Numerical analysis of piled rafts

An approximate numerical method for the analysis of piled raft foundations is presented. The raft is modelled as a thin plate and the piles as interacting non-linear springs. Both the raft and the piles are interacting with the soil which is modelled as an elastic layer. Two sources of non-linearity are accounted for: (i) the unilateral contact at the raft–soil interface and (ii) the non-linear load–settlement relationship of the piles. Both theoretical solutions and experimental results are used to verify that, despite the approximations involved, the proposed method of analysis can provide satisfactory solutions in both linear and non-linear range. © 1998 John Wiley & Sons, Ltd.     

Elastic models for nonlinear response of rigid passive piles

Recent study indicates that the response of rigid passive piles is dominated by elastic pile–soil interaction and may be estimated using theory for lateral piles. The difference lies in that passive piles normally are associated with a large scatter of the ratio of maximum bending moment over maximum shear force and induce a limiting pressure that is ~1/3 that on laterally loaded piles. This disparity prompts this study. This paper proposes pressure‐based pile–soil models and develops their associated solutions to capture response of rigid piles subjected to soil movement. The impact of soil movement was encapsulated into a power‐law distributed loading over a sliding depth, and load transfer model was adopted to mimic the pile–soil interaction. The solutions are presented in explicit expressions and can be readily obtained. They are capable of capturing responses of model piles in a sliding soil owing to the impact of sliding depth and relative strength between sliding and stable layer on limiting force prior to ultimate state. In comparison with available solutions for ultimate state, this study reveals the 1/3 limiting pressure (of the active piles) on passive piles was induced by elastic interaction. The current models employing distributed pressure for moving soil are more pertinent to passive piles (rather than plastic soil flow). An example calculation against instrumented model piles is provided, which demonstrates the accuracy of the current solutions for design slope stabilising piles. Copyright © 2014 John Wiley & Sons, Ltd.     

Negative skin friction on single piles in a layered half-space

Settlement of the surrounding soil due to surcharge placement may give rise to negative skin friction developed in piles. In this paper, a simple discrete element approach using subgrade reaction method is proposed to analyse negative skin friction on single piles. The pile is embedded in a two-layer soil where the upper soil layer undergoes consolidation while the lower soil layer acts as a stiffer bearing stratum. Two different and uncoupled deformation modes, one at the pile shaft and the other at the pile toe have been assumed in the determination of the soil stiffness. The effects of a compressible bearing stratum and embedment length of the pile in the bearing stratum are considered in the analysis. This simple approach is verified by comparison with rigorous methods of modelling the soil as an elastic continuum. Three reported case histories are analysed and the computed results are shown to be in reasonable agreement with the field measurements.     

桩承式围堤对邻近桥梁桩基的影响分析

桩承式围堤是将上部围堤或堆载荷重通过桩筏基础传递到深层较硬的土层,以减少由于围堤或堆载对邻近桩基产生负摩阻力和侧向推力的一种围堤式构筑物。采用基于Mindlin应力解的桩伐基础简化分析方法、弹性和弹塑性三维数值模拟了嘉兴港海盐港区围堤对杭州湾跨海大桥产生的负摩阻力和侧向推力。通过上述3种方法的分析比较,结果表明,采用的简化分析方法与弹性和弹塑性三维数值模拟结果吻合较好,可作为桩承式围堤结构基础的分析和设计方法。     

Boundary element analysis of axially loaded piles embedded in a multi-layered soil

In a field, piles are likely installed in a multi-layered soil. Analysis of axially loaded piles in a multi-layered soil is complicated and deserves more attention. A boundary element method is used in this study to analyze an axially loaded single pile in a multi-layered soil using the solution for vertical and horizontal axisymmetric ring loads in a multi-layered elastic medium. Good and reasonable agreement is obtained between the proposed and published solutions for a single pile in a homogenous soil, a finite soil, and a Gibson soil. The proposed solution is also used to evaluate an axially loaded single pile in a multi-layered (8 layers) soil.     

桩基承台梁受力分析的幂级数解答

将桩基承台梁视为置于弹性地基上的有限长梁,将竖向桩体及承台梁下桩间土体视为刚度不同的弹簧系列,基于Winkler弹性地基梁理论,推导出考虑桩土共同工作的承台梁竖向位移控制微分方程,并给出其幂级数半解析解,进而导得了在集中荷载、外加弯矩及分布荷载共同作用下桩基承台梁的竖向位移、转角、弯矩及剪力的计算公式。最后通过与链杆法、Newmark法的比较,验证了本文幂级数解答的正确性。在此基础上,探讨分析了基桩差异性、承台梁下土体作用、桩径及荷载形式等因素对桩基承台梁受力变形的影响。研究表明：当考虑上述因素影响时,桩基承台梁的竖向变形、弯矩及桩顶反力均发生不同程度的变化,因此,在实际的设计计算中应予以考虑。     

Vertical response of pile raft foundations subjected to tunneling‐induced ground movements in layered soil

A simplified analysis method has been developed to estimate the vertical movement and load distribution of pile raft foundations subjected to ground movements induced by tunneling based on a two‐stage method. In this method, the Loganathan–Polous analytical solution is used to estimate the free soil movement induced by tunneling in the first stage. In the second stage, composing the soil movement to the pile, the governing equilibrium equations of piles are solved by the finite difference method. The interactions between structural members (such as pile–soil, pile–raft, raft–soil, and pile–pile) are modeled based on the elastic theory method of a layered half‐space. The validity of the proposed method is verified through comparisons with some published solutions for single piles, pile groups, and pile rafts subjected to ground movements induced by tunneling. Good agreements between these solutions are demonstrated. The method is also used for a parametric study to develop a better understanding of the behavior of pile rafts influenced by tunneling operation in layered soil foundations. Copyright © 2011 John Wiley & Sons, Ltd.     

层状饱和土体中排桩对简谐荷载隔振效果分析

根据Biot理论,利用已有的传递、透射矩阵法得到层状饱和土体内部受竖向圆形分布荷载作用下的基本解,再由Muki虚拟桩法,建立了频域内层状土-桩的第二类Fredholm积分方程。通过离散方法求解积分方程,得到了评价隔振效果的振幅比。与已知文献结果比较,验证了方法的正确性。数值结果表明：对于同种类型的振源,采用相同的隔振系统,在上软下硬的多层土体中的隔振效果比在上硬下软的土层中要好。采用较长的桩或刚度较大的桩,或桩之间的距离加密都可得到好的隔振效果。     

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.     

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.     

Finite layer analysis of laterally loaded piles in cross-anisotropic soils

This paper presents a finite layer method for the analysis of laterally loaded piles in isotropic and cross-anisotropic layered soils. Excellent agreement is found between the isotropic solutions computed by the finite layer method and the more rigorous finite element method. Some theoretical solutions are presented to demonstrate the effect of soil anisotropy. Two full scale field case histories have been analysed by the method using isotropic and cross-anisotropic soil models.     

Response of rigid piles during passive dragging

This paper develops a three‐layer model and elastic solutions to capture nonlinear response of rigid, passive piles in sliding soil. Elastic solutions are obtained for an equivalent force per unit length p_s of the soil movement. They are repeated for a series of linearly increasing p_s (with depth) to yield the nonlinear response. The parameters underpinning the model are determined against pertinent numerical solutions and model tests on passive free‐head and capped piles. The solutions are presented in non‐dimensional charts and elaborated through three examples. The study reveals the following:

• On‐pile pressure in rotationally restrained, sliding layer reduces by a factor α, which resembles the p‐multiplier for a laterally loaded, capped pile, but for its increase with vertical loading (embankment surcharge), and stiffness of underlying stiff layer: α = 0.25 and 0.6 for a shallow, translating and rotating piles, respectively; α = 0.33–0.5 and 0.8–1.3 for a slide overlying a stiff layer concerning a uniform and a linearly increasing pressure, respectively; and α = 0.5–0.72 for moving clay under embankment loading.
• Ultimate state is well defined using the ratio of passive earth pressure coefficient over that of active earth pressure. The subgrade modulus for a large soil movement may be scaled from model tests.
• The normalised rotational stiffness is equal to 0.1–0.15 for the capped piles, which increases the pile displacement with depth.

The three‐layer model solutions well predict nonlinear response of capped piles subjected to passive loading, which may be used for pertinent design. Copyright © 2016 John Wiley & Sons, Ltd.     

一种半无限土体中圆孔扩张的分析方法

在静压桩贯入问题的研究中,常用无限土体中圆孔扩张法来模拟桩端对土体的扩张。实际上,压桩问题属于半无限问题,必须考虑从无限问题转化到半无限问题后地面边界处应力的差异。针对半无限问题中地表应力的修正,在现有研究的基础上引入了应力函数解答来求解弹性条件下半无限问题,很好地修正了地表应力,得到了相应的解答。与原有的解答相比,提出的解答能够更好地反映半无限的特性,为进一步分析压桩问题奠定了基础。     

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.     

Vertical harmonic vibration of piled raft foundations in layered soils

This paper develops a method to analyze the piled raft foundation under vertical harmonic load. This method takes into account the interactions among the piles, soil, and raft. The responses of the piles and raft are formulated as a series of equations in a suitable way and that of layered soils is simulated with the use of the analytical layer‐element method. Then, according to the equilibrium and continuity conditions at the piles–soil–raft interface, solutions for the piled raft systems are obtained and further demonstrated to be correct through comparing with the existing results. Finally, some examples are given to investigate the influence of the raft, pile length‐diameter ratio, and layering on the response of the piled raft foundations. Copyright © 2017 John Wiley & Sons, Ltd.     

A numerical method for laterally loaded piles

A numerical model for a laterally loaded pile in an elastic continuum is presented. The governing differential equations for vertical piles in a homogeneous and a layered soil are obtained by using variational calculus. Two parameters, k and t, are used in this approach to represent the elastic foundation, and an iterative technique is adopted to obtain a consistent energy solution. Both free and fixed headed piles have been considered. Two kinds of boundary conditions of practical interest at the pile tip, floating tip and clamped tip, are also considered. The proposed method has been validated by comparison of the results with those obtained by other available methods. Typical solutions are presented and recommendations are given for their use in design problems.     

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.     

Variational elastic solution for axially loaded piles in multilayered soil

Most analytical or semi‐analytical solutions of the problem of load‐settlement response of axially loaded piles are based on the assumption of zero radial displacement. These solutions also are only applicable to piles embedded in either a homogeneous or a Gibson soil deposit. In reality, soil deposits consist of multiple soil layers with different properties, and displacements in the radial direction within the soil deposit are not zero when the pile is loaded axially. In this paper, we present a load‐settlement analysis applicable to a pile with circular cross section installed in multilayered elastic soil that accounts for both vertical and radial soil displacements. The analysis follows from the solution of the differential equations governing the displacements of the pile–soil system obtained using variational principles. The input parameters needed for the analysis are the pile geometry and the elastic constants of the soil and pile. We compare the results from the present analysis with those of an analytical solution that considers only vertical soil displacements. The analysis presented in this paper also provides useful insights into the displacement and strain fields around axially loaded piles. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

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.