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.     

Development of a coupled pile-to-pile interaction model for the dynamic analysis of pile groups subjected to vertical loads

Acta Geotechnica - This paper presents a new analytical model for calculating the dynamic performance of pile groups subjected to vertical loads. The derived solution allows considering the robust...     

Approximate computer analysis of pile groups subjected to loads and ground movements

This paper describes the development of an approximate approach for the analysis and design of piles subjected to axial and lateral loading and also to vertical and horizontal ground movements. The analysis involves a number of simplifications in order to make it feasible to implement. For example, it considers the behaviour of a ‘representative’ pile in a group to characterize the behaviour of all piles in the group, and adopts approximations to derive free-field interaction factors from the conventional interaction factors for direct loading. The analysis has been implemented via a computer program called EMbankment PIle Group (EMPIG) and has the ability to incorporate the following features:

• 1. single piles or pile groups,
• 2. applied vertical, lateral and moment loading on the pile cap,
• 3. the effects of axial and lateral soil movements caused by embankment construction,
• 4. a layered soil profile,
• 5. non-linear axial and lateral response of the piles.

Comparisons between solutions from EMPIG and other independent programs suggest that it is capable of providing results of adequate accuracy for practical design purposes. The analysis has been used to investigate the effects of pile rake on a typical bridge abutment group. The presence of raked piles can have a detrimental effect on group behaviour, especially in the presence of ground movements. Large lateral deflections can be generated and axial forces and moments in the piles are increased. Comparisons are also made with the results of centrifuge model tests on abutment pile groups. Copyright © 1999 John Wiley & Sons, Ltd.     

A new dynamic interaction factor for the analysis of pile groups subjected to vertical dynamic loads

Τhis paper presents an analytical method for calculating the steady-state impedance factors of pile groups of arbitrary configuration subjected to harmonic vertical loads. The derived solution allows considering the effect of the actual pile geometry on the contribution of pile-soil-pile interaction to the response of the group, via the introduction of a new dynamic interaction factor, defined on the basis of soil resistance instead of pile displacements. The solution is first validated against a published solution for single piles that accounts for the effect of pile geometry on the generated ground vibrations. Accordingly, we show that the derived soil attenuation factor agrees well with existing solutions for pile groups in the high frequency range, but considerable differences are observed in both the stiffness and damping components of the computed impedance when the relative spacing between piles decreases. Numerical results obtained for typical problem parameters suggest that ignoring pile geometry effects while estimating the contribution of pile-soil-pile interaction in the response may lead to inaccurate results, even for relative large pile group spacings.

     

群桩扭转非线性模型

建立了一个非线性数学模型来分析群桩扭转问题。该模型利用非线性荷载传递曲线来模拟桩的非线性响应,采用Mindlin解计算各桩水平力间的相互作用,用Randolph解析解分析得到各桩间扭矩对水平力的影响。在各单桩中引入经验性的耦合系数,分析桩身水平变形引起的土体反力对该桩扭转承载力的影响。对比计算结果与离心机模型试验数据,表明该模型能够模拟群桩扭转中主要的桩-土-桩相互作用和荷载耦合作用,较好地反映了实际情况。     

分层土中群桩水平动力阻抗的改进计算

采用动力Winkler地基梁模型,建立了主动桩和被动桩的简化解析运动方程,考虑地基土的分层特性、桩身剪切变形和转动惯量,提出了计算分层地基中单桩和群桩动力阻抗的改进计算方法,并与已有文献的计算结果进行了对比,结果表明：改进方法的计算结果与现场实测更接近。在低频段,改进方法的计算结果与已有文献结果较一致,但随着桩身剪切模量的减小,两者差异增大。差异主要是由考虑桩身剪切变形和转动惯量引起的,且前者影响较大,在低频段差异亦十分明显,而后者影响较小,在群桩阻抗峰值区域和高频段差异明显,需考虑桩身转动惯量的影响。     

层状地基中群桩水平振动

在考虑地基土分层的基础上,采用动力Winkler地基模型模拟桩土相互作用并运用传递矩阵,求解层状地基中的单桩和群桩的阻抗函数.在计算动力相互作用因子时考虑了被动桩与土的相互作用.最后将相互作用因子和群桩阻抗的本文解与精确解进行对比,验证了本文方法的有效性.     

Estimation of fundamental period for structures supported on pile foundations

One of the significant effects of considering soil-structure interaction in the analysis of structures is the increase in the fundamental natural period compared to the fundamental natural period of a similar structure, fixed at the base. Applied Technology Council (ATC) originally set forth some provisions to calculate the fundamental natural period of flexible based structures using the period of a similar structure, fixed at the base, and lateral and rocking stiffness coefficients of the foundation. These provisions became the basis of current soil-structure interaction recommendations in several building codes. The fundamental natural periods of structures founded on different types of foundations computed using recommendations of the ATC are compared with those computed using a simplified model to perform soil-structure interaction of shear-type structures. Results show that the provisions given in ATC may be used for structures supported on shallow footings but may not be applicable for structures supported on pile foundations or foundations having the ratio of lateral to rotational stiffness coefficients different from those of shallow foundations. An equation, similar to the equation recommended by ATC, is presented to estimate the fundamental natural period of structures supported on pile foundations. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analysis of creep settlement of pile groups in linear viscoelastic soil

This paper presents the analysis of creep settlement of pile groups for line pile groups, square pile groups, and rectangular pile groups undergoing creep settlements over a period of time. The soil is treated as a viscoelastic material and is modeled using a three-parameter viscoelastic model. The damping component (dashpot) takes care of the permanent time-dependent deformations in three-parameter viscoelastic model. An approach suggested by Mindlin has been employed to calculate the stress distribution along the pile length in a group. The viscoelastic problem is converted into an elastic problem by the application of Laplace transform. Results in the form of variation of interaction factors for parameters such as pile length to diameter ratio, pile spacing, Poisson's ratio, and modulus ratio have been presented. Comparison has been made between interaction factors for piles groups undergoing immediate settlements and creep settlements. Finally, a typical predictive example has been presented for a 3 × 3 pile group showing creep settlement. The load rearrangement due to creep settlements causes about 5% to 35% increase in base resistance over time. Interaction factors for pile groups (2 × 1, 3 × 1, 2 × 2, and 3 × 2) undergoing creep settlement is about 15% to 55% higher than the interaction factors considering only the immediate settlements for pile group spacing less than or equal to 5d.     

基于矢量匹配-劳斯法的群桩阻抗改进模型

采用薄层法算出群桩基础的频域阻抗,将群桩阻抗等效于一个单输入单输出系统,并表示为一个复数的频域传递函数。基于矢量匹配法（VF法）,通过对传递函数拟合得到任意分层地基的群桩阻抗函数的集总参数形式。采用VF法对整体频域拟合,可以得到多项分式分式阻抗形式,进而扩展成为Wu-Lee模型。结果表明,VF法拟合得到的动力柔度函数可以精确地匹配分层地基动力柔度函数,由于多项分式的形式可以直接扩展成为Wu-Lee集总参数模型,且数值稳定。对于高频阻抗拟合需要采用高阶数,进行劳斯（Routh）降阶,得到较好的效果。     

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。     

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。     

竖向荷载下群桩-土-承台相互作用数值分析

在大桩径、小桩距的群桩条件下,不仅有来自桩侧、桩端和承台传递的多重应力叠加,还有群桩对桩间土的夹持作用影响,桩-土-承台之间作用更加复杂。用有限差分软件模拟固定桩距、桩径,变化竖向荷载下桩-土-承台的相互作用。从各层土的侧摩阻力、不同位置桩的桩顶荷载、荷载-沉降关系、桩间土体位移等方面的计算结果分析桩-土-承台之间的相互影响。结果表明,荷载超出117.8 MN（略大于Pu/2,Pu为群桩极限承载力）后,群桩对上部桩间土的夹持作用开始减小,桩侧上部侧摩阻力增大;桩侧下部侧摩阻力在多重应力叠加作用下呈减小趋势,不同位置的桩侧摩阻力影响范围有差异;用群桩沉降达到5%倍桩径时的荷载作为群桩的竖向极限承载力是可取的;当沉降与桩径的比值超出1%后,承台分担荷载的比例逐渐增大,群桩分担荷载的比例减小。     

地面超载条件下土体侧移模式及对邻近桩基影响分析

建立了三维数值模型,进行堆载-弹塑性地基-桩基共同作用有限元数值分析。在地面超载条件下,对自由场土体的侧向位移模式进行了探讨,得出了土体侧向变形规律。在此基础上,对堆载作用下邻近桩基的力学性状进行了分析,包括不同堆载大小、不同堆载距离和不同桩间距等情况下桩基的侧向变形和弯矩的变化规律。分析结果表明：随着堆载的增加,桩基的变形和弯矩都有显著的增长,桩基逐渐弯曲。在同样条件下,增加桩的刚度,桩身弯矩迅速减小,桩身刚度很大时,会发生整体侧移。桩间距和堆载距离对桩身弯矩和变形有重要影响,随着桩间距和堆载距离的增大,桩身的变形和弯矩都将减小。     

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。     

On the influence of vertical loads on the lateral response of pile foundation

The influence of vertical loads on the lateral response of group piles installed in sandy soil and connected together by a concrete cap is studied through finite elements analyses. The analyses focus on the five piles in the middle row of 3 × 5 pile groups. The vertical load is applied by enforcing a vertical displacement equivalent to 2% of the pile diameter through the pile cap prior to the application of the lateral loads. The results have shown that the lateral resistance of the leading pile (pile 1) does not appear to vary considerably with the vertical load. However, the vertical load leads to 23%, 36%, 64%, and 82% increase in the lateral resistance of piles 2–5, respectively. The increase in the lateral pressures in the sand deposit is the major driving factor to contribute the change in the lateral resistance of piles, depending on the position of the pile in the group. The distribution of lateral loads among piles in the group tends to be more uniform when vertical loads were considered leading to a more economical pile foundation design.     

基于尖点突变理论的端承桩竖向承载力分析

国内外关于单桩竖向极限承载力的确定方法很多,但至今还未找到较为完善、科学和经济的方法求解桩的极限承载力的方法,因此尝试将尖点突变理论引入单桩竖向极限承载力的计算中,并与静载荷试验和抛物线法相结合,推导出端承桩单桩竖向极限承载力的计算公式。实例验证表明,当桩的位移值较小时,计算值接近实测值;当桩的位移值较大时,计算值与实测值偏离较大。结论可运用于实践。     

水平和竖向地震作用下液化场地群桩基础动力响应试验研究

为研究水平和竖向(双向)耦合地震作用下液化场地群桩基础的动力响应,设计了可液化地基-群桩基础-框筒结构动力相互作用体系振动台模型试验。选取不同类型模拟地震波作为振动台试验激励,通过对比水平地震作用和双向耦合地震作用下土体加速度、超孔隙水压力和群桩应变等试验结果,进而分析双向耦合地震作用对可液化地基和群桩基础动力响应的影响。研究结果表明:双向耦合地震作用下,液化场地土体竖向加速度峰值随土体埋深高度的减小而逐渐增大;饱和砂土的液化效应与双向耦合地震作用和输入地震波的类型有关;相比水平地震作用,不同种类波双向耦合地震作用下群桩基础桩身中部和底部的应变峰值增大,桩顶应变峰值变化略有不同;双向耦合地震作用加剧了建筑结构群桩体系的摇摆和倾斜。研究结果对可液化地基上群桩基础的抗震设计和防灾减灾具有十分重要的研究意义。     

基坑开挖时邻近桩基性状的数值分析

基坑开挖时尤为关注的问题是土体侧向移动对邻近桩基的不利影响,土体的侧向移动使邻近桩基产生侧向位移和附加应力及弯矩,甚至可能使上部建筑物功能失效。采用土工有限元软件Plaxis 8.2对内支撑排桩支护基坑开挖过程进行数值模拟,分析了基坑开挖时对邻近桩基的各种影响因素,包括单排桩、双排桩在不同开挖深度、支护桩的刚度、桩基刚度、桩基距基坑开挖面距离、桩身的约束和桩长条件下桩身水平位移和弯矩的变化特性。     

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.