Beam–solid contact formulation for finite element analysis of pile–soil interaction with arbitrary discretization

This paper presents an embedded beam formulation for discretization independent finite element (FE) analyses of interactions between pile foundations or rock anchors and the surrounding soil in geotechnical and tunneling engineering. Piles are represented by means of finite beam elements embedded within FEs for the soil represented by 3D solid elements. The proposed formulation allows consideration of piles and pile groups with arbitrary orientation independently from the FE discretization of the surrounding soil. The interface behavior between piles and the surrounding soil is represented numerically by means of a contact formulation considering skin friction as well as pile tip resistance. The pile–soil interaction along the pile skin is considered by means of a 3D frictional point‐to‐point contact formulation using the integration points of the beam elements and reference points arbitrarily located within the solid elements as control points. The ability of the proposed embedded pile model to represent groups of piles objected to combined axial and shear loading and their interactions with the surrounding soil is demonstrated by selected benchmark examples. The pile model is applied to the numerical simulation of shield driven tunnel construction in the vicinity of an existing building resting upon pile foundation to demonstrate the performance of the proposed model in complex simulation environments. Copyright © 2014 John Wiley & Sons, Ltd.     

Three dimensional elasto‐plastic interface for embedded beam elements with interaction surface for the analysis of lateral loading of piles

This paper presents a numerical formulation for a three dimensional elasto‐plastic interface, which can be coupled with an embedded beam element in order to model its non‐linear interaction with the surrounding solid medium. The formulation is herein implemented for lateral loading of piles but is able to represent soil‐pile interaction phenomena in a general manner for different types of loading conditions or ground movements. The interface is formulated in order to capture localized material plasticity in the soil surrounding the pile within the range of small to moderate lateral displacements. The interface is formulated following two different approaches: (i) in terms of beam degrees of freedoms; and (ii) considering the displacement field of the solid domain. Each of these alternatives has its own advantages and shortcomings, which are discussed in this paper. The paper presents a comparison of the results obtained by means of the present formulation and by other well‐established analysis methods and test results published in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Analysis of lateral loading of pile groups using embedded beam elements with interaction surface

The numerical simulation of soil-pile interaction problems, by means of full 3D finite element models, involves a large number of degrees of freedom (DOF) and difficulties during the mesh generation process. In order to reduce the unknowns and simplify and properly analyze such class of geotechnical problems, the so-called embedded beam elements (EBE) have recently been developed. In a preceding contribution of the authors, an improved EBE formulation, which brings into play the soil-pile interaction surface, was proposed with the aim to localize material plasticity in the soil surrounding the pile. This embedded beam model couples two different finite elements, each described by distinct kinematics (ie, solid and beam). The coupling is incorporated in the formulation by means of kinematical constrains established over the solid and beam displacement fields on the interaction surface. One of the main advantages of the embedded elements is that the addition of beams structural members immersed within the 3D soil model does not represent a constraint for the solid mesh, which can be adopted independently from the beam mesh. In this paper, the lateral loading of pile groups is studied by means of the proposed EBE approach with elasto-plastic interfaces. In order to represent a rigid cap, a master node and a special set of kinematical restrictions are incorporated into the formulation. The paper presents results obtained by means of the present formulation compared against other well-established analysis methods and test results published in the literature, for both elastic and elasto-plastic cases.     

Three-dimensional finite element analysis for soil slopes stabilisation using piles

This paper presents the analytical methods of slope-stabilising piles using the three-dimensional (3-D) finite element (FE) analysis with the strength reduction method (SRM). This 3-D FE model is employed to overcome the limitations observed in two-dimensional (2-D) FE analysis. The solutions obtained from 3-D FE analyses are verified to be less conservative in this paper. The 3-D analysis is considered to be of particular importance to pile-slope problems. The soil that flows between piles cannot be taken account properly in the 2-D FE analysis. The method adopted in this paper can avoid the assumption of soil movement and the pressure distribution along the piles subjected to soil movement. The numerical analysis employs the Mohr–Coulomb failure criterion with the strength reduction technique for soil and an elastic member for piles. The spacing effect of the pile is considered in the 3-D model, the S/D (S: centre to centre, D: diameter of pile) ratio, equal to 4.0, is found to be equivalent to the single pile stabilisation. The middle portion of the slope is identified as the optimal location to place the piles. The proper length of the pile, which can be used to stabilise the slope, is also examined using 3-D FE analyses. It is concluded that L/H greater or equal 0.70 is recommended (L: pile length, H: slope height). The numerical analyses are conducted based on a coupled analysis, which simultaneously considers both the slope stability and the pile response. The failure mechanisms of the pile-slope system subjected to the pile locations, pile head conditions and pile length are each discussed. The contact pressure, shear force and moment along the piles are presented to illustrate the pile stabilising mechanism herein.     

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.     

基于高性能有限单元的单桩稳定性分析法

现行的桩基设计方法主要基于线弹性理论及采用半经验假定,难以准确地检验长桩在土体非线性条件下的稳定性。基于非线性有限单元分析理论,提出了高性能桩单元分析法用于非线性分析,可直接检验单桩稳定性且无需假定桩的计算长度系数。在桩单元推导过程中,通过整合在单元内部的连续弹簧以考虑土-结构相互作用（SSI）,能够大幅提升计算效率。使用牛顿-拉夫逊迭代法进行迭代运算,利用推导的相应单元切线刚度矩阵预测位移,并通过割线关系减少每一步迭代中产生的误差,在桩的大变形条件下采用更新拉格朗日法确定平衡条件。算例验证表明,桩单元模型在考虑土体非线性条件下,能高效、可靠地对单桩进行分析和设计。     

Thermo-hydro-mechanical response of a large piled raft equipped with energy piles: a parametric study

This paper presents the results of a parametric study in which a series of fully coupled, 3-dimensional thermo-hydro-mechanical Finite Element (FE) analyses has been conducted to investigate the effects of the thermal changes imposed by the regular performance of a GSHP system driven by energy piles on a very large piled raft. The FE simulation program has been focused mainly on the evaluation of the following crucial aspects of the energy system design: the assessment of the soil–pile–raft interaction effects during thermal loading conditions; the quantification of the influence of the thermal properties of the soil and of the geometrical layout of the energy piles on the soil–foundation system response, and the evaluation of the influence of the active pile spacing on the thermal performance of the GSHP–energy pile system. The results of the numerical simulations show that the soil–pile–raft interaction effects can be very important. In particular, the presence of a relatively rigid raft in direct contact with the soil is responsible for axial load variations in inactive piles of the same order of those experienced by the thermo-active piles, even when the latter are relatively far and temperature changes in inactive piles are small. As far as the effect of pile spacing is concerned, the numerical simulations show that placing a high number of energy piles in a large piled raft with relatively small pile spacings can lead to a significant reduction of the overall heat exchange from the piles to the soil, thus reducing the thermal efficiency of the system.     

Numerical simulations of landslide-stabilizing piles: a remediation project in Söke,Turkey

A catastrophic landslide following a rainy season occurred in the backyard of a school building in Söke, Turkey. The landslide caused property damage and adversely affected the present forest cover. Immediately after the landslide, double-row stabilizing piles were designed and constructed based on the findings of two-dimensional (2D) finite element (FE) analyses to take an urgent precaution. To remedy the problem, pile displacements were monitored using inclinometers, and it was observed that the measured displacements were greater than the values calculated in the design stage. Accordingly, two different three-dimensional (3D) numerical FE models were used in tandem with the inclinometer data to determine the load transfer mechanism. In the first model, numerical analyses were made to predict the pile displacements, and while the model predicted successfully the displacement of the piles constructed in the middle with reasonable accuracy, it failed for the corner piles. In the second model, the soil load transfer between piles was determined considering the sliding mass geometry, the soil arching mechanism and the group interaction between adjacent piles. The results of the second model revealed that the middle piles with large displacements transferred their loads to the corner piles with smaller displacements. The generated soil loads, perpendicular to the sliding direction, restricted pile deformations and piles with less displacement were subjected to greater loads due to the bowl-shaped landslide. A good agreement between the computed pile displacements and inclinometer data indicates that the existing soil pressure theories should be improved considering the position of the pile in the sliding mass, the depth and deformation modulus of stationary soil, the relative movement between the soil and piles and the relative movement of adjacent piles.     

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.     

Expanded superposition method for impedance functions of inclined‐pile groups

This paper presents a superposition method expanded for computing impedance functions (IFs) of inclined‐pile groups. Closed‐form solutions for obtaining horizontal, vertical, and rocking IFs, estimated by using pile‐to‐pile interaction factors, are proposed. IFs of solitary inclined piles, crossed IFs, and explicit incorporation of compatibility conditions for pile‐head movements are also appropriately taken into consideration. All of these factors should be known in advance and will be computed and shown for the most relevant cases. The accuracy of the proposed closed‐form solutions is verified for 2 × 2 and 3 × 3 square inclined‐pile groups embedded in an isotropic viscoelastic homogeneous half‐space soil medium, with hysteretic damping. The pile‐to‐pile interaction factors are computed by means of a three‐dimensional time‐harmonic boundary elements–finite elements coupling formulation. The results indicate that the IFs obtained from the proposed method are in good agreement with those obtained from the coupling formulation. Furthermore, crossed vertical‐rocking IFs of solitary piles need to be appropriately considered for obtaining rocking IFs when the number of piles is small. Copyright © 2015 John Wiley & Sons, Ltd.     

考虑基坑开挖影响的群桩基础竖向承载性状数值分析

对土体采用Mohr-Coulomb弹塑性本构模型,用接触面单元模拟桩-土相互作用,利用ABAQUS建立桩筏基础--地基--基坑开挖三维有限元分析模型。对基坑开挖影响下的群桩基础竖向承载性状进行了分析,讨论了桩顶反力分布、桩身轴力、桩侧摩阻力以及开挖引起的桩身水平位移及其弯矩的变化规律,并进行了考虑基坑开挖与不考虑基坑开挖的群桩基础竖向承载性状的对比分析。通过研究,取得了基坑开挖对高层建筑桩筏基础影响的基本认识,这些认识对于改进桩筏基础设计理论有一定的参考意义。     

Dynamic analysis of piles and pile groups embedded in non-homogeneous soils

A hybrid boundary element formulation for the steady state analysis of piles and pile groups embedded in a soil stratum in which the modulus increases linearly with depth is presented. The piles are represented by compressible columns or flexible beams and the soil as a hysteretic, layered medium. The explicit Green's function corresponding to dynamic loads in the interior of a layered stratum, developed earlier by Kausel is used in the study. The governing differential equations for the pile domain are solved for a distributed periodic loading intensity and those for the soil domain by a system of boundary elements at the pile-soil interface. These are then assembled into a system of algebraic equations by satisfying interface equilibrium and compatibility. The results of the analysis have been compared against those from alternative formulations, e.g. finite elements, and confirm the accuracy of the proposed formulation. Representative results for single piles and pile groups are presented.     

A modulus‐multiplier approach for non‐linear analysis of laterally loaded pile groups

A modulus‐multiplier approach, which applies a reduction factor to the modulus of single pile p–y curves to account for the group effect, is presented for analysing the response of each individual pile in a laterally loaded pile group with any geometric arrangement based on non‐linear pile–soil–pile interaction. The pile–soil–pile interaction is conducted using a 3D non‐linear finite element approach. The interaction effect between piles under various loading directions is investigated in this paper. Group effects can be neglected at a pile spacing of 9 times the pile diameter for piles along the direction of the lateral load and at a pile spacing of 6 times the pile diameter for piles normal to the direction of loading. The modulus multipliers for a pair of piles are developed as a function of pile spacing for departure angle of 0, 90, and 180sup>/sup> with respect to the loading direction. The procedure proposed for computing the response of any individual pile within a pile group is verified using two well‐documented full‐scale pile load tests. Copyright © 2006 John Wiley & Sons, Ltd.     

堆载下被动桩与土体相互作用的FLAC三维分析

被动桩问题是近年来岩土工程领域的一个研究热点,但是对于堆载下桩、土之间复杂的相互作用一直缺乏系统的三维分析。本文采用FLAC3D建立了有限差分模型,对单排桩三维工作性状进行分析,重点研究堆载条件、桩身刚度及土层分布对桩身位移和桩侧土压力的影响情况,并籍此对软土地基的桩、土共同作用机理加以阐述,得出一些有益结论。分析表明,软土地基中桩侧土压力的分布可简化为线性模式,本文对此进行了线性拟合。     

A three dimensional embedded beam element for reinforced geomaterials

This paper presents the formulation and verification of a 3D embedded beam element, which is intended for numerical modelling of three dimensional problems concerned by reinforced geomaterials. This element permits analysis of reinforced geomaterial structures with simplified meshes, that do not need to account for reinforcement orientation. The paper is composed of four sections. Section 1 discusses the need for the development of a particular beam element for soil reinforcement, which can be easily used in practical applications. Section 2 describes the mathematical formulation of this element, while Section 3 deals with its verification on various examples. Section 4 illustrates an application of this element by analysing the behaviour of a group of micropiles containing inclined elements and subjected to lateral loading. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

Three-dimensional finite element study of a single pile response to multidirectional lateral loadings incorporating the simplified state-dependent dilatancy model

Waves and winds can induce lateral loads on piles, which are often multidirectional. The objective of this study is to investigate the response of a single pile subjected to unidirectional and multidirectional lateral loadings using the finite element analysis program ABAQUS. A simplified version of the state-dependent dilatancy model was implemented and embedded into the program to simulate the behavior of the soil around the pile. The results of the analyses indicate that the lateral resistance of the pile along one horizontal direction under multidirectional loading is lower than that under unidirectional loading. The degree of reduction of the resistance increases with the aspect ratio of the displacement path at the pile head. The directions of the force increment vector and the displacement increment vector are generally non-coaxial under multidirectional loading. The soil-pile interaction and soil responses under multidirectional loading are also significantly different than those under unidirectional loading.     

软土地层高承台桥梁群桩基础横向承载特性研究

高承台群桩基础是高速铁路桥梁基础的一种常用形式,受到风、地震等荷载作用影响,常常需要承受较大的横向荷载。采用室内物理模型试验和三维有限元程序ABAQUS对软土地层中单桩、群桩的横向承载特性进行了研究,软土采用修正剑桥黏土本构模型,试验结果与有限元计算结果吻合较好。群桩研究方案包括了桩数的变化以及桩间距的变化。结果表明,群桩基础的基桩平均横向承载力（总承载力/桩数）较单桩基础显著增加,且水平荷载方向桩间距越大,其横向承载力越大;群桩基础基桩受力存在三维空间效应,不同位置基桩受力大小排序为角桩最大,其次为边桩,最小为中间桩,弯矩极值差异可达20%,群桩基础桩周土影响范围距外围基桩边缘净距离约为16D (D为桩径)。桩与桩相互影响效应对群桩水平承载不利,承台约束效应对水平承载有利。探讨了考虑上述两种效应的群桩效应系数计算方法,通过计算验证了该方法在软土地区高承台群桩基础横向承载力计算中的适用性。     

Method of initial parameters for laterally loaded piles embedded in layered soils

The method of initial parameters (MIP) was originally developed to solve the problem of a beam on an elastic foundation with applied concentrated forces along the span, which introduce discontinuities in the mathematical formulation of the problem. MIP is modified in this paper so that it can be used for solving the problem of a laterally loaded pile with discontinuities due to soil layering along the length of the pile. In this paper, the basis of MIP is outlined, and its use to find the deflection, slope, bending moment and shear force of laterally loaded piles is illustrated. Example problems of laterally loaded piles embedded in multi-layered soil media are provided.