Interaction between torsional and axial pile responses

The effect of axial load on the torsional pile response and the effect of torque on the axial pile response are investigated. To perform this investigation, a computer program was developed which uses the transfer matrix method to analyse a pile supported by a series of coupled axial and torsional elasto-plastic springs. The study indicated that the ultimate torsional and axial pile capacities, as well as the axial displacements and rotations, are significantly affected by the combined load action.     

Torsional piles in non-homogeneous media

The torsional response of a pile exhibits features which are a mixture of those for axial and lateral response. At low load levels, the response is dominated by interaction with the upper soil layers and by the pile rigidity itself, similar to laterally loaded piles. However, failure will generally occur by the whole pile twisting, and so the latter part of the response incorporates the integrated effect of all soil penetrated by the pile, as is the case for axial loading.

In view of the above, solutions for the torsional response of pile must endeavour to incorporate accurate modelling of the soil stiffness profile, and also pay appropriate attention to the gradual development of slip (relative twist) between pile and soil. The paper presents analytical and numerical solutions for the torsional response of piles embedded in non-homogeneous soil, where the stiffness profile follows a simple power law with depth. The solutions encompass: (1) vertical non-homogeneity of soil expressed as a power law; (2) non-linear soil response, modelled using a hyperbolic stressstrain law; (3) effect of relative slip between pile and soil for non-homogeneous stiffness and limiting shaft friction; (4) expressions for the critical pile slenderness ratio (or length) beyond which the pile head response becomes independent of the pile length.

The solutions are developed using a load transfer approach, with each soil layer acting independently from neighbouring layers, and are expressed in terms of Bessel functions of non-integer order, and as simple non-dimensionalised charts. The solutions are applied to two well-documented case histories in the latter part of the paper.     

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.     

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.     

盾构隧道施工对邻近承载桩基影响研究

针对苏州轻轨1号线成层非均质土地基,选用Mohr-Coulomb弹塑性本构模型,建立三维有限元数值模型,研究非均质土中盾构隧道施工对邻近承载桩基工作性状的影响规律。数值计算结果表明,随着成层非均质土中各土层软硬程度差异的增大,隧道开挖会在邻近承载单桩引起明显反弯点,且桩体沉降亦随之增大;位于上软下硬成层土中的承载单桩桩身正弯矩更大,且该正弯矩出现在桩身中上部的反弯点部位,而上硬下软成层土中的承载单桩下部出现更大的负弯矩;与均质土中同位置承载单桩相比,位于上软下硬成层土中承载单桩桩顶及桩端轴力均更大,而位于上硬下软成层土中承载单桩桩顶轴力则更小。不同竖向集中荷载作用下,非均质土中盾构隧道开挖引起的承载群桩中前桩水平位移沿桩身分布与同位置承载单桩重合,后桩挠曲程度小于承载单桩;盾构隧道施工对承载群桩内力的影响明显高于对变形的影响。     

BEM analysis of the interaction factor for vertically loaded dissimilar piles in saturated poroelastic soil

This paper focuses on an analysis by the boundary element method (BEM) of the pile-to-pile interaction for pile groups with dissimilar piles of different pile lengths embedded in saturated poroelastic soil. The behaviour of the poroelastic homogeneous soil is governed by Biot’s consolidation equations. The pile–soil system is decomposed into extended soil and fictitious piles. Considering the compatibility of vertical strain between fictitious piles and soil, the second kind of Fredholm integral equations were obtained to predict the axial force and settlement along pile shafts numerically. For the analysis of the interaction factor, two loading conditions for a two-dissimilar-pile system were proposed: (a) only one pile is loaded and (b) each pile is subjected to a load proportional to the pile length. Furthermore, the two-pile system was extended to pile groups with a rigid cap to capture the optimum design where each pile shares the same loading at the pile heads. The optimum results require shortening the peripheral piles and elongating internal piles, and the consolidation effect needs to be considered due to the adjustment of loading distribution among piles.     

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.     

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。     

水平偏心受荷群桩p乘子计算

水平偏心受荷群桩同时发生水平移动和绕承台中心的转动,使基桩的运动方向各不相同,因此基桩的运动方向成为影响群桩效应的一个关键因素。研究发现：水平偏心受荷的两根桩,前桩运动方向与两桩连线夹角0o≤η≤90o,后桩夹角?90o≤θ≤90o;量化两桩间桩?土?桩相互作用的折减系数与η和θ密切相关,η和θ组合存在一个范围,在该范围内两桩不存在相互作用;当两桩存在相互作用时,相互作用对后桩的影响往往大于对前桩的影响。通过将定量描述水平受荷群桩群桩效应的p乘子概念拓展到水平偏心受荷群桩,综合运用理论分析、试验和数值计算成果,提出了折减系数计算公式,进而给出了广义p乘子经验计算公式。通过试验案例验证了该计算公式的合理性。     

软土地层桥梁群桩基础桩土共同作用性状的非线性有限元分析

通过对某高速铁路特大桥群桩基础进行三维非线性有限元分析,并结合现场试验得出的规律进行相应的对比分析,研究了软土地层桥梁群桩基础桩身轴力、桩侧摩阻力、基底土体附加应力、孔隙水压力分布、超孔隙水压力消散和群桩基础荷载沉降规律。计算结果表明,基桩所承受的轴力,角桩＞边桩＞中心桩,角桩和边桩的轴力沿桩身减小的幅度较大,而中心桩的轴力沿桩身减小的幅度稍小;各基桩桩侧摩阻力的发挥情况,侧摩阻力值总体上呈角桩＞边桩＞中心桩,相对滑移量基本呈上大下小的形态,即桩身上部桩-土之间产生的相对滑移量较中下部要大;外荷载作用下产生的土体附加应力和超孔隙水压力主要集中在承台底以下土体的一定范围内,其衰减梯度沿深度方向逐渐降低,随着固结时间的延长,群桩基础沉降达到稳定。     

An approximate numerical analysis of pile–raft interaction

This paper presents an approximate method of numerical analysis of piled–raft foundations in which the raft is modelled as a thin plate and the piles as interacting springs of appropriate stiffness. Allowance is made for the development of limiting pressures below the raft and of the ultimate axial load capacity of the piles. Comparisons between this analysis and existing solutions verify that, despite the approximations involved, the analysis can provide solutions of adequate accuracy for the settlement and pile load distribution within a piled raft. Comparisons are also made with the results of a series of centrifuge tests and with measurements of the performance of a full-scale piled raft. In both cases, the analysis predicts very well the settlement and proportion of load carried by the piles.     

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.     

竖向荷载作用下挤扩支盘桩的试验研究及设计分析

结合实际工程,通过挤扩支盘桩的静载荷试验和桩身轴力测试试验,深入地分析了竖向荷载作用下挤扩支盘桩的荷载传递机理和变形特性,同时,给出了挤扩支盘桩的单桩承载力计算公式。结果表明,挤扩支盘桩在加荷后期支盘承担50 %以上荷载,且支盘阻力体现端承力的性质;挤扩支盘桩与普通直桩相比,单桩承载力可提高60 %～100 %。     

砂土中隧道开挖对邻近桩基竖向影响的简化计算方法

基于砂土中隧道开挖引起的土体竖向位移经验公式,分析隧道开挖对邻近桩基础的竖向影响。采用两阶段计算方法,将邻近桩基础视为竖向被动桩,依据砂土中隧道开挖引起地表及地表以下土体产生的沉降槽,考虑桩土相互作用的非线性,得到砂土中隧道开挖对邻近桩基础轴力影响的简化计算方法,并与土工离心试验结果进行对比,验证了该方法的合理性。在研究过程中,分析了隧道覆盖层厚度、隧道直径、隧道与桩之间的距离、隧道土体损失率、桩长、桩径等因素。研究结果表明,桩身轴力随着覆盖层厚度的增加而减小,随隧道直径和土体损失率的增大而增加;隧道与桩之间距离为2.5倍隧道直径时对轴力的影响最大;随着桩长、桩径的增加,桩身轴力逐渐增加。     

考虑加筋与遮帘效应计算群桩沉降的相互作用系数法

群桩中各基桩在地基土中的加筋与遮帘效应是客观存在的,然而,在目前的桩基沉降理论与实践中,相关的研究仍显不足。基于剪切变形法理论,考虑桩的加筋与遮帘效应,求得各基桩在自身桩顶荷载作用下产生的沉降以及其引起相邻桩的附加沉降量,由此提出群桩中任两桩的相互作用系数简化公式,同时,也得到各基桩桩侧及桩端桩-土接触等效弹簧刚度,并基于荷载传递法原理,建立了成层地基条件下各基桩在自身桩顶荷载作用下的桩身位移平衡方程,推导出各土层层顶处桩身沉降、轴力与层底处桩身沉降、轴力之间的递推关系,进而将公式推广到高、低承台群桩基础计算中。工程算例分析表明,用该方法计算有较高的精度,求得的荷载-沉降曲线及两桩相互作用系数与实测值吻合较好;相互作用系数要明显小于弹性理论计算结果。     

Vertically loaded piles in non-homogeneous media

Analytical methods for the axial responses of piles can be classified under three broad categories of (1) simple but approximate analytical solutions, (2) one-dimensional numerical algorithms, (3) full axisymmetric analyses using boundary or finite element approaches. The first two categories rely on the so-called load transfer approach, with interaction between pile and soil determined by independent springs distributed along the pile shaft and at the pile base. The non-linear spring stiffness is related to the elastic–plastic properties of the actual soil partly by empirically based correlations and partly by theoretical arguments based on simplified models of the pile–soil system. This paper presents new closed-form solutions for the axial response of piles in elastic–plastic, non-homogeneous, media. The solutions fall in the first of the three categories above, and have been verified through extensive parametric studies using more rigorous one-dimensional and continuum analyses. The effect of non-homogeneity and partial slip on the load and displacement profiles along the pile shaft is explored, and comparisons are presented with experimental data. © 1997 John Wiley & Sons, Ltd.     

Experimental study on the mechanical behaviour of a heat exchanger pile using physical modelling

This study aims to provide knowledge on the thermo-mechanical behaviour of heat exchanger piles, through a laboratory scale model. The model pile (20 mm in external diameter) was embedded in dry sand. The behaviour of the axially loaded pile under thermal cycles was investigated. After applying the axial load on the pile head, the pile temperature was varied between 5 and 30 °C. Seven tests, corresponding to various axial loads ranging from 0 to 70 % of the pile estimated bearing capacity, were performed. The results on pile head displacement show that heating under low axial load induced heave and cooling induced settlement; the pile temperature-displacement curve was found to be reversible and compatible with the thermal expansion curve of the pile. However, at higher axial loads, irreversible settlement of the pile head was observed after a few thermal cycles. The axial load profile measured by the strain gauges evidenced that the pile head load was mainly transferred to the pile toe. Nevertheless, thermal cycles modified significantly the mobilised skin friction along the pile. The total pressure measured at various locations in the soil mass was also slightly influenced by the thermal cycles.     

轴向荷载对斜桩水平承载特性影响试验及理论研究

斜群桩受水平荷载作用时,群桩中的基桩受到径向荷载、轴向荷载和弯矩的共同作用。为研究轴向荷载对斜桩水平承载特性的影响,完成了3根单桩以及1组1×2斜桩的大尺寸模型试验。试验结果表明：轴向拉力作用会降低斜桩的水平刚度和极限承载力;而轴向压力作用则会使其水平刚度和极限承载力提高。基于桩侧浅层土体楔形破坏假定,推导了考虑轴向荷载影响的斜桩水平极限土抗力计算公式,提出了桩侧土抗力的p-y曲线方法,并通过模型试验及现场试验验证其合理性。     

Analytical solution for distributed torsional low strain integrity test for pipe pile

Low strain integrity tests (LSITs) are the most popular non-destructive methods for pile testing. However, traditional LSITs have encountered unprecedented challenges as the need for long pile and existing pile testing keeps multiplying. Compared to traditional longitudinal excitations, the torsional wave is less influenced by the velocity attenuation effect and can be subjected at the pile shaft for existing piles. Distributed torsional LSIT is proposed in this article with the presentation of the corresponding analytical solutions that exhibiting the velocity responses along the pile shaft. The solution is verified with previous simplified theoretical and rigorous finite element method (FEM) answers. At the end, the application of this method is exhibited through the identification of necking and concrete segregation defects on pipe piles, which shows the advantage of this method on long pile testing.     

微型桩组合抗滑结构受力机制的现场试验研究

针对有顶板连接的“八”字形微型桩组合结构,依托广大（广通至大理）线扩能改造工程,现场监测微型桩工作状态下轴力变化,对微型桩组合支护体系应用于分级开挖边坡加固的受力机制进行研究分析。结果表明：在滑坡推力作用下,各排桩桩身轴向力的分布形式不尽相同,沿推力方向依次呈现出反“S”型、“双弓”型和“S”型的分布规律;各排桩峰值轴力均为拉力,比例关系为：靠山侧桩:中间桩:靠路侧桩=2.5:4.1:3.2,其中靠山侧桩最大轴力出现在桩体下部,中间桩出现在中上部,靠路侧桩最大轴力出现在桩体上部;顶部承台对有斜桩的微型桩群的制约协调作用比一般的竖直桩群显著,水平荷载作用下的桩群易发生较大的挠曲变形,在群桩效应、坡体滑裂面等的综合影响下,引发桩体拉-压等受力形式的转变;组合结构的受力机制表现为先承受滑坡主推力的前两排桩受拉,第3排桩底部嵌固段受压,且随着持续推力作用受压区存在向上发展趋势;各单桩桩身轴力以拉力为主,有利于内部钢筋受拉优势的发挥。