Dynamic stiffness of deep foundations with inclined piles

The influence of inclined piles on the dynamic response of deep foundations and superstructures is still not well understood and needs further research. For this reason, impedance functions of deep foundations with inclined piles, obtained numerically from a boundary element–finite element coupling model, are provided in this paper. More precisely, vertical, horizontal, rocking and horizontal–rocking crossed dynamic stiffness and damping functions of single inclined piles and 2 × 2 and 3 × 3 pile groups with battered elements are presented in a set of plots. The soil is assumed to be a homogeneous viscoelastic isotropic half‐space and the piles are modeled as elastic compressible Euler–Bernoulli beams. The results for different pile group configurations, pile–soil stiffness ratios and rake angles are presented. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

多桩型复合地基作用机理与动力特性研究

对由碎石桩和CFG桩构成的多桩型复合地基的作用机理进行分析,通过数值模拟,对多桩型复合地基的动力特性进行研究,探讨桩型配比、桩径、桩长、CFG桩桩体刚度和碎石桩桩体渗透性等设计参数对多桩型复合地基动力特性的影响。研究结果表明:相同条件下地震期多桩型复合地基的动变形小于碎石桩复合地基而大于CFG桩复合地基,震后沉降量相对较小,在工程设计时碎石桩与CFG桩的桩型配比宜为4∶5;随桩体长度、桩体直径和CFG桩刚度的增加,多桩型复合地基地震期的竖向动变形逐渐减小;随碎石桩桩体渗透性的增加,多桩型复合地基中的超动孔隙水压力减小,震后沉降量降低。     

Efficient analysis of pile-group effect on seismic stiffness and strength design of buildings

A new efficient method is developed for the analysis of pile-group effects on the seismic stiffness and strength design of buildings with pile foundations. An efficient continuum model consisting of a dynamic Winkler-type soil element and a pile is used to express the dynamic behavior of the structure-pile-soil system with only a small numerical error. The pile-group effect is taken into account through the influence coefficients among piles which are defined for interstory drifts and pile-head bending moments. It is shown that, while the pile-group effect reduces the interstory drift of buildings in general, it may increase the bending moment of piles at the head. This means that the treatment without the pile-group effect results in the conservative design for super-structures and requires a revised member design for piles.     

Dynamic response of pile groups with different configurations

A general methodology is outlined for a complete seismic soil—pile-foundation—structure interaction analysis. A Beam-on-Dynamic-Winkler-Foundation (BDWF) simplified model and a Green's-function-based rigorous method are utilized in determining the dynamic response of single piles and pile groups. The simplified model is validated through comparisons with the rigorous method. A comprehensive parameter study is then performed on the effect of pile group configuration on the dynamic impedances of pile foundations. Insight is gained into the nature of dynamic pile—soil—pile interaction. The results presented herein may be used in practice as a guide in obtaining the dynamic stiffness and damping of foundations with a large number of piles.     

液化场地桥梁群桩-土耦合体系强震反应分析

针对振动台试验,采用u-p形式控制方程表述饱和砂土的动力属性,选用土的多屈服面塑性本构模型刻画饱和砂土和黏土的力学特性,引入非线性梁-柱单元模拟桩,建立试验受控条件下液化场地群桩-土强震相互作用分析的三维有限元模型,并通过试验结果验证数值建模途径与模拟方法的正确性。以实际工程中常用的2×2群桩为例,建立桩-土-桥梁结构强震反应分析三维有限元模型。基于此,针对不同群桩基础配置对液化场地群桩-土强震相互作用影响展开具体分析。对比发现,桩的数量相同时,桩排列方向与地震波输入方向平行时比垂直时桩基受力减小5%~10%,而对场地液化情况无明显影响;相同排列形式下,三桩模型中土体出现液化的时间约比双桩模型延缓5s,桩上弯矩和剪力减小33%~38%。由此可见,桩基数量增加,桩-土体系整体刚度更大,场地抗液化性能显著,桩基对上部桥梁结构的承载性能明显增强,其安全性与可靠性更高。这对实际桥梁工程抗震设计具有一定的借鉴意义。     

Dynamic response of single piles embedded in transversely isotropic layered media

Dynamic response of single piles embedded in transversely isotropic layered media is investigated using the finite element method combined with dynamic stiffness matrices of the soil derived from Green's functions for ring loads. The influence of soil anisotropy on the dynamic behaviour of piles is examined through a series of parametric studies.     

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.     

Cyclic behavior of laterally loaded concrete piles embedded into cohesive soil

Modern seismic design codes stipulate that the response analysis should be conducted by considering the complete structural system including superstructure, foundation, and ground. However, for the development of seismic response analysis method for a complete structural system, it is first imperative to clarify the behavior of the soil and piles during earthquakes. In this study, full‐scale monotonic and reversed cyclic lateral loading tests were carried out on concrete piles embedded into the ground. The test piles were hollow, precast, prestressed concrete piles with an outer diameter of 300 mm and a thickness of 60 mm. The test piles were 26 m long. Three‐dimensional (3D) finite element analysis was then performed to study the behavior of the experimental specimens analytically. The study revealed that the lateral load‐carrying capacity of the piles degrades when subjected to cyclic loading compared with monotonic loading. The effect of the use of an interface element between the soil and pile surface in the analysis was also investigated. With proper consideration of the constitutive models of soil and pile, an interface element between the pile surface and the soil, and the degradation of soil stiffness under cyclic loading, a 3D analysis was found to simulate well the actual behavior of pile and soil. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

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.     

Kinematic interaction factors of deep foundations with inclined piles

The beneficial or detrimental role of battered piles on the dynamic response of piled foundations has not been yet fully elucidated. In order to shed more light on this aspect, kinematic interaction factors of deep foundations with inclined piles, are provided for single‐battered piles, as well as for 2 × 2 and 3 × 3 groups of piles subjected to vertically incident plane shear S waves. Piles are modelled as linear‐elastic Bernoulli beams, whereas soil is assumed to be a linear, isotropic, homogeneous viscoelastic half‐space. Different pile group configurations, pile‐soil stiffness ratios, and rake angles are considered. The relevance and main trends observed in the influence of the rake angle on the kinematic interaction factors of the analysed foundations are inferred from the presented results. An important dependence of the kinematic interaction factors on the rake angle is observed together with the existence of an inclination angle at which cap rotation and excitation become out of phase in the low‐to‐mid frequency range. The existence of a small batter angle that provides minimum cap rotation is also shown. Copyright © 2014 John Wiley & Sons, Ltd.     

基坑排桩对建筑抗震性的影响分析

以往对建筑抗震性影响因素的研究仅限于施工材料、技术手段等外部条件,忽略了基坑土体安全系数、基坑状态对建筑抗震性的影响,一定程度上削弱了建筑的抗震性能。本文从基坑排桩角度对建筑抗震性的影响展开分析,通过有限元强度折减法获取土体的安全系数与基坑状态的判断标准,在该标准下基于土体安全系数采用有限元强度折减法计算公式,获取各个土层计算参数。基于该参数使用ABAQUS有限元软件构建基坑排桩有限元分析模型(土体和桩体分别采用莫尔-库仑弹塑性模型和二维弹性模型)。实验采用所提分析方法,从基坑排桩排距、刚度两方面对建筑抗震性能进行分析。实验结果表明,当基坑排桩排距进行适当取值时,建筑抗震性越好;双排桩的刚度越大,建筑抗震性越好,且随着刚度的增加建筑抗震性能趋于平稳。     

考虑挤土效应时楔形桩纵向振动阻抗研究

基于复刚度传递多圈层平面应变模型,研究考虑桩周土挤土效应时成层地基中楔形桩的纵向振动问题。首先根据桩周土体的纵向成层情况并考虑楔形桩的变截面特性,将桩土系统沿纵向划分为有限个微元段,对每个微元段的桩周土体建立复刚度传递多圈层平面应变模型,并通过剪切复刚度递推方法求得桩周土作用在桩身的剪切复刚度;然后将求得的剪切复刚度代入桩身纵向振动控制方程,运用Laplace变换技术和阻抗函数递推方法,推导得到考虑桩周土挤土效应时成层地基中楔形桩纵向振动时桩顶复阻抗的解析解;最后,采用参数研究方法在低频范围内分析挤土效应对桩顶复阻抗的影响及其规律。     

Transient response of single piles under horizontal excitations

The general time-domain boundary element in cylindrical co-ordinates developed for the study of wave propagation in a layered half-space is extended to the response analysis of single piles under horizontal transient excitations. The pile is treated as a beam, and therefore, only the bending stiffness has to be considered in the analysis. As required by the non-axisymmetric nature of the problem, the soil is modelled by boundary (cylindrical) elements with the vertical, radial and tangential displacements as well as their corresponding tractions as independent variables. The characteristic matrices for the two different types of element can be formed in the usual manner, and they are combined to form the equation of motion for the whole system by virtue of compatibility and equilibrium conditions along the pile-soil interface. The transient responses of a pile under Heaviside loads are found to converge to the static values. Parametric studies are carried out to reveal the influences of pile-soil stiffness ratio (E_p/E_s) and soil layering.     

Kinematic internal forces in deep foundations with inclined piles

This paper presents a parametric study that looks into the influence of pile rake angle on the kinematic internal forces of deep foundations with inclined piles. Envelopes of maximum kinematic bending moments, shear forces and axial loads are presented along single inclined piles and 2 × 2 symmetrical square pile groups with inclined elements subjected to an earthquake generated by vertically incident shear waves. Inclination angles from 0° to 30° are considered, and three different pile–soil stiffness ratios are studied. These results are obtained through a frequency–domain analysis using a boundary element–finite element code in which the soil is modelled by the boundary element method as a homogeneous, viscoelastic, unbounded region, and the piles are modelled by finite elements as Euler–Bernoulli beams. The rotational kinematic response of the pile foundations is shown to be a key factor on the evolution of the kinematic internal forces along the foundations. Copyright © 2015 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.     

Dynamic stiffness and kinematic response of single piles in inhomogeneous soil

The effect of soil inhomogeneity on dynamic stiffness and kinematic response of single flexural elastic piles to vertically-propagating seismic SH waves is explored. A generalized parabolic function is employed to describe the variable shear wave propagation velocity in the inhomogeneous stratum. A layered soil with piece-wise homogeneous properties is introduced to approximate the continuous inhomogeneity in the realm of a Beam-on-Dynamic-Winkler-Foundation model. The problem is treated numerically by means of a layer transfer-matrix (Haskell–Thompson) formulation, and validated using available theoretical solutions and finite-element analyses. The role of salient model parameters such as pile-head fixity conditions, pile-to-soil stiffness ratio, surface-to-base shear wave velocity ratio and rate of inhomogeneity is elucidated. A new normalization scheme for inertial and kinematic response of such systems is presented based on an average Winkler wavenumber. With reference to long piles in moderately inhomogeneous soils, results indicate that: (a) kinematic pile response is essentially governed by a single dimensionless frequency parameter accounting for pile-to-soil stiffness ratio, pile slenderness and soil inhomogeneity and (b) definition of a characteristic pile wavelength allows an approximate estimation of pile elastodynamic response for preliminary design or analysis. Issues related to domain discretization and Winkler moduli are discussed.     

Horizontal dynamic stiffness of pile groups: Approximate expressions

A number of solutions and computer programs are already available to determine the dynamic stiffness of complete pile foundations, assuming linear elastic soil behavior and perfect bonding between the piles and the surrounding soil. These are assumptions that would be generally valid for properly designed machine foundations where very small strains should be expected. A number of approximate formulations have also been developed. Among these the most commonly used one is that proposed by Poulos (1971) [12] for the static case, computing interaction coefficients between the heads of two piles considered by themselves, then forming a matrix of these coefficients to obtain the interaction between the heads of all the piles in the group. Additional approximations have been suggested, particularly for the computation of the interaction coefficients, using closed form expressions. In this paper, approximate expressions that can be used for preliminary estimates, at the very early stages of the design, without the need of computers, are presented. They are intended for pile groups with pile spacing of the order of 3 diameters, typical relations between the modulus of elasticity of the piles and that of the soil between 100 and 1000, and very small amplitude vibrations.