Load distribution in large pile groups under static and dynamic loading

Research on the action of pile groups in resisting lateral loading is usually based on analysis, field and centrifuge tests of small pile groups. The interaction between piles in these groups is modelled by modifying the lateral resistance p–y curves developed for a single pile using row dependent reduction factors or a group factor for the entire group to simulate the effect of soil–pile–soil interaction. The modifying factors for the p–y curves and the appropriate group factors for pile groups are based entirely on static tests and there is no direct verification that these factors are appropriate to handle the dynamic loading of earthquake induced ground motions. In this paper we investigate the interaction effects between piles under static and seismic loading using the computer program VERSAT-P3D, which uses an equivalent linear constitutive model for the soil. The analytical procedure is calibrated using data from a static field load test on a single pile. Several pile groups, 2 × 2, 3 × 3, 4 × 4, 5 × 5, 8 × 8, 10 × 10, 10 × 2 and 15 × 2 were analysed for the study. Each group was subjected to static pushover and earthquake loading and the distribution of static and dynamic shear forces at various lateral displacements were evaluated. The study shows that the distribution of load within a pile group under dynamic loading varies significantly from the distribution under static loading and is strongly load intensity dependent. Current practice assumes that the distributions are similar.     

Nonlinear lateral interaction in pile dynamics

A model for pile lateral response to transient dynamic loading and to harmonic loading is presented allowing for nonlinear soil behaviour, discontinuity conditions at the pile-soil interface and energy dissipation through different types of damping. The approach is used to establish equivalent linear stiffness and damping parameters of single piles as well as dynamic interaction factors for approximate nonlinear analysis of pile groups. The applicability of these parameters to the pile-group analysis was examined, and a reasonable agreement with the direct analysis was found. The superposition technique may be used to analyze the response of small pile groups. Also, the dynamic stiffness of pile groups is greatly affected by both the nonlinear behavior of the soil and the slippage and gapping between the pile and soil. For a basic range of soil and pile parameters, equivalent linear stiffness and damping parameters of single piles and interaction factors for approximate nonlinear analysis are provided.     

土-桩-框架结构非线性相互作用的精细数值模型及其验证

利用有限元软件ABAQUS,建立了土-桩-框架结构非线性相互作用（SSI）的二维精细有限元模型,分别采用记忆型粘塑性嵌套面模型和损伤塑性模型模拟土体和混凝土材料,采用梁单元和rebar单元模拟RC桩基及其内部纵筋,采用接触面对法模拟桩土接触效应,取得了良好的计算效果。将自由场、框架、土-桩-框架结构模型的分析结果和其它成熟的计算软件进行对比,验证了数值模型的有效性。分析发现：桩基外侧靠近承台处的土体的非线性反应很强烈,而桩基内部土体的非线性反应较小,很大程度上只是跟随群桩一起运动。由于桩土动力接触,桩顶的加速度反应可能超出上部结构,并且桩顶的加速度时程曲线上有非常明显的＂针＂状突变。随着地震动强度的增加,上部框架逐渐表现出单自由度体系的动力特征,加速度反应谱有从多个波峰退化为单一波峰的趋势。     

Pile–soil–pile interaction in pile groups with batter piles under dynamic loads

A simple analytical solution is developed for computing the dynamic interaction tensor for floating pile groups with batter piles. For this purpose, the governing differential equations are derived for an unloaded batter floating pile closely spaced to another loaded pile with the same properties. The reaction of soil against pile deformation is modeled by the springs and dashpots along the length of the pile. The soil is assumed linear viscous elastic and the pile behavior is linear elastic. The closed form solutions of governing equations are obtained using appropriate boundary conditions. The results are verified and compared with rigorous and approximate analytical solutions for vertical piles. The proposed method can be readily applied by engineers in the design of pile groups with batter piles.     

3D numerical simulation of flow field around twin piles

In this study to identify the flow pattern and local scour mechanism around pile groups, the flow field was simulated using FLOW-3D software. A pair of pile on a flat-bed channel with side by side and tandem arrangements was investigated. To establish Navier–Stokes equations, the RNGk-ε turbulence model was used and the results were verified using experimental data. In case of FLOW-3D capability, it was found that the software was able to properly simulate the expected interaction between the pile groups. The results of flow field simulation showed that Reynolds number and the pile spacing are the most influential variables in forming vortices. The flow around tandem pile and the downward flow around wake vortices were more intense and complicate in comparison with side by side arrangements and single pile.     

A model for the 3D kinematic interaction analysis of pile groups in layered soils

The paper presents a numerical model for the analysis of the soil–structure kinematic interaction of single piles and pile groups embedded in layered soil deposits during seismic actions. A finite element model is considered for the pile group and the soil is assumed to be a Winkler‐type medium. The pile–soil–pile interaction and the radiation problem are accounted for by means of elastodynamic Green's functions. Condensation of the problem permits a consistent and straightforward derivation of both the impedance functions and the foundation input motion, which are necessary to perform the inertial soil–structure interaction analyses. The model proposed allows calculating the internal forces induced by soil–pile and pile‐to‐pile interactions. Comparisons with data available in literature are made to study the convergence and validate the model. An application to a realistic pile foundation is given to demonstrate the potential of the model to catch the dynamic behaviour of the soil–foundation system and the stress resultants in each pile. Copyright © 2009 John Wiley & Sons, Ltd.     

A Study of Piles during Earthquakes: Issues of Design and Analysis

The seismic response of pile foundations is a very complex process involving inertial interaction between structure and pile foundation, kinematic interaction between piles and soils, seismically induced pore-water pressures (PWP) and the non-linear response of soils to strong earthquake motions. In contrast, very simple pseudo-static methods are used in engineering practice to determine response parameters for design. These methods neglect several of the factors cited above that can strongly affect pile response. Also soil–pile interaction is modelled using either linear or non-linear springs in a Winkler computational model for pile response. The reliability of this constitutive model has been questioned. In the case of pile groups, the Winkler model for analysis of a single pile is adjusted in various ways by empirical factors to yield a computational model for group response. Can the results of such a simplified analysis be adequate for design in all situations?The lecture will present a critical evaluation of general engineering practice for estimating the response of pile foundations in liquefiable and non-liquefiable soils during earthquakes. The evaluation is part of a major research study on the seismic design of pile foundations sponsored by a Japanese construction company with interests in performance based design and the seismic response of piles in reclaimed land. The evaluation of practice is based on results from field tests, centrifuge tests on model piles and comprehensive non-linear dynamic analyses of pile foundations consisting of both single piles and pile groups. Studies of particular aspects of pile–soil interaction were made. Piles in layered liquefiable soils were analysed in detail as case histories show that these conditions increase the seismic demand on pile foundations. These studies demonstrate the importance of kinematic interaction, usually neglected in simple pseudo-static methods. Recent developments in designing piles to resist lateral spreading of the ground after liquefaction are presented. A comprehensive study of the evaluation of pile cap stiffness coefficients was undertaken and a reliable method of selecting the single value stiffnesses demanded by mainstream commercial structural software was developed. Some other important findings from the study are: the relative effects of inertial and kinematic interactions between foundation and soil on acceleration and displacement spectra of the super-structure; a method for estimating whether inertial interaction is likely to be important or not in a given situation and so when a structure may be treated as a fixed based structure for estimating inertial loads; the occurrence of large kinematic moments when a liquefied layer or naturally occurring soft layer is sandwiched between two hard layers; and the role of rotational stiffness in controlling pile head displacements, especially in liquefiable soils. The lecture concludes with some recommendations for practice that recognize that design, especially preliminary design, will always be based on simplified procedures.     

Nonlinear analysis for dynamic lateral pile response

An analysis of pile lateral response to transient dynamic loading and to harmonic loading is presented allowing for nonlinear soil behavior, discontinuity conditions at the pile-soil interface and energy dissipation through different types of damping. Furthermore, the effect of neighbouring piles is taken into account for piles in a group. The validity of the approach was examined and a reasonable agreement with field tests and more rigorous solutions was found. Equivalent linear stiffness and damping parameters of single piles and interaction factors for approximate nonlinear analysis are presented.     

Dynamic analysis of piles and pile groups embedded in homogeneous soils

A boundary element formulation for the dynamic analysis of axially and laterally loaded single piles and pile groups is presented. The piles are represented by compressible beam-column elements and the soil as a hysteretic elastic half-space. The governing equations of motion for the pile domain have been solved exactly for distributed periodic loading intensities. These solutions are then coupled with a numerical solution for the motion of the soil domain by satisfying equilibrium and compatibility at the pile-soil interface. The results obtained from the analysis compare favourably with those from alternative analyses, e.g. finite element, but at greatly reduced computational costs.     

Large‐scale 3D inversion of potential field data

Inversion of gravity and/or magnetic data attempts to recover the density and/or magnetic susceptibility distribution in a 3D earth model for subsequent geological interpretation. This is a challenging problem for a number of reasons. First, airborne gravity and magnetic surveys are characterized by very large data volumes. Second, the 3D modelling of data from large‐scale surveys is a computationally challenging problem. Third, gravity and magnetic data are finite and noisy and their inversion is ill posed so regularization must be introduced for the recovery of the most geologically plausible solutions from an infinite number of mathematically equivalent solutions. These difficulties and how they can be addressed in terms of large‐scale 3D potential field inversion are discussed in this paper. Since potential fields are linear, they lend themselves to full parallelization with near‐linear scaling on modern parallel computers. Moreover, we exploit the fact that an instrument’s sensitivity (or footprint) is considerably smaller than the survey area. As multiple footprints superimpose themselves over the same 3D earth model, the sensitivity matrix for the entire earth model is constructed. We use the re‐weighted regularized conjugate gradient method for minimizing the objective functional and incorporate a wide variety of regularization options. We demonstrate our approach with the 3D inversion of 1743 line km of FALCON gravity gradiometry and magnetic data acquired over the Timmins district in Ontario, Canada. Our results are shown to be in good agreement with independent interpretations of the same data.     

A numerical model for the dynamic analysis of inclined pile groups

The paper presents a numerical model for the dynamic analysis of pile groups with inclined piles in horizontally layered soil deposits. Piles are modelled with Euler–Bernoulli beams, while the soil is supposed to be constituted by independent infinite viscoelastic horizontal layers. The pile–soil–pile interaction as well as the hysteretic and geometric damping is taken into account by means of two‐dimensional elastodynamic Green's functions. Piles cap is considered by introducing a rigid constraint; the condensation of the problem permits a consistent derivation of both the dynamic impedance matrix of the soil–foundation system and the foundation input motion. These quantities are those used to perform inertial soil–structure interaction analyses in the framework of the substructure approach. Furthermore, the model allows evaluating the kinematic stress resultants in piles resulting from waves propagating in the soil deposit, taking into account the pile–soil–pile interactions. The model validation is carried out by performing accuracy analyses and comparing results in terms of dynamic impedance functions, kinematic response parameters and pile stress resultants, with those furnished by 3D refined finite element models. To this purpose, classical elastodynamic solutions are adopted to define the soil–pile interaction problem. The model results in low computational demands without significant loss of precision, compared with more rigorous approaches or refined finite element models. Copyright © 2015 John Wiley & Sons, Ltd.     

强震活动有限元模型研究及其初步应用--以西南地区为例

在强震成组孕育与群体活动研究的基础上，本文基于有限元方法，初步建立了西南地区有限元动力学模型，并讨论了因发生地震而产生的应力变化对整个西南地区的应力调整情况。初步结果表明，许多强震均发生在应力增强区。因此，强震活动有限元模型的建立对判定未来强震危险区有一定作用。     

Nonlinear 3D finite element analysis of soil–pile–structure interaction system subjected to horizontal earthquake excitation

The dynamic response of a seismic soil–pile–structure interaction (SSPSI) system is investigated in this paper by conducting nonlinear 3D finite element numerical simulations. Nonlinear behaviors such as non-reflecting boundary condition and soil–pile–structure interaction modeled by the penalty method have been taken into account. An equivalent linear model developed from the ground response analysis and the modified Drucker–Prager model are separately used for soil ground. A comparison of the two models shows that the equivalent linear soil model results in an underestimated acceleration response of the structure under this ground shaking and the soil behavior should be considered as a fully-nonlinear constitutive model in the design process of the SSPSI system. It was also observed that the dynamic response of the system is greatly affected by the nonlinearity of soil–pile interface and is not sensitive to the dilation angle of the soil. Furthermore, the effect of the presence of pile foundations on SSPSI response is also analyzed and discussed.     

Numerical modeling of local scour of non-uniform graded sediment for two arrangements of pile groups

A three-dimensional(3D) non-hydrostatic numerical model is established to investigate local scour around four aligned circular piles in uniform and non-uniform sediment mixtures and to provide information for improving scour countermeasures design. In the current study, unsteady Reynolds averaged Navier-Stokes(URANS) equations along with a Re-normalization Group(RNG) k-ε model were applied to simulate the flow field. A non-uniform sediment transport model was applied to estimate the bedload tran...     

Seismic response of tall building considering soil-pile-structure interaction

The seismic behavior of tall buildings can be greatly affected by non-linear soil-pile interaction during strong earthquakes. In this study a 20-storey building is examined as a typical structure supported on a pile foundation for different conditions: (1) rigid base, i.e. no deformation in the foundation: (2) linear soil-pile system; and (3) nonlinear soil-pile system. The effects of pile foundation displacements on the behavior of tall building are investigated, and compared with the behavior of buildings supported on shallow foundation. With a model of non-reflective boundary between the near field and far field, Novak’s method of soil-pile interaction is improved. The computation method for vibration of pile foundations and DYNAN computer program are introduced comprehensively. A series of dynamic experiments have been done on full-scale piles, including single pile and group, linear vibration and nonlinear vibration, to verify the validity of boundary zone model.     

基于FLAC3D路桥不稳定边坡治理工程的动力响应研究

抗滑桩广泛应用于边坡支护工程,但路桥不稳定边坡抗滑桩对其进行加固时,其在地震作用下的动力响应问题仍未定论。以道真至瓮安高速公路河槽大桥不稳定边坡治理工程为依托,以SIMQKE_GR软件拟合地震设计反应谱,利用FLAC3D有限差分软件建立数值模型,对比地震作用下抗滑桩等支挡结构设立与否对路桥不稳定边坡的动力响应变化规律的影响。结果表明:（1）加速度放大系数无论是沿坡内还是抗滑桩,其值沿竖向均存在一定的震荡变化,但在抗滑桩支护情况下,其震荡幅度明显变小,加速度放大系数变化更平稳。（2）速度放大系数随着高度的增加逐渐减小,未加抗滑桩时速度放大系数在顶层附近出现大幅度波动,添加了抗滑桩的情况下其震荡幅度明显趋缓,变化更稳定。（3）坡体在施加抗滑桩后,治理效果明显,残余位移最大值由无抗滑桩的16.9 cm变为有抗滑桩的1 cm,但最大值均位于边坡表层碎石土和粉质黏土附近。     

基于多卫星平台永久散射体雷达干涉提取三维地表形变速度场

永久散射体雷达干涉(PSI)技术及其应用于区域地表形变监测已成为雷达遥感领域的研究热点之一.使用单一卫星平台所获取的单侧视SAR影像时间序列进行PSI分析,仅能获取沿雷达视线(LOS)方向的一维地表位移信息.本文提出了基于多平台永久散射体雷达干涉提取三维地表形变速度场的模型与算法,其基本策略是:首先针对每一卫星平台的SAR影像时间序列进行PSI分析,并计算各地面目标沿LOS向的位移速度值,然后联合各平台所对应的LOS向位移速度值进行建模,并基于最小二乘方法解算各地面目标的三维位移速度分量.实验选取天津市西北部作为测试区,使用2007—2010年所获取的39幅TerraSAR-X影像、23幅ENVISAT ASAR影像和16幅ALOS PALSAR影像进行分析,经联合解算得到了该测试区域的垂直位移速度场以及南北向和东西向水平位移速度分量.与地面水准和已有GPS观测结果对比分析表明:多平台PSI的垂直位移速度场精度可达毫米级,而其水平位移速度分量与已有GPS结果基本一致.多平台PSI分析无需引入任何外部形变参考信息,便可以实现形变场的偏差校准和三维形变场的恢复.     

Simplified discrete systems for dynamic analysis of structures on footings and piles

A simplified discrete system in the form of a simple oscillator is developed to simulate the dynamic behavior of a structure founded through footings or piles on compliant ground, under harmonic excitation. Exact analytical expressions for the fundamental natural period and the corresponding damping coefficients of the above system are derived, as function of geometry and the frequency-dependent foundation impedances. In an effort to quantify the coupling between swaying and rocking oscillations in embedded foundations such as piles, the reference system is translated from the footing–soil interface to the depth where the resultant soil reaction is applied, to ensure a diagonal impedance matrix. The resulting eccentricity is a measure of the coupling effect between the two oscillation modes. The amounts of radiation damping generated from a single pile and a surface footing are evaluated. In order to compare the damping of a structure on a surface footing and a pile, the notion of static and geometric equivalence is introduced. It is shown that a pile may generate significantly higher radiation damping than an equivalent footing, thus acting as an elementary protective system against seismic action.     

A lumped parameter model for time‐domain inertial soil‐structure interaction analysis of structures on pile foundations

The paper presents a lumped parameter model for the approximation of the frequency‐dependent dynamic stiffness of pile group foundations. The model can be implemented in commercial software to perform linear or nonlinear dynamic analyses of structures founded on piles taking into account the frequency‐dependent coupled roto‐translational, vertical, and torsional behaviour of the soil‐foundation system. Closed‐form formulas for estimating parameters of the model are proposed with reference to pile groups embedded in homogeneous soil deposits. These are calibrated with a nonlinear least square procedure, based on data provided by an extensive non‐dimensional parametric analysis performed with a model previously developed by the authors. Pile groups with square layout and different number of piles embedded in soft and stiff soils are considered. Formulas are overall well capable to reproduce parameters of the proposed lumped system that can be straightforwardly incorporated into inertial structural analyses to account for the dynamic behaviour of the soil‐foundation system. Some applications on typical bridge piers are finally presented to show examples of practical use of the proposed model. Results demonstrate the capability of the proposed lumped system as well as the formulas efficiency in approximating impedances of pile groups and the relevant effect on the response of the superstructure.     

三维频率域可控源电磁反演研究

对于三维可控源电磁,反演计算效率、张量测量、旁侧效应以及阴影效应是目前研究的热点.本文正演采用基于库仑规范条件的耦合势有限体积算法,反演采用有限内存BFGS(L-BFGS)算法.合成数据反演结果表明:(1)有限内存BFGS法比非线性共轭梯度法,在反演计算效率上具有一定的优势,更适合求解大规模三维可控源电磁反演问题.(2)张量可控源电磁法相对于标量可控源电磁法,前者在模型分辨率上优于后者.(3)在某个区域无法布置测网的情况下,我们可利用旁侧效应在异常体周围布置测网进行三维反演,从而获得真实异常体的信息.同时,为避免阴影效应,我们应在测网外增加可控源电磁控制点,使得三维反演的数据更加完备.