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.     

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.     

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.     

Integral equation method for analysis of piled rafts with dissimilar piles under vertical loading

In a piled raft, the length and arrangement of piles has a significant effect on the stresses and deflections of the raft. The use of piles with different dimensions and properties below a raft is an innovative concept and can optimize the design of a piled raft. In this study, an integral equation method with a fictitious pile model was adopted to analyze the piled raft foundation with dissimilar piles. The Fredholm integral equations of the second kind were obtained for this problem. The loads shared by piles and subsoil, the load transfer, and the settlement of the piled raft were obtained using numerical calculation. The results from the present method were compared with those in the literature. An optimization technique was introduced to design piled rafts with dissimilar piles. The stiffening effect of piles on the surrounding soil is also discussed as compared the conventional interaction factor approach.     

Numerical Analysis of Pile–Soil–Pile Interaction in Pile Groups with Batter Piles

Battered piles are usually used to counteract lateral forces in a pile group. As there is little spacing between piles, they are affected by one another, and there is interaction between them. In this study, pile–soil–pile interaction in a group of battered piles was numerically simulated using finite element analysis. Double and frictional pile groups under static lateral and axial loadings were analyzed separately. The effects of batter angle, slenderness ratio, spacing between piles, pile–soil stiffness ratio, and soil plasticity on interaction factors were computed and presented in curves.     

竖向荷载下刚性板桩筏基础分析方法

根据群桩中桩侧摩阻力分布规律,在桩筏基础中基于弹性理论中的变形协调关系、桩体物理方程和力的平衡关系,推导了竖向荷载作用下桩筏基础的荷载和位移之间的刚度矩阵,从而提出了一种刚性板下桩筏基础的分析方法。刚性板桩筏基础分析中考虑了4种相互作用,分别为桩-土-桩、桩-土-板、板-土-桩和板-土-板相互作用。基础中各桩可具有不同的桩长、桩半径和刚度等特性。应用该方法不需要划分桩-土体单元,分析中的计算矩阵仅与基础中桩数和筏板下土节点数量相关而与其他变量无关,分析过程简洁通用。通过与各种分析方法的比较验证,证明该方法是合理可行的。     

Optimisation of pile groups

The optimisation of pile groups is studied using an optimisation technique in conjunction with a discrete element method for pile group settlement analysis. It is demonstrated that it is possible to optimise the performance of pile groups by minimising the load differentials between piles and/or differential settlements. This could be achieved by apportioning the lengths of the group piles to meet the requirement of their positions in the group. Numerical examples are presented to illustrate this principle.     

加筋效应对群桩相互作用系数的影响

群桩相互作用系数通常是采用平面应变模型进行分析,其研究方法具有较多的近似性。基于更为严格的虚拟桩模型,应用群桩相互作用的积分方程解答,以两桩相互作用的基本模型为例,研究加筋效应对群桩相互作用的影响。与弹性理论法和Mylonakis & Gazetas解答的对比表明,加筋效应对群桩相互作用系数有着较为明显的影响,并指出Mylonakis & Gazetas基于剪切位移法所得解答中存在的一些主要问题。     

公路桥超长群桩的有效桩长研究

针对公路桥梁超长群桩的有效桩长问题,对国内公路桥梁桩基的荷载状况进行统计分析,得出桩顶应力主要分布在6～21 MPa范围。进行了长径比为96的桩间距分别为3D、4.5D和6D的3组不同群桩的超长群桩模型试验,得到3种不同桩间距的超长群桩中单桩轴力随着不同荷载的分布图,按照桩身轴力趋于0的桩截面的深度确定有效桩长,并利用指数函数关系分别拟合了3种不同桩间距的桩顶应力与有效桩长之间的关系。根据竖向荷载作用下群桩模型试验与实际原型之间的相似关系,确定公路桥超长群桩与荷载对应的有效桩长取值范围,研究了超长群桩的有效桩长与桩间距之间的关系,并对桥梁桩基有效桩长的取值与桩间距提出了建议。     

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。     

Nonlinear response of laterally loaded piles and pile groups

In spite of extensive studies on laterally loaded piles carried out over years, none of them offers an expedite approach as to gaining the nonlinear response and its associated depth of mobilization of limiting force along each pile in a group. To serve such a need, elastic–plastic solutions for free‐head, laterally loaded piles were developed recently by the author. They allow the response to be readily computed from elastic state right up to failure, by assigning a series of slip depths, and a limiting force profile. In this paper, equivalent solutions for fixed‐head (FixH) single piles were developed. They are subsequently extended to cater for response of pile groups by incorporating p‐multipliers. The newly established solutions were substantiated by existing numerical solutions for piles and pile groups. They offer satisfactory prediction of the nonlinear response of all the 6 single piles and 24 pile groups investigated so far after properly considering the impact of semi‐FixH restraints. They also offer the extent to ultimate state of pile groups via the evaluated slip depths. The study allows ad hoc guidelines to be established for determining input parameters for the solutions. The solutions are tailored for routine prediction of the nonlinear interaction of laterally loaded FixH piles and capped pile groups. Copyright © 2008 John Wiley & Sons, Ltd.     

Bearing capacity of pile groups under vertical eccentric load

The paper deals with the problem of the bearing capacity of pile groups under vertical eccentric load. Widespread practice is to consider the achievement of the axial capacity on the outermost pile as the ultimate limit state of the pile group. However, this approach neglects the ductility of the foundation system and may be thereby overconservative. With the aim of proposing an alternative and more rational approach, a novel formulation for interaction diagrams based on theorems of limit analysis is presented and discussed. The methodology is applicable to the general case of groups of unevenly distributed, dissimilar piles. Piles’ connections to the pile cap are modeled as either hinges or rigid-plastic internal fixities. An application example to a slender structure is also provided, showing that the proposed approach can lead to significant advantages over the traditional design.

     

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.

     

Design method of piled-raft foundations under vertical load considering interaction effects

The paper has proposed a design method considering interaction effects for a piled raft foundation. In this method, the raft is considered as a plate supported by a group of piles and soil. The ultimate load capacity of the pile group is taken into account in calculating the settlement when the foundation is subjected to a large vertical external load. In addition, this method supports estimation of the nonlinear behaviour of the piled raft foundation by considering the nonlinear behaviour of the piles.A step-by-step procedure to apply the proposed method to calculate the settlement and distribution of the bending moment of the piled raft foundation is introduced. To verify the reliability of the proposed method, models of a 16-pile raft and a 9-pile raft with different pile lengths embedded in homogeneous silica sand were tested in a centrifuge and comparisons were made between the results of the proposed method, the results of centrifuge tests, and those of Plaxis 3D. Good agreement between centrifuge modelling and the proposed method is demonstrated, thus showing the potential of the proposed method.     

夯实水泥土桩复合地基共同作用的试验研究

为研究夯实水泥土桩复合地基中桩体、垫层、地基土的共同作用及其工作性状,进行了不同桩长、不同配比单桩载荷试验,不同桩长的单桩及四桩复合地基载荷试验,不同面积置换率的9桩复合地基载荷试验。通过专门的测试元件对复合地基中的地基土反力分布、桩侧摩阻力等进行测定。根据试验结果分析了复合地基破坏模式,探讨了桩体、垫层、地基土的相互作用特性。对地基土反力分布特征、桩土荷载分担比、桩土应力比、单桩及复合地基中桩侧摩阻力分布特征等进行了研究。     

Axial and lateral response of pile groups embedded in nonhomogeneous soils

A numerical method of analysis based on elasticity theory is presented for the analysis of axially and laterally loaded pile groups embedded in nonhomogeneous soils. The problem is decomposed into two systems, namely the group piles acted upon by external applied loads and pile–soil interaction forces, and a layered soil continuum acted upon by a system of pile–soil interaction forces at the imaginary positions of the piles. The group piles are discretized into discrete elements while the nonhomogeneous soil behaviour is determined from an economically viable finite element procedure. The load–deformation relationship of the pile group system is then determined by considering the equilibrium of the pile–soil interaction forces, and the compatibility of the pile and soil displacements. The influence of soil nonlinearity can be studied by limiting the soil forces at the pile–soil interface, and redistributing the ‘excess forces’ by an ‘initial stress’ process popular in elasto-plastic finite element analysis. The solutions from this approach are compared with some available published solutions for single piles and pile groups in homogeneous and nonhomogeneous soils. A limited number of field tests on pile groups are studied, and show that, in general, the computed response compares favourably with the field measurements.     

考虑桩土相互作用的变截面高墩自振频率计算分析

针对变截面群桩基础高墩的几何特性,将桥墩与群桩基础简化为空间整体,在考虑桥墩变截面特性及桩土相互作用的基础上,提出群桩基础变截面桥墩分析模型;将分析模型分解成群桩基础的刚体变形与桥墩的弹性变形两个部分,分别基于能量法与有限单元法求解相应的自振频率,并采用Southwell频率合成法,将整体计算模型表示成两个部分的合成,从而导出变截面桥墩的自振频率,通过算例证明该方法的实用性,并分析了桥墩参数对自振频率的影响,获及了一些定性的结论。结果表明,变截面高墩自振频率的计算分析中,桩-土相互作用的影响不容忽视,考虑桩土相互作用和桥墩本身的非线性更符合工程实际。     

Variation of limiting lateral soil pressure with depth for pile rows in clay

Pile group interaction effects on the lateral pile resistance are investigated for the case of a laterally loaded row of piles in clay. Both uniform undrained shear strength and linearly increasing with depth shear strength profiles are considered. Three-dimensional finite element analyses are presented, which are used to identify the predominant failure modes and to calculate the reduction in lateral resistance due to group effects. A limited number of two-dimensional analyses are also presented in order to examine the behaviour of very closely spaced piles. It is shown that, contrary to current practice, group effects vary with depth; they are insignificant close to the ground surface, increase to a maximum value at intermediate depths and finally reduce to a constant value at great depth. The effect of pile spacing and pile–soil adhesion are investigated and equations are developed for the calculation of a depth dependent reduction factor, which when multiplied by the limiting lateral pressure along a single pile, provides the corresponding variation of soil pressure along a pile in a pile row. This reduction factor is used to perform p–y analyses, which show that, due to this variation of group effects on the lateral soil pressures with depth, the overall group interaction effects depend on the pile length. Comparisons are also made with approaches used in practice that assume constant with depth reduction factors.     

边坡桩-土相互作用的土拱力学模型与桩间距问题

桩-土相互作用机制是边坡抗滑桩设计需要考虑的重要因素之一。基于抗滑桩在侧向荷载作用下的受力条件,通过土力学和弹性力学的基本理论,导出了桩-土作用下桩后土体任意点的应力解析解,建立了土拱的力学模型;获得了土拱应力的等值线分布,得出了双曲拱、扩肩拱、马鞍拱和圆弧拱4种土拱形态,分析了不同桩间距、桩宽、桩后距离及土体力学特性对土拱效应的影响及其变化规律,阐明了土拱的作用机制。以拱体内土体破坏时的极限平衡状态为依据,基于Mohr-Coulomb抗剪强度理论建立了最大桩间距控制方程,并给出了具体的工程实例,对桩-土相互作用机制和抗滑桩设计理论研究具有一定的参考价值。     

Analytic hierarchy process for assessing factors influencing the stability of soil slopes reinforced with piles

Changes in the stability of slopes reinforced with piles involve a complex interaction process between piles, soil, hydrogeological conditions and the engineering geological environment. Correlation analysis between each influencing factor will contribute to a better overall understanding of the main influencing factors. This is of great significance for disaster prevention and the optimization of soil slopes reinforced with piles. The 17 factors influencing the stability of soil slopes reinforced with piles were analyzed in this study, and the weighting of each influencing factor was determined using the analytic hierarchy process along with the experiences of various experts and the author’s experience. The results showed that: (1) soil rheological characteristics and physical and mechanical soil properties have the maximum weighting on the stability of soil slopes reinforced with piles; that is, they are the most important factors influencing the stability of soil slopes reinforced with piles; (2) embedded pile depth or pile anchoring depth and the pile position have the second greatest weighting; (3) rainfall, pile sectional dimensions and pile spacing, are also important factors. Each of these factors was not weighted less than 0.059.