Elastoplastic multiphase model for simulating the response of piled raft foundations subject to combined loadings

A multiphase model and corresponding computational time‐saving finite element code is proposed in this paper for predicting the settlements experienced by a piled raft foundation when subject to the combined action of vertical and lateral loadings. This model, which is formulated in the framework of an elastoplastic behaviour for the soil and the reinforcing piles as well, explicitly accounts for the shear and flexural behaviour of the latter. Starting from a simple analytical example where all the concepts attached to this model are clearly illustrated, the main stages leading to its finite element implementation are then presented. The numerical tool thus elaborated, is applied to the simulation of a pile‐reinforced strip foundation submitted to a horizontally applied seismic load in addition to a permanent vertical load. One of the key results of such a simulation in terms of design recommendation, lies in the conclusion that, while the shear and flexural contributions of the reinforcement play quite a negligible role in the case of a vertical load (as compared with their axial resistance), they remain absolutely essential for withstanding the seismic lateral loading. Copyright © 2006 John Wiley & Sons, Ltd.     

Three‐dimensional nonlinear finite element analysis of pile groups in saturated porous media using a new transmitting boundary

The dynamic behaviour of pile groups subjected to an earthquake base shaking is analysed. An analysis is formulated in the time domain and the effects of material nonlinearity of soil, pile–soil–pile kinematic interaction and the superstructure–foundation inertial interaction on seismic response are investigated. Prediction of response of pile group–soil system during a large earthquake requires consideration of various aspects such as the nonlinear and elasto‐plastic behaviour of soil, pore water pressure generation in soil, radiation of energy away from the pile, etc. A fully explicit dynamic finite element scheme is developed for saturated porous media, based on the extension of the original formulation by Biot having solid displacement (u) and relative fluid displacement (w) as primary variables (u–w formulation). All linear relative fluid acceleration terms are included in this formulation. A new three‐dimensional transmitting boundary that was developed in cartesian co‐ordinate system for dynamic response analysis of fluid‐saturated porous media is implemented to avoid wave reflections towards the structure. In contrast to traditional methods, this boundary is able to absorb surface waves as well as body waves. The pile–soil interaction problem is analysed and it is shown that the results from the fully coupled procedure, using the advanced transmitting boundary, compare reasonably well with centrifuge data. Copyright © 2007 John Wiley & Sons, Ltd.     

Simple superposition approach for dynamic analysis of piled embedded footings

The effectiveness and accuracy of the superposition method in assessing the dynamic stiffness and damping coefficients (impedance functions) of embedded footings supported by vertical piles in homogeneous viscoelastic soil is addressed. To this end, the impedances of piled embedded footings are compared to those obtained by superposing the impedance functions of the corresponding pile groups and embedded footings treated separately, with the magnitude of the relative average differences being around 10–30%. The results are presented in a set of dimensionless graphs and simple expressions that can be used to estimate the dynamic stiffness and damping of piled embedded footings, provided that the impedance functions of the two individual components are known. This is precisely the reason why the superposition approach studied here is appealing, because such impedance functions for both embedded footings and pile groups are available for a wide range of cases. How to estimate the kinematic response functions of the system when those of the individual components are known is also discussed. To address the problem, parametric analyses performed using a 3D frequency‐domain elastodynamic BEM‐FEM formulation are presented for different pile–soil stiffness contrasts, embedment depths, pile‐to‐pile separations and excitation frequencies. Vertical, horizontal, rocking, and cross‐coupled horizontal‐rocking impedance functions, together with translational and rotational kinematic response functions, are discussed. The results suggest that the superposition concept, in conjunction with a correction strategy as that presented herein, can be employed in geotechnical design. For kinematic effects, the response functions of the embedded footing are found to provide reasonable estimates of the system's behaviour. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

地震荷载下长短桩复合地基的群桩效应系数分析

长短桩复合地基中,地震发生时,短桩在降低长桩所受剪力和弯矩影响中起到重要作用。本研究对弹性地基中的钢管桩基础实行了静态有限元分析,以及动态离心模型试验,通过桩径、桩长、桩间距等参数进行剪切波速,长桩剪力弯矩的对比分析,得到一种新的水平向群桩效应系数计算方法,并通过对模型建筑物的模拟,验证了该方法的有效性与实用性。结果表明,静态有限元数值模拟分析和离心模型试验结果有较好拟合,不同震级作用下通过该方法均能给出较为合理的系数。本文结果可为长短桩复合桩基的抗震性能提供重要参考,实际工程中,通过调整桩径,桩长,短桩数量等参数,可以提出更为合理的设计施工方案。     

Three‐dimensional finite element analyses of passive pile behaviour

Piles may be subjected to lateral soil pressures as a result of lateral soil movements from nearby construction‐related activities such as embankment construction or excavation operations. Three‐dimensional finite element analyses have been carried out to investigate the response of a single pile when subjected to lateral soil movements. The pile and the soil were modelled using 20‐node quadrilateral brick elements with reduced integration. For compatibility between the soil–pile interface elements, 27‐node quadrilateral brick elements with reduced integration were used to model the soil around the pile adjacent to the soil–pile interface. A Mohr–Coulomb elastic–plastic constitutive model with large‐strain mode was assumed for the soil. The analyses indicate that the behaviour of the pile was significantly influenced by the pile flexibility, the magnitude of soil movement, the pile head boundary conditions, the shape of the soil movement profile and the thickness of the moving soil mass. Reasonable agreement is found between some existing published solutions and those developed herein. Copyright © 2005 John Wiley & Sons, Ltd.     

Depth of Fixity of Piles in Clay Under Dynamic Lateral Load

Dynamic experiments were carried out on instrumented model aluminium single piles embedded in clay of different consistencies to study its bending behaviour under lateral loads. Piles with different length to diameter ratios were used. Dynamic lateral load of different magnitudes ranging from 7 to 30 N at wide range of frequencies from 2 to 50 Hz were applied. The load transferred to the pile, pile head displacement and the strain variation along the pile length were measured using a dedicated data acquisition system. Static lateral load tests were also performed to investigate the magnification of dynamic response of piles in clay. It is found that the maximum bending moment due to dynamic load is magnified by about 1.5–4 times in comparison to the static load for short piles but about 9 times for long piles. Depth of fixity and effective pile length is also largely amplified under dynamic loads, thus indicating that a pile which behaves as a flexible pile under static load, may not exhibit flexible behaviour under dynamic load.     

A study of the effect of driving on pre‐bored piles

A finite element model for pile‐driving analysis is developed and used to investigate the behaviour of pre‐bored piles, which are then driven the last 1.25 or 2.25 m to their final design depth. The study was conducted for the case of saturated clays. The model traces the penetration of the pile into the soil and accommodates for large deformations. The non‐linear behaviour of the clay in this study is predicted using the bounding‐surface‐plasticity model, as applied to isotropic cohesive soils. The details of the 3‐D numerical modelling and computational schemes are presented. A significant difference was observed in the pile displacement during driving, and in the computed soil resistance at the pile tip, particularly at the earliest driving stages. No difference in soil resistance at the soil pile interface along the pile shaft was detected between the pre‐bored piles whether driven 1.25 or 2.25 m. Copyright © 2002 John Wiley & Sons, Ltd.     

超长PHC管桩桩顶沉降特性的动静对比分析

通过静载荷试验可直接测到桩顶的荷载-沉降（Q-s）曲线。由管桩内预先埋设的应变计的内力测试结果可计算出土阻力与桩-土相对位移的关系,并进一步做高应变测试和拟合分析,得出了高应变拟合的Q-s曲线。对Q-s曲线作动静结果对比分析,探讨了在深厚软土中的超长PHC管桩的桩顶沉降特性。结果表明,当荷载不大时,高应变拟合的沉降大于静载实测的沉降,但当荷载接近极限值时高应变的沉降小于静载的沉降。结果亦表明,当超长PHC管桩桩身穿过一定深度的好土层、桩端进入全风化或更好的岩层时,不管是静载试验还是高应变动力测试,都很难使土阻力得到充分发挥,此时静载实测的和高应变拟合的Q-s曲线都呈缓变型特征。     

Interaction between different internal length scales in strain localization analysis of fully and partially saturated porous media—the 1‐D case

The paper analyses the interaction between two internal length scales during dynamic strain localization in multiphase porous materials. The first internal length is introduced in the mathematical model by the gradient‐dependent plasticity for the solid skeleton, while the second one is naturally contained in the multiphase model and is due to the seepage process of the water via Darcy's law, which induces a rate‐dependent behaviour of the solid skeleton. Numerical results of a one‐dimensional example of water saturated porous medium demonstrate the competing effect between these two length scales. The porous medium is here treated as a multiphase continuum, with the pores filled by water and air, the last one at constant atmospheric pressure. Copyright © 2005 John Wiley & Sons, Ltd.     

预制静压桩静动载现场试验分析

原位试验是获取桩基设计参数和了解桩基力学性能的最客观、最可靠方法。基于现有疲劳机和千斤顶等试验设备,研制了桩顶静载和动载组合加载装置,为现场静、动载试验解决了一个技术性难题。利用该装置对某工程混凝土预制静压桩进行了模拟交通荷载的现场静、动载试验。通过单桩竖向抗压静载试验和动载试验,分析了静动载对桩身轴力分布、桩身侧摩阻力和基桩沉降的影响及其变化规律。试验结果表明：在静动载作用下桩身侧摩阻力的分布规律基本一致,并且随着振动次数的增加,桩身上部侧摩阻力减小、下部略有增加,但动载循环超过30万次后,侧摩阻力趋于稳定。     

Influence of gas generation in electro‐osmosis consolidation

This paper presents a numerical model for the elasto‐plastic electro‐osmosis consolidation of unsaturated clays experiencing large strains, by considering electro‐osmosis and hydro‐mechanical flows in a deformable multiphase porous medium. The coupled governing equations involving the pore water flow, pore gas flow, electric flow and mechanical deformation in unsaturated clays are derived within the framework of averaging theory and solved numerically using finite elements. The displacements of the solid phase, the pressure of the water phase, the pressure of the gas phase and the electric potential are taken as the primary unknowns in the proposed model. The nonlinear variation of transport parameters during electro‐osmosis consolidation are incorporated into the model using empirical expressions that strongly depend on the degree of water saturation, whereas the Barcelona Basic Model is employed to simulate the elasto‐plastic mechanical behaviour of unsaturated clays. The accuracy of the proposed model is evaluated by validating it against two well‐known numerical examples, involving electro‐osmosis and unsaturated soil behaviour respectively. Two further examples are then investigated to study the capability of the computational algorithm in modelling multiphase flow in electro‐osmosis consolidation. Finally, the effects of gas generation at the anode, the deformation characteristics, the degree of saturation and the time dependent evolution of the excess pore pressure are discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

An experimental study on static and dynamic bending behaviour of piles in soft clay

Static and dynamic lateral load tests were carried out on model aluminium single piles embedded in soft clay to study its bending behaviour. Model aluminium piles with length to diameter ratios of 10, 20, 30 and 40 were used. Static lateral load tests were conducted on piles by rope and pulley arrangement upto failure and load–deflection curves were obtained. Dynamic lateral load tests were carried out for different magnitudes of load ranging from 7 to 30 N at wide range of frequencies from 2 to 50 Hz. The load transferred to the pile, pile head displacement and the strain variation along the pile length were measured using a Data Acquisition System. Safe static lateral load capacity for all piles is interpreted from load–deflection curves. Dynamic characteristics of the soil–pile system were arrived from the acquired experimental data. The soil–pile system behaves predominantly in nonlinear fashion even at low frequency under dynamic load. The displacement amplitude under dynamic load is magnified by 4.5–6.5 times the static deflection for all piles embedded in soft clay. But, the peak magnification factor reduces with an increase in the magnitude of lateral load mainly because of increase of hysteretic damping at very soft consistency. The maximum BM occurs at the fundamental frequency of the soil–pile system. Even the lower part of the pile affects the pile head response to the inertial load applied at the pile head. The maximum dynamic BM is magnified by about 1.5 times the maximum static BM for model piles in tested consistency of clay. The maximum dynamic BM occurs at a depth of about 1.5 times the depth of maximum static BM for model piles, which indicates an increase of active pile length under dynamic load.     

边坡抗滑桩加固的三维有限元计算

本文以王山村滑坡为研究对象,围绕其工程中静力抗滑稳定问题,通过室内试验对影响王山村滑坡稳定性的地质构造、场地工程条件等内在因素进行分析评价。在此基础上,利用大型商业软件ABAQUS对边坡抗滑桩加固模型进行有限元计算分析。通过对加固在边坡模型底部、中部及上部3个常见桩位稳定性系数的计算,得到了3个桩位的稳定性系数。计算结果表明：加固在模型中部桩位的安全系数最高,为1.58。为综合考虑静力作用下坡脚应力集中及动力作用下的坡顶加速度放大效应,设计了加固在边坡中点附近的上部桩位和下部桩位,并分别对其稳定性进行求解,计算结果显示两种桩位都具有较高的安全系数,分别为1.35和1.56。最后通过对模型坡面上5种桩位安全系数的对比,验证了上部桩及下部桩的可行性,可作为工程实践的参考方案。     

Lateral load distributions on grouped piles from dynamic pile‐to‐pile interaction factors

The load distributions of the grouped piles under lateral loads acting from one side of the pile cap could be approximately modeled using the elasticity equations with the assumptions that the underground structure is rigid enough to sustain the loads, and only small deformations of the soils are yielded. Variations of the soil–pile interactions along the depths are therefore negligible for simplicity. This paper presents the analytical modeling using the dynamic pile‐to‐pile interaction factors for 2 × 2 and 2 × 3 grouped piles. The results were found comparative with the experimental and numerical results of other studies. Similar to others' findings, it was shown that the leading pile could carry more static loads than the trailing pile does. For the piles in the perpendicular direction with the static load, the loads would distribute symmetrically with the centerline whereas the middle pile always sustains the smallest load. For steady‐state loads with operating frequencies up to 30 Hz, the pile load distributions would vary significantly with the frequencies. It is interesting to know that designing the pile foundation needs to be cautioned for steady‐state vibrations as they are a problem of machine foundation. However, for transient loads or any harmonic loads acting upon relatively higher frequencies, the pile loads could be regarded as uniformly distributed. It is hoped that the numerical results of this paper will be helpful in the design practice of pile foundation. Copyright © 2008 John Wiley & Sons, Ltd.     

Multiphase model for inclusion‐reinforced geostructures: Application to rock‐bolted tunnels and piled raft foundations

A multiphase model is proposed to describe the mechanical behaviour of geomaterials reinforced by linear inclusions. This macroscopic approach considers the reinforced soil or rock mass as the superposition of continuous media. Equations of motion and constitutive laws of the model are first derived. Its implementation in a finite element computer code is then detailed. A modified implicit algorithm for elastoplastic problems is proposed. The model and its implementation are fully validated for rock‐bolted tunnels (comparison with scale model experiments) and piled raft foundations (comparison with the classical ‘hybrid method’). The Messeturm case history is finally presented to assess the handiness of the approach for real structures. Copyright © 2001 John Wiley & Sons, Ltd.     

Influence of pile installation on adjacent structures

Pile installation leads to significant changes in the main state variables of the surrounding soil. In addition, the installation process may have an influence on adjacent or intersecting structures such as pile grillages. In this paper, three‐dimensional numerical analyses are presented to investigate the effects of pile driving with open or closed cross‐sections on the surrounding soil and on adjacent structures. Two different installation methods are used: quasi‐static pile jacking and vibratory pile driving. The numerical models are evaluated and verified using data from field tests performed in situ during the construction of the quay wall at the container terminal CT4 in Bremerhaven. Two case studies are presented to characterize the main influence factors for additional loading on adjacent structures due to pile installation. Finally, a parametric study is conducted showing the influence of the installation method, pile cross‐section and distance of a pile from an existing structure on the additional loading for this structure. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

砂土中单桩静载室内模型试验及颗粒流数值模拟

通过自行设计的可视化模型箱,进行了单桩静载室内模型试验,考虑了不同桩径、不同土体密实度等影响因素,研究了单桩的沉降模式、桩侧摩阻力和桩端阻力的发挥性状及随沉降的发展模式,并通过拍摄跟踪和图像处理技术,研究了桩端和桩周土体的孔隙率的变化规律;对二维颗粒流程序进行开发,模拟了单桩静载过程中桩端阻力和桩周土体孔隙率的变化情况。结果表明,颗粒流数值模拟能够较好地模拟单桩静载过程,研究成果进一步揭示了单桩静载过程的宏细观机制。