A simplified analysis method for piled raft and pile group foundations with batter piles

A simplified method of numerical analysis has been developed to estimate the deformation and load distribution of piled raft foundations subjected to vertical, lateral, and moment loads, using a hybrid model in which the flexible raft is modelled as thin plates and the piles as elastic beams and the soil is treated as springs. Both the vertical and lateral resistances of the piles as well as the raft base are incorporated into the model. Pile–soil–pile, pile–soil–raft and raft–soil–raft interactions are taken into account based on Mindlin's solutions for both vertical and lateral forces. The validity of the proposed method is verified through comparisons with several existing methods for single piles, pile groups and piled rafts. Workable design charts are given for the estimation of the lateral displacement and the load distribution of piled rafts from the stiffnesses of the raft alone and the pile group alone. Additionally, parametric studies were carried out concerning batter pile foundations. It was found that the use of batter piles can efficiently improve the deformation characteristics of pile foundations subjected to lateral loads. Copyright © 2002 John Wiley & Sons, Ltd.     

Vertical loads effect on the lateral pile group resistance in sand

Vertical loads effect on the lateral response of a 3×5 pile group embedded in sand is studied through a two-dimensional finite element analysis. The soil-pile interaction in three-dimensional type is idealized in the two-dimensional analysis using soil-pile interaction springs with a hysteretic nonlinear load displacement relationship. Vertical loads inducing a vertical pile head displacement of 0.1-pile diameter increase the lateral resistance of the single pile at a 60 mm lateral deflection by 8%. Vertical loads inducing the same vertical displacement applied to a pile group spaced at 3.92-pile diameter increase the overall lateral resistance by 9%. The effect on individual piles, however, depends on the pile position. The vertical load decreases the lateral resistance of the leading pile (pile 1) by 10% and increases the lateral resistances of piles 2, 3, 4, and 5 by 9%, 14%, 17%, and 35%, respectively. Vertical loads applied to the pile group increase the confining pressures in the sand deposit confined by the piles but the rate of increase in those outside the group is relatively small, resulting in the difference in a balance of lateral soil pressures acting at the back of and in front of the individual pile.     

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.     

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.     

Response of Pile Groups Driven in Sand Subjected to Combined Loads

Although the loads applied on piles are usually a combination of both vertical and lateral loads, very limited experimental research has been done on the response of pile groups subjected to combined loads. Due to pile–soil–pile interaction in pile groups, the response of a pile group may differ substantially from that of a single pile. This difference depends on soil state and pile spacing. This paper presents results of experiments designed to investigate pile interaction effects on the response of pile groups subjected to both axial and lateral loads. The experiments were load tests performed on model pile groups (2 × 2 pile groups) in calibration chamber sand samples. The model piles were driven into the sand samples prepared with different relative densities using a sand pluviator. The combined load tests were performed on the model pile groups subjected to different axial load levels, i.e., 0 (pure lateral loading), 25, 50, and 75% of the ultimate axial load capacity of the pile groups, defined as the load corresponding to a settlement of 10% of the model pile diameter. The combined load test results showed that the bending moment and lateral deflection at the head of the piles increased substantially for tests performed in the presence of axial loads, suggesting that the presence of axial loads on groups of piles driven in sand is detrimental to their lateral capacity.     

水平荷载下导管架平台桩基础的非线性有限元分析

导管架平台桩基础的控制荷载主要为风荷载、波浪荷载、地震荷载等水平荷载,为研究水平荷载下导管架平台桩基础的承载特性,采用非线性有限元分析方法对水平荷载下桩-土之间的相互作用进行研究,提出了有效模拟桩基水平承载特性的有限元模型,分析了模型桩的刚度、直径、土质参数中水平土压力系数、剪胀角对桩基承载特性的影响及水平荷载下群桩承载特性,并将有限元计算结果与API规范及模型试验结果进行对比。研究结果表明,非线性有限元分析方法分析水平荷载下桩-土相互作用是可行的,计算结果可为导管架平台的桩基设计提供参考。     

TECHNICAL NOTE. Model study of H-piles subjected to combined loading

A series of model tests on H-piles subject to lateral and vertical loading have been performed so that the experimental data could be used to calibrate a finite element programme. Experiments on model H-piles in dry silca sand were performed to determine the influence of lateral displacements on the vertical load-carrying capacity of the piles. The results from the nonlinear finite element computer program were compared to the experimental results and were found to be conservative. The experimental results showed greater pile capacities and lower bending moments than were predicted by the finite element program.     

钙质砂地基单桩承载特性模型试验研究

根据实际工程中单桩受力特点,对足尺桩基进行等比例缩尺,考虑不同埋深、砂土颗粒级配等影响因素,开展室内小尺寸模型单桩的竖向拉拔、水平推移和竖向压载试验,分析桩身变位、变形、轴力等参数与桩基埋深、桩周砂土特性等因素的相互关系,探究钙质砂地基中单桩在不同受力方向下的承载性状,进而剖析钙质砂中桩-土相互作用机制。研究表明,钙质砂地基中,单桩变位、变形特点随着受力方向、埋深、桩周砂土特性等的变化存在明显差异;增大桩的埋深对竖向抗拔桩的意义大过竖向抗压桩;相同条件下桩在承受竖向抗压荷载时,增大埋深的作用主要体现在加载初期,随着荷载的逐渐增大,最终差别将逐渐减小;竖向抗压桩承载过程由以侧摩阻力承载为主发展为以桩端阻力承载为主;颗粒破碎和重分布会引起抗拔桩εmax在加载后期出现衰减;宽级配钙质砂中桩的抗拔能力较强,而单一粒组的钙质砂则在维持桩身稳定方面占优势;桩侧剪碎时的桩侧阻力衰减是随着颗粒破碎逐渐发生的,而桩端压碎时的桩侧阻力衰减主要发生在砂土被压碎瞬间。研究结果对钙质砂地基中的不同功能桩基的优化、设计和施工具有重要指导价值。     

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.     

Buckling loads of fully embedded vertical piles

Determination of critical buckling loads of columns in a medium which offers resistance to lateral deflections depend on:

• (a) Length of the pile, L.
• (b) Flexural stiffness of the pile, EI.
• (c) Stiffness of the soil, K, and
• (d) Boundary conditions of the pile, both at the top and the tip.

In this paper, solutions for buckling loads have been obtained in closed form by energy methods for fully embedded vertical piles for boundary conditions, pinned top-pinned tip, fixed top-fixed tip, and a linear variation of soil stiffness. The effects of pile length, soil stiffness, and boundary conditions on buckling loads and mode of buckling have been studied for pile lengths up to 24 m with EI of 477 tm², K₀ [A] from 0 to 2000 t/m² and N_h [B] from 0 to 2000 t/m³.     

Nonlinear three-dimensional analysis of pile group supported columns considering pile cap flexibility

A numerical method that takes into account the coupling between the rigidities of the piles, the cap, and the column has been developed for analyzing the response of pile group supported columns. Special attention is given to consideration of pile cap flexibility. A load transfer approach using t–z/q–z and p–y curves is used for the analysis of single piles. The finite element technique is used to combine the pile stiffness with the stiffness of the cap and column. The numerical method developed has been verified by comparing the results with other numerical methods for pile groups. Through comparative studies, it has been found that the maximum load on the individual piles in a group is highly influenced by pile cap flexibility. The prediction of the lateral loads and bending moments in the pile cap is much more conservative in the present analysis than in FBPier 3.0 and shows a definitely larger lateral load and bending moment for various cap thicknesses.     

高速铁路超长桥桩承载特性试验研究

超长桩广泛已应用于土木工程各个领域,但黄土地区超长桩的承载性状和变形特性尚不十分清楚,需要进一步研究。通过对郑西铁路客运专线某特大桥的4根超长桩现场测试项目的资料分析,得出了超长桩桩身轴力及侧阻力的变化规律,对超长桩的承载特性有了更为清晰的了解。试验结果表明,在桩顶竖向荷载作用下,桩身轴力随荷载的增加发生了局部调整,砂性土层的桩侧摩阻力具有增强效应,黏性土层的桩侧摩阻力具有退化效应;单桩竖向刚度随桩顶荷载的增加而减小,单桩竖向刚度降低40 %～70 %。     

竖向力与水平向力同时作用下管桩的性状研究

用解析方法研究了管桩在轴向力和水平向力（倾斜力）联合作用下的受力及变形性状。在高层建筑、桥梁工程、海洋工程、新型海堤护岸等工程中桩基自由长度上作用土压力、风荷载、波浪荷载等荷载型式,基桩经常在竖向、水平向荷载同时作用下工作。国内外学者通过大量试验和理论研究得出了计算竖向、水平向荷载下基桩内力和挠度的半经验公式以及张氏法公式。为了分析竖向、水平向荷载同时作用下自由荷载的作用,在现行m法假设的基础上,从弹性桩的挠曲微分方程出发,导出了任意自由荷载作用下桩任意截面的水平变位、倾角、弯矩、剪力和地基反力计算表达式。桩的挠曲微分方程是分段函数,包括地上部分和地下部分桩,相应的内力和变位求解也分为两段。最后通过一个算例分析了桩顶竖向荷载、桩顶水平力和自由荷载对桩身的受力性状各参数的影响。计算结果表明, 桩顶水平力对桩身最大弯矩和桩顶水平变位的影响最大,而桩周内外摩阻力及桩身自重对桩身受力性状影响较小。     

复杂地基反力模式下高承台嵌岩灌注桩的屈曲稳定分析

为探讨桩侧地基土反力对高承台嵌岩灌注桩桩身屈曲稳定的影响,假定地基反力系数呈更为复杂的幂分布,基于弹性地基梁理论建立桩土体系总势能方程,采用最小势能原理,导出了桩身屈曲临界荷载与稳定计算长度的解析解,并据此获得了地基反力系数分布模式、桩身自重及桩侧摩阻力等对桩身屈曲稳定的影响规律。工程应用分析结果表明,考虑地基反力系数为一般幂分布时,桩身屈曲分析结果更趋合理。     

斜桩基础受力特性研究

斜桩在群桩中起到承受较大水平荷载的作用,被广泛应用于桥梁、码头以及大型输电线路等建构筑物的基础中。群桩基础中,斜桩对竖向和水平荷载的分担作用不仅是力的分解问题,还与群桩中斜桩与直桩的单桩轴向和侧向刚度有关,进行斜桩群桩基础分析需要考虑轴向与侧向刚度的耦合。通过对直桩、斜桩的单桩侧向和轴向承载特性的分析以及群桩基础荷载分担情况的分析,揭示了斜桩基础的受力性状。负斜桩单桩侧向刚度最大,直桩次之,正斜桩最小。桩长对单桩轴向刚度的影响非常明显,桩长越长,轴向刚度越大,轴向刚度与侧向刚度之间的差异也就更加显著。群桩基础大部分竖向荷载由桩轴向力承担;当轴向刚度与侧向刚度的比值较小,基础水平荷载主要由桩侧向力承担;当轴向刚度与侧向刚度的比值很大,基础水平荷载主要由桩轴向力承担;当桩的倾斜角较小时,由基础水平荷载引起的桩轴向力较大。     

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。     

天津厚地层超长钻孔灌注桩单桩承载特性研究

天津市某主塔楼桩基选用后压浆超长钻孔灌注桩,为了掌握超长后压浆钻孔灌注桩在该地层的工程特性,共设计了2组（共8根）试桩进行单桩竖向抗压静载试验。试桩中安装了振弦式钢筋计和分层沉降管以反映桩侧摩阻力和桩身分层沉降状态。对试验数据进行对比分析和计算结果表明,桩侧注浆可以明显提高超长桩的侧摩阻力;采用预压加载可以增强超长桩的弹性,减少桩顶的沉降;卸荷稳定后试桩具有桩侧阻力,桩身上段所受阻力为负摩阻力,下段为正摩阻力,同时具有的桩身轴力使试桩产生一定的压缩,其压缩量为残余变形量的重要组成部分     

Response evaluation for horizontally loaded fixed‐head pile groups using 3‐D non‐linear analysis

The response of laterally loaded pile foundations may be significantly important in the design of structures for such loads. A static horizontal pile load test is able to provide a load–deflection curve for a single free‐head pile, which significantly differs from that of a free‐ or fixed‐head pile group, depending on the particular group configuration. The aim of this paper is to evaluate the influence of the interaction between the piles of a group fixed in a rigid pile cap on both the lateral load capacity and the stiffness of the group. For this purpose, a parametric three‐dimensional non‐linear numerical analysis was carried out for different arrangements of pile groups. The response of the pile groups is compared to that of the single pile. The influence of the number of piles, the spacing and the deflection level to the group response is discussed. Furthermore, the contribution of the piles constituting the group to the total group resistance is examined. Finally, a relationship is proposed allowing a reasonable prediction of the response of fixed‐head pile groups at least for similar soil profile conditions. Copyright © 2005 John Wiley & Sons, Ltd.     

桩基动刚度影响因素分析

动刚度是桩基动测分析中一个重要指标,研究动刚度的影响因素有着现实的工程意义。为了分析完整桩和缺陷桩单桩动刚度的变化规律和影响因素,推导并求解了竖向简谐荷载作用下考虑两个变截面桩的导纳响应解析解。利用测试数据验证了该模型能有效计算导纳共振频率值和动刚度值。同时,对513根相同型式桥桩进行机械阻抗法测试,并对其动刚度进行统计分析。研究表明：（1）桩端支撑刚度和桩长对动刚度影响较大,端承桩动刚度随桩长增加而降低,纯摩擦桩情况与之相反。摩擦桩在桩长较长时其动刚度可能大于端承桩。（2）桩身缺陷体积改变量与动刚度变化成正相关。（3）动刚度对桩身缩颈缺陷敏感度较高,在一定程度上可以用于判断桩身完整性和承载能力。     

Response of 1 × 2 pile group under eccentric lateral loading

A large scale model test of a 1 × 2 pile group was conducted in silts to investigate its behavior under eccentric lateral loading. The model pile group consisted of two well instrumented steel piles and was installed in a large soil tank with a close spacing of three-pile diameters on centers. The test results revealed that the eccentricity of lateral loads had limited effect on the overall performances of the 1 × 2 pile group, but significantly contributed to the unevenness of internal forces of the individual piles. The coupling effect between the lateral deflection and torque gave rise to the substantial increase in the torsional resistance of individual piles within the group, comparing to that of a torsionally loaded single pile. The contribution provided by the torsional resistances of individual piles in resisting the external torque continually decreased when the applied lateral load increased. In addition, a three-dimensional finite-element analysis for the pile group was performed and the simulated response was found to be in good agreement with the measured test results. Based on the same model, more cases with different loading conditions were further analyzed. It could be concluded from the analyses that the layout of individual piles within the group obviously affected the behavior of the 1 × 2 pile group under eccentric lateral loads.