Finite element analysis of mechanisms of pile group behaviour

Solutions are presented for the non-linear load-settlement behaviour of square-configuration pile groups. The groups are represented by an equivalent axially symmetric model, and a non-linear finite element is used to examine the mechanisms of group behaviour and their variation with pile spacing. It is shown that, at close spacings, the block failure mechanism occurs, with significant plastic zones being developed below the group and full pile-soil slip only being developed along the outer piles. As the pile spacing increases, the failure mechanism gradually changes to the ‘single-pile’ mode, whereby full pile-soil slip occurs along all piles. Within the limitations of accuracy of the finite element solution, the values of group settlement ratio and efficiency are in reasonable agreement with values derived from existing theories.     

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.     

A method for the analysis of large vertically loaded pile groups

An iterative method is described for the analysis of vertically loaded pile groups with a large number of vertical piles. The individual pile response is modelled using load-transfer (t–z) curves while pile–soil–pile interaction is determined using Mindlin's solution. The present method not only keeps all the advantages of the so-called ‘hybrid method’, but also makes it possible for practising engineers to solve problems of large non-uniformly arranged pile groups in a time-saving way using a personal computer. Good agreement between the present method of analysis and the direct method is observed. A case history is analysed and the computed response of a large pile group compares favourably with the field measurement. Copyright © 1999 John Wiley & Sons, Ltd.     

基于联合求解法的疏桩地基沉降计算方法研究

疏桩基础作为一种工期短、效果好的软土地基处理方式,在工程中的应用越来越广泛。考虑带桩帽的PTC（预应力混凝薄壁管桩）刚性桩桩侧摩阻力分布规律,将桩侧摩阻力假定为2个三角形拼合的分布形式。联合应用Mindlin-Geddes解答及Boussinesq解答,推导出了疏桩补偿地基中的附加应力的计算公式。结合具体算例,计算复合地基的沉降变形量。研究表明,该联合方法的沉降计算结果比传统方法偏小,与实测数据较为吻合。当桩间距大于8倍桩径时,随着桩间距的增加,疏桩补偿地基的附加应力场基本不变,但沉降量相应增大。对于桩间距较大的疏桩补偿地基,采用长、短桩组合形式较为合理。通过设置深层水泥土搅拌桩来加固软土路堤,能有效控制沉降量。     

A simplified analysis method for piled raft foundations subjected to ground movements induced by tunnelling

A simplified method of numerical analysis has been developed to estimate the deformation and load distribution of piled raft foundations subjected to ground movements induced by tunnelling 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, the piles as elastic beams, and the soil is treated as interactive springs. The interactions between structural members, pile–soil–pile, pile–soil–raft and raft–soil–raft interactions, are modelled based on Mindlin's solutions for both vertical and lateral forces. The validity of the proposed method is verified through comparisons with some published solutions for single piles and pile groups subjected to ground movements induced by tunnelling. Thereafter, the solutions from this approach for the analysis of a pile group and a piled raft subjected to ground movements induced by tunnelling are compared with those from three‐dimensional finite difference program. Good agreements between these solutions are demonstrated. The method is then used for a parametric study of single piles, pile groups and piled rafts subjected to ground movements induced by tunnelling. Copyright © 2005 John Wiley & Sons, Ltd.     

An analytical continuum model for axially loaded end-bearing piles in inhomogeneous soil

An approximate static solution is derived for the elastic settlement and load-transfer mechanism in axially loaded end-bearing piles in inhomogeneous soil obeying a power law variation in shear modulus with depth. The proposed generalised formulation can handle different types of soil inhomogeneity by employing pertinent eigenexpansions of the dependent variables over the vertical coordinate, in the form of static soil “modes”, analogous to those used in structural dynamics. Contrary to available models for homogeneous soil, the associated Fourier coefficients are coupled, obtained as solutions to a set of simultaneous algebraic equations of equal rank to the number of modes considered. Closed-form solutions are derived for the (1) pile head stiffness; (2) pile settlement, axial stress, and side friction profiles leading to actual, depth-dependent Winkler moduli, (3) displacement and stress fields in the soil; and (4) average, depth-independent Winkler moduli to match pile head settlement. The predictive power of the model is verified via comparisons against finite element analyses. The applicability to inhomogeneous soil of an existing regression formula for the average Winkler modulus is explored.     

Response of Vertically Loaded Pile in Clay: A Probabilistic Study

This study presents the response of a vertically loaded pile in undrained clay considering spatially distributed undrained shear strength. The probabilistic study is performed considering undrained shear strength as random variable and the analysis is conducted using random field theory. The inherent soil variability is considered as source of variability and the field is modeled as two dimensional non-Gaussian homogeneous random field. Random field is simulated using Cholesky decomposition technique within the finite difference program and Monte Carlo simulation approach is considered for the probabilistic analysis. The influence of variance and spatial correlation of undrained shear strength on the ultimate capacity as summation of ultimate skin friction and end bearing resistance of pile are examined. It is observed that the coefficient of variation and spatial correlation distance are the most important parameters that affect the pile ultimate capacity.     

软土区旋喷式插筋微型桩工艺试验研究

软土地质条件下建筑物的沉降变形和承载力要求越来越高,对基础施工工艺提出了较高要求。在高压旋喷施工工艺的基础上,提出旋喷式插筋微型桩施工工艺,开展了微型桩工艺试验研究,结果表明该工艺大幅提高了单桩桩基承载性能,为实际工程应用提供了技术数据支持。     

层状地基群桩沉降研究

考虑了桩的加筋与遮帘效应,通过剪切位移法依据力与位移的协调条件得出桩的柔度系数。在此基础上建立土的成层性模型,根据桩顶与桩底的物理关系推导了桩顶沉降与荷载关系的解析解。通过工程算例进行比较,结果表明, 以土层状模型建立的群桩沉降计算方法是可行的。分析表明, 加固区土层不同分布对桩沉降有所影响,浅部土模量的提高有利于减小沉降。     

A non‐linear coupled finite element–boundary element model for the prediction of vibrations due to vibratory and impact pile driving

This paper presents a non‐linear coupled finite element–boundary element approach for the prediction of free field vibrations due to vibratory and impact pile driving. Both the non‐linear constitutive behavior of the soil in the vicinity of the pile and the dynamic interaction between the pile and the soil are accounted for. A subdomain approach is used, defining a generalized structure consisting of the pile and a bounded region of soil around the pile, and an unbounded exterior linear soil domain. The soil around the pile may exhibit non‐linear constitutive behavior and is modelled with a time‐domain finite element method. The dynamic stiffness matrix of the exterior unbounded soil domain is calculated using a boundary element formulation in the frequency domain based on a limited number of modes defined on the interface between the generalized structure and the unbounded soil. The soil–structure interaction forces are evaluated as a convolution of the displacement history and the soil flexibility matrices, which are obtained by an inverse Fourier transformation from the frequency to the time domain. This results in a hybrid frequency–time domain formulation of the non‐linear dynamic soil–structure interaction problem, which is solved in the time domain using Newmark's time integration method; the interaction force time history is evaluated using the θ‐scheme in order to obtain stable solutions. The proposed hybrid formulation is validated for linear problems of vibratory and impact pile driving, showing very good agreement with the results obtained with a frequency‐domain solution. Linear predictions, however, overestimate the free field peak particle velocities as observed in reported field experiments during vibratory and impact pile driving at comparable levels of the transferred energy. This is mainly due to energy dissipation related to plastic deformations in the soil around the pile. Ground vibrations due to vibratory and impact pile driving are, therefore, also computed with a non‐linear model where the soil is modelled as an isotropic elastic, perfectly plastic solid, which yields according to the Drucker–Prager failure criterion. This results in lower predicted free field vibrations with respect to linear predictions, which are also in much better agreement with experimental results recorded during vibratory and impact pile driving. Copyright © 2008 John Wiley & Sons, Ltd.     

Negative skin friction on pile groups

A numerical procedure is presented for the downdrag analysis of group piles which penetrate a consolidating upper soil layer to socket into a firm bearing stratum of finite stiffness. The settlement of the consolidating upper soil layer under a surcharge load is estimated using Terzaghi's one-dimensional consolidation theory. Parametric solutions are presented to show the influence of various parameters on the performance of the socketed pile groups in terms of the development of the induced downdrag forces and associated pile head settlements. In general, pile–soil–pile interaction has the beneficial effect of reducing the downdrag forces and settlements of the group piles when compared to the corresponding single pile values, provided that the soil settlements are not so large as to cause full slippage at the interface in all the piles. Reasonable agreement is obtained between the theoretical and experimental results for pile groups subjected to negative skin friction.     

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.     

成层Gibson地基中单桩沉降的非线性分析

针对成层Gibson地基模型,研究了轴向荷载作用下单桩的非线性沉降响应。利用最小势能原理求得桩土体系的控制方程,获得了土体位移的解析解及桩身沉降的差分方程式。将土体看作线弹性理想塑性材料,分析了土体的非线性对桩身位移的影响,提出了考虑非线性的单桩沉降响应计算方法,利用Maple编制了相应的分析程序。通过算例研究了土性参数及桩长径比对端承单桩沉降的影响。将研究结果应用于桩基静载荷试验成果的分析,结果表明,两者吻合较好,证明了该方法的合理性。     

高速铁路穿透型CFG桩复合地基沉降计算修正系数分析

为掌握铁路工程CFG桩复合地基在路堤荷载作用下的沉降计算修正系数变化特点,基于武汉－广州高速铁路24个路堤断面的地基沉降测试数据,结合地勘和设计参数,分析了地基沉降计算修正系数的变化规律及工后沉降的时间效应特征,结果表明,软弱土层浅薄的穿透型CFG桩复合地基具有优良的沉降控制效果,对应的地基沉降计算修正系数在0.63～0.17之间,较当量压缩模量相当的《铁路工程地基处理技术规范》推荐值偏低约1/3;地基沉降表现出显著的时间效应特征,地基工后沉降占最终沉降的比值有随时间逐渐降低的趋势;路堤填筑速率加快和地基布桩间距加大,对穿透型CFG桩复合地基工后沉降占最终沉降的比值有明显增大作用,地基沉降稳定所需的时间更长。     

Development of a three-dimensional soil model for the dynamic analysis of end-bearing pile groups subjected to vertical loads

This paper presents a new analytical model for calculating the steady-state impedance of pile groups subjected to vertical dynamic loads. The derived solution allows considering effects of radially but also vertically propagating soil waves on the soil attenuation function, pile interaction factor, and pile group impedance. The proposed model provides accurate estimates of the soil stress field and of the response of the pile group in the low as well as in the high-frequency range, unlike earlier solutions based on the plane-strain model to describe the soil surrounding the piles, which ignores the vertical soil stress gradient. The latter assumption results in underestimating pile group impedance and overestimating radiation damping for frequencies lower than the cutoff frequencies of the system, which are explicitly captured with the proposed solution.     

承台外区土阻力群桩效应及效应系数的有限元分析

利用三维弹塑性有限元方法,对复合桩基承台外区土阻力群桩效应及其效应系数进行了研究,讨论了土类、桩长、桩距、桩数等对承台外区土阻力群桩效应及其群桩效应系数的影响,结果表明(1)承台外区土阻力随承台宽与桩长之比 (B/L)的增大而增大,但增幅不大;随桩距S增大而增大;受桩数n的影响不大。(2)承台外区群桩效应系数随B/L增大几乎无变化;随S增大而增大;不随n变化而变化。(3)承台外区群桩效应系数与土类有关。     

Foundation settlement statistics via finite element analysis

The dispersion observed in soil data comes both from the spatial variability which greatly influences the behavior of large structures and from errors in testing. Thus, the geotechnical engineering deals with uncertainties for which deterministic approaches are not suitable. The resort to probabilistic techniques, enables modeling uncertainties by analyzing their dispersion effect on the global behavior of the structure. The scope of this paper is analyzing settlement and differential settlement variability of a pair of foundations on random heterogeneous medium. The random soil properties of interest are the elastic modulus, and the Poisson ratio. The elastic modulus is modeled as a spatially random field by adopting the lognormal distribution, which enables analyzing its large variability. Because soil Poisson ratio is bounded in practice between two extreme values, its random field is obtained by using the Beta distribution. In this study, one proposes for the Beta field determination, a mapping technique on the probability distribution function diagram, by solving a non-linear equation. However, the mean and variance are unchanged through the mapping operation. Because the soil Poisson ratio is a positive parameter, one prefers to perform the mapping operation with the probability function of the lognormal distribution. Also, the proposed technique can be used for other bounded soil properties such as the porosity. In this paper, settlement and differential settlement statistics prediction are carried out using Monte Carlo simulations combined with deterministic finite element method (DFEM). A performed parametric study shows the following: (i) as the variability of the elastic modulus increases as settlement and differential settlement statistics are important, also, settlement statistics decreases as the Poisson ratio variability increases, and differential settlement statistics do not seem be affected by its variability. (ii) settlement and differential settlement statistics are important for positive inter-property correlation. (iii) a great influence of the correlation lengths on settlement and differential settlement statistics.     

桩基负摩阻力时间效应试验研究

由于黏土固结缓慢,桩基负摩阻力存在明显的时间效应,然而目前相关研究仍显不足。设计实施了能实现桩顶加载及较大超载值的单桩及双桩负摩阻力模型试验,桩周土采用砂土和软黏土夹层,测定了模型桩身应力、桩顶位移以及土体分层沉降随固结时间的变化。试验结果显示,沉降、负摩阻力具有明显的时间效应。土表超载作用下土体沉降带动桩沉降,桩与土体的沉降均表现出早期快、后期慢的趋势。试验加载初期,黏土夹层处的负摩阻力略小于砂层,但随土体固结而增长,其基本变化规律与沉降相同。因桩端砂土层沉降稳定迅速,中性点随桩身沉降增长略呈上移趋势。此外,相同荷载作用下桩间距较小的双桩,由于下拉力较小,其沉降较小。试验条件下,3D桩间距的负摩阻力群桩效应系数在0.71～0.77之间,6D桩间距时不存在负摩阻力群桩效应。     

General elastic analysis of piles and pile groups

This paper describes the development of a boundary element analysis for the behaviour of single piles and pile groups subjected to general three‐dimensional loading and to vertical and lateral ground movements. Each pile is discretized into a series of cylindrical elements, each of which is divided into several sub‐elements. Compatibility of vertical, lateral and rotational movements is imposed in order to obtain the necessary equations for the pile response. Via hierarchical structures, 12 non‐zero sub‐matrices in a global matrix are derived for the basic influence factors. Solutions are presented for a series of cases involving single piles and pile groups. In each case, the solutions are compared with those from more simplified existing pile analyses such as those developed by Randolph and by Poulos. It is shown that for direct loading effects (e.g. the settlement of piles due to vertical loading), the simplified analyses work well. However, for ‘off‐line’ response (such as the lateral movement due to vertical loading) the differences are greater, and it is believed that the present analysis gives more reliable estimates. Copyright © 2000 John Wiley & Sons, Ltd.     

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.