrate the major influencing parameters on the pile-slope stability problem. Through comparative studies, it has been found that the factor of safety in slope is much more conservative for an uncoupled analysis than for a coupled analysis based on three-dimensional finite element analysis.     

A Winkler model approach for vertically and laterally loaded piles in nonhomogeneous soil

An investigation is made to present analytical solutions provided by a Winkler model approach for the analysis of single piles and pile groups subjected to vertical and lateral loads in nonhomogeneous soils. The load transfer parameter of a single pile in nonhomogeneous soils is derived from the displacement influence factor obtained from Mindlin's solution for an elastic continuum analysis, without using the conventional form of the load transfer parameter adopting the maximum radius of the influence of the pile proposed by Randolph and Wroth. The modulus of the subgrade reaction along the pile in nonhomogeneous soils is expressed by using the displacement influence factor related to Mindlin's equation for an elastic continuum analysis to combine the elastic continuum approach with the subgrade reaction approach. The relationship between settlement and vertical load for a single pile in nonhomogeneous soils is obtained by using the recurrence equation for each layer. Using the modulus of the subgrade reaction represented by the displacement influence factor related to Mindlin's solution for the lateral load, the relationship between horizontal displacement, rotation, moment, and shear force for a single pile subjected to lateral loads in nonhomogeneous soils is available in the form of the recurrence equation. The comparison of the results calculated by the present method for single piles and pile groups in nonhomogeneous soils has shown good agreement with those obtained from the more rigorous finite element and boundary element methods. It is found that the present procedure gives a good prediction on the behavior of piles in nonhomogeneous soils. Copyright © 2011 John Wiley & Sons, Ltd.     

Computerised processing of ground investigation data and use in predicting the load-settlement behaviour of piled foundations

A new computer program “PILESET” is developed for use in predicting the bearing capacity and load-settlement behaviour of axially loaded single piles. The program can analyse almost any soil profile and accommodates (a) displacement piles (b) replacement (c) friction piles, (d) end-bearing piles, (e) under-reamed piles and (f) partially sleeved piles. A variety of soil input data can be used, including: (i) standard penetration tests, (ii) cone/piezo-cone tests, (iii) pressure-meter tests and (iv) laboratory tests. The above data types can be combined, if desired, for pile analysis by PILESET. The program calculates the shaft and base capacities of a pile based on 23 methods published in design guides in over 10 European countries. PILESET also predicts the pile load-settlement curve using five published methods, which include two modified load transfer (t-z) approaches formulated by the author. To demonstrate the capabilities of the program, analysis is carried out for case study involving seven full-scale screw piles formed in sand and tested to failure. In each case, the load-settlement curve computed using the author’s modified method in PILESET is found to be in excellent agreement with the actual pile test results.