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.     

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.     

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.     

Pile group settlement: A probabilistic approach

The uncertain settlement response of pile groups is determined using a ‘hybrid’ formulation and a first-order perturbation technique. The spatially varying soil modulus, which gives rise to the uncertainties in the pile group settlement, is modeled as a homogeneous random field. The random field is assumed to be one-dimensional since the ‘hybrid’ formulation does not account for horizontal variation in the soil properties. Using the proposed method, the coefficient of variation of the pile group settlement is computed. The single-pile solutions obtained compare favorably with the solutions from a conventional stochastic finite element analysis. Pile groups of sizes ranging from two to twenty-five piles are studied. It is observed that the coefficient of variation is not significantly affected by the pile spacing as well as the group size. By defining an appropriate performance function, the reliability index of a pile group system is also found to be approximately the same as that of a single-pile system. These observations suggest that the solutions for a single pile may be used to estimate the uncertainties in the settlement response of pile groups.     

Analysis of piled raft with nodular pile subjected to vertical load using a Winkler model approach

An investigation is made to present analytical solutions provided by a Winkler model approach for analysis of piled rafts with nodular pile subjected to vertical loads in nonhomogeneous soils. The vertical stiffness coefficient along a piled raft with the nodular pile in nonhomogeneous soils is derived from the displacement given by the Mindlin solution for elastic continuum analysis. The vertical stiffness coefficients for the bases of the raft and the nodular part in the nodular pile in a soil are expressed by the Muki solution for the 3‐D elastic analysis. The relationship between settlement and vertical load on the pile base is presented considering the Mindlin solution and the equivalent thickness in the equivalent elastic method. The interaction factor between the shaft of the nodular pile and the soil is expressed taking into account the Mindlin solution and the equivalent elastic modulus. The relationship between settlement and vertical load for a piled raft with the nodular pile in nonhomogeneous soils is obtained by using the recurrence equation of influence factors of the pile for each layer. The percentage of each load carried by both nodular pile and raft subjected to vertical load is represented through the vertical influence factors proposed here. Comparison of the results calculated by the present method for piled rafts with nodular piles in nonhomogeneous soils has shown good agreement with those obtained from the finite element method and a field test. Copyright © 2016 John Wiley & Sons, Ltd.     

A Winkler model approach for vertically and laterally loaded piles in nonhomogeneous soil

An investigation is made to present analytical solutions provided by a Winkler model approach for the analysis of single piles and pile groups subjected to vertical and lateral loads in nonhomogeneous soils. The load transfer parameter of a single pile in nonhomogeneous soils is derived from the displacement influence factor obtained from Mindlin's solution for an elastic continuum analysis, without using the conventional form of the load transfer parameter adopting the maximum radius of the influence of the pile proposed by Randolph and Wroth. The modulus of the subgrade reaction along the pile in nonhomogeneous soils is expressed by using the displacement influence factor related to Mindlin's equation for an elastic continuum analysis to combine the elastic continuum approach with the subgrade reaction approach. The relationship between settlement and vertical load for a single pile in nonhomogeneous soils is obtained by using the recurrence equation for each layer. Using the modulus of the subgrade reaction represented by the displacement influence factor related to Mindlin's solution for the lateral load, the relationship between horizontal displacement, rotation, moment, and shear force for a single pile subjected to lateral loads in nonhomogeneous soils is available in the form of the recurrence equation. The comparison of the results calculated by the present method for single piles and pile groups in nonhomogeneous soils has shown good agreement with those obtained from the more rigorous finite element and boundary element methods. It is found that the present procedure gives a good prediction on the behavior of piles in nonhomogeneous soils. Copyright © 2011 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.     

Static analysis of vertically loaded pile group in multilayered transversely isotropic soils

In this paper, a coupling approach is presented to study the static responses of vertically loaded pile group embedded in multilayered transversely isotropic soils. The individual pile in pile group is modeled by the finite element method, while the analytical layer-element method is applied to represent the soil's behavior. Then, the interaction equation of piles and soils is obtained by considering the force equilibrium and displacement compatibility conditions and solved by a FORTRAN program. The results computed by the proposed approach compare favorably with those from some existing solutions and field test. Some typical parametric analysis cases are investigated to study the effect of soil anisotropy, pile stiffness ratio, and pile spacing on the behavior of vertically loaded pile group.     

Settlement analysis of rectangular piles in nonhomogeneous soil using a Winkler model approach

An analytical approach using a Winkler model is investigated to provide analytical solutions of settlement of a rectangular pile subjected to vertical loads in nonhomogeneous soils. For a vertically loaded pile with a rectangular cross section, the settlement influence factor of a normal pile in nonhomogeneous soils is derived from Mindlin's solution for elastic continuum analysis. For short piles with rectangular and circular cross sections, the modified forms of settlement influence factors of normal piles are produced taking into account the load transfer parameter proposed by Randolph for short circular piles. The modulus of subgrade reaction along a rectangular pile in nonhomogeneous soils is expressed by using the settlement influence factor related to Mindlin's solution to combine the elastic continuum approach with the subgrade‐reaction approach. The relationship between settlement and vertical load for a rectangular pile in nonhomogeneous soils is available in the form of the recurrence equation. The formulation of settlement of soils surrounding a rectangular pile subjected to vertical loads in nonhomogeneous soils is proposed by taking into account Mindlin's solution and both the equivalent thickness and the equivalent elastic modulus for layers in the equivalent elastic method. The difference of settlement between square and circular piles is insignificant, and the settlement of a rectangular pile decreases as the aspect ratio of the rectangular pile cross section increases. The comparison of results calculated by the present method for a rectangular pile in nonhomogeneous soils has shown good agreement with those obtained from the analytical methods and the finite element method. Copyright © 2014 John Wiley & Sons, Ltd.     

Influence of a point sink on a pile group in saturated multilayered soils with anisotropic permeability

The behavior of a pile group is solved using the finite element method, and the fundamental solution of saturated multilayered soils with anisotropic permeability is obtained by the analytical layer element method. Based on the supposition of no slip occurring at the pile‐soil interface, the governing equations of the interaction between the pile group and the soils due to a point sink are established in the Laplace‐Hankel transformed domain by considering the pile‐soil compatibility condition. Numerical results are presented to study the effect of point sink pumping, the properties of soils, and the geometries of piles on the behavior of the pile group.     

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.     

Discrete layer analysis of axially loaded piles and pile groups

This paper presents a simple discrete layer approach for the settlement analysis of axially loaded piles and pile groups. The soil profile may be arbitrarily layered and underlain by either a stiff or rigid stratum. The pile-soil-pile interaction is determined using a modified form of Mindlin's solution for finite soil depth. Good agreement between the present approach and more rigorous finite element and boundary element approaches is observed for the analysis of piles and pile groups embedded in finite soil layers. Settlement predictions obtained from the present approach also agree reasonably well with measurements from a number of published pile tests. Although the emphasis of this paper is on linear elastic solutions, it can easily be extended to include non-linear response.     

Analysis of pile-soil interaction under lateral loading using infinite and finite elements

In order to gain a better understanding of pile-soil interaction under lateral loading, this paper presents a numerical analysis which combines the infinite and finite element method. Interest is focused on the group effect on ultimate lateral soil resistance. Firstly, a single isolated pile is analysed and reasonably good agreement is found between existing analytical solutions and results obtained by the present method. A limited parametric study is also presented and some parameters influencing the ultimate lateral soil resistance are identified. The analysis of pile groups is then considered and it is shown that the group effect tends to reduce pile capacity when the spacings between piles are within the practical ranges. The extent of the reduction depends on the arrangement of piles within the group.     

群桩荷载位移特性研究

将杆系结构有限单元法与荷载传递迭代法相耦合,形成一桩基沉降分析计算的混合法。采用近似解析解中Randolph and Wroth’Model与双曲线模型相结合,模拟桩身与桩周介质边界上剪切滑移的非线性。桩间相互作用在采用弹性理论Mindlin方程解答计算,并考虑了桩间“加筋与遮帘”作用。桩周土介质非均质性特征,采用指数函数模拟。分析了刚性承台下群桩桩数、桩长、桩间距和桩土模量比等群桩工作特性的影响。尤其是桩台基础沉降对群桩相互作用影响机制的研究,对桥梁拼接等对桩基础沉降要求严格的工程有重要的借鉴意义。     

考虑桩土侧移的被动桩中土拱效应数值分析

被动桩对侧向位移的土层起到遮拦作用的机制主要是土拱效应。采用土工有限元软件Plaxis Tunnel 3D 1.2,对堆载荷载作用下邻近桩基中的土拱效应产生机制和性状进行三维数值分析,指出目前被动桩中土拱效应二维有限元分析存在的问题。考虑桩土侧移与相对位移,再利用土工有限元软件Plaxis2D 8.2详细地研究了侧向土体位移大小、桩身水平位移大小、土体性质以及桩土接触面性质等影响因素对土拱效应性态和桩土荷载分担比的影响。     

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。     

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.     

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.     

Three‐dimensional finite element analysis of the interaction between tunneling and pile foundations

This paper concerns analysis of the impact of construction of urban tunnels on adjacent pile foundations. It is carried out using an elastoplastic three‐dimensional finite element modelling. Numerical simulations are performed in two stages, which concern, respectively, the application of the pile axial loading and the construction of the tunnel in presence of the pile foundations. Analysis is carried out for both single piles and groups of piles. Results of numerical simulations show that tunneling induces significant internal forces in adjacent piles. The distribution of internal forces depends mainly on the position of the pile tip regarding the tunnel horizontal axis and the distance of the pile axis from the centre of the tunnel. Analysis of the interaction between tunneling and a group of piles reveals a positive group effect with a high reduction of the internal forces in rear piles. Copyright © 2002 John Wiley & Sons, Ltd.     

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.