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.     

Flexible support of a pile embedded in unsaturated soil under Rayleigh waves

Under the action of Rayleigh waves, pile head is easy to rotate with a concrete pile cap, and pure fixed-head condition is rarely achieved, which is a common phenomenon for it usually occurs on the precast piles with insufficient anchorage. In addition, the propagation characteristics of Rayleigh wave have been changed significantly due to the existence of capillary pressure and the coupling between phases in unsaturated soil, which significantly affects the pile-soil interaction. In order to study the above problems, a coupled vibration model of unsaturated soil–pile system subjected to Rayleigh waves is established on the basis that the pile cap is equivalent to a rigid mass block. Meanwhile, the soil constitution is simplified to linear-elastic and small deformations are assumed to occur during the vibration phase of soil–pile system. Then, the horizontal dynamic response of a homogeneous free-field unsaturated soil caused by propagating Rayleigh waves is obtained by using operator decomposition theory and variable separation method. The dynamic equilibrium equation of a pile is established by using the dynamic Winkler model and the Timoshenko beam theory, and the analytical solutions of the horizontal displacement, rotation angle, bending moment and shear force of pile body are derived according to the boundary conditions of flexible constraint of pile top. Based on the present solutions, the rationality of the proposed model is verified by comparing with the previous research results. Through parametric study, the influence of rotational stiffness and yield bending moment of pile top on the horizontal dynamic characteristics of Rayleigh waves induced pile is investigated in detailed. The analysis results can be utilized for the seismic design of pile foundation under Rayleigh waves.     

近断层脉冲型地震下建筑地桩基础沉降分析

传统基于碰撞回弹系数Stereo-mechanical方法在分析建筑地桩基础的沉降位移过程中未考虑地桩基础碰撞的能量损耗,造成分析结果存在准确性和可信度较低的问题。因此提出改进的Kelvin建筑地桩基础碰撞沉降分析方法,以解决基于碰撞回弹系数Stereo-mechanical法存在的问题。采用线性阻尼构建Kelvin模型,分析地桩基础碰撞靠近阶段和回弹阶段的阻尼做功,构建地桩基础碰撞转换单自由度体系振动模型,实现对地桩基础的相对沉降速度和相对沉降位移的有效运算,基于建筑地桩基础碰撞沉降发生初始和结束时刻的能量和动量守恒定理,得到建筑地桩基础的最大沉降位移,实现对建筑地桩基础沉降的有效分析。实验结果说明,所提方法能提高地桩基础沉降分析的准确性和可信度。     

单桩基础在无限层地基中的横向地震反应分析

本文通过对分层弹性地基中单桩基础按Ｗｉｎｋｌｅｒ（温克尔）地基土模型特性分析，建立了合理的力学模型。通过动力分析，给出了桩基础横向自振特性及在横向动力与地震载荷作用下强迫反应的解析解。文中的解析公式为分层弹性地基中单桩基础在横向动力与地震载荷作用下的动力反应分析提供了一种新的解析方法。     

Winkler model for dynamic response of composite caisson-piles foundations: Lateral response

As the first part of a sequence focusing on the dynamic response of composite caisson-piles foundations (CCPFs¹), this paper develops a simplified method for the lateral response of these foundations. A Winkler model for the lateral vibration of the CCPF is created by joining the two components, the caisson and the pile group, where the four-spring Winkler model is utilized for the caisson and axial–lateral coupled vibration equations are derived for the pile group. For determining the coefficients of the four-spring Winkler model for the caissons, embedded footing impedance is used and a modification on the rotational embedment factor is made for the sake of the geometrical difference between shallow footings and caissons. Comparisons against results from finite element simulations demonstrate the reliability of this modified four-spring Winkler model for caissons in both homogenous and layered soils. The proposed simplified method for the lateral vibration of CCPFs is verified also by 3D finite element modeling. Finally, through an example, the idea of adding piles beneath the caisson is proved to be of great significance to enhance the resistance of the foundation against lateral dynamic loads.     

强震作用下桩-土-断层非线性动力相互作用特性

为研究强震区跨断层桥梁桩基非线性动力相互作用特性,依托海文大桥实体工程,利用MIDAS/GTS有限元软件,建立了桩-土-断层相互作用模型,分析0.20~0.60g地震动强度下断层上下盘桩基加速度响应、桩顶水平位移、桩身弯矩以及桩身剪力响应情况。结果表明:覆盖层土体对桩身加速度放大作用明显,且随着输入地震动强度的增大,放大作用逐渐减弱;覆盖层对地震波的滤波作用显著,随着输入地震动强度的增大,滤波作用逐渐减弱;上盘桩基达到桩顶峰值加速度的时刻滞后于下盘;随着输入地震动强度的增大,上、下盘桩的桩顶产生的永久位移和水平位移峰值逐渐变大,上盘桩顶产生的永久位移和桩顶峰值位移均大于下盘,产生显著的"上盘效应";不同强度地震动作用下,断层上、下盘桩基弯矩均在上部土层界面处达到峰值,剪力均在基岩面处达到峰值,下盘桩基弯矩和剪力峰值大于上盘桩基,呈现出显著的"下盘效应"。在桥梁桩基抗震设计时,应着重考虑断层上、下盘桩基的差异和不同强度地震作用对桩基承载特性的影响。     

Effect of a forced harmonic vibration pile to its adjacent pile in layered elastic soil with double-shear model

A new model named double-shear model based on Pasternak foundation and Timoshenko beam theory is developed to evaluate the effect of a forced harmonic vibration pile to its adjacent pile in multilayered soil medium. The double-shear model takes into account the shear deformation and the rotational inertia of piles as well as the shear deformation of soil. The piles are simulated as Timoshenko beams, which are embedded in a layered Pasternak foundation. The differential equation of transverse vibration for a pile is solved by the initial parameter method. The dynamic interaction factors for the layered soil medium are obtained by the transfer matrix method. The formulation and the implementation have been verified by means of several examples. The individual shear effects of soil and piles on the interaction factors are evaluated through a parametric study. Compared to Winkler model with Euler beam, the present model gives much better results for the dynamic interaction of piles embedded in stiff soil with small slenderness ratios. Finally, the effect of a forced long pile to a short pile embedded in multilayered soil medium is studied in detail.     

An investigation into the Winkler modeling of the cyclic response of rigid footings

The response of shallow foundations under lateral cyclic loading is generally nonlinear and involves rocking, sliding, settlement, and may also involve foundation uplift and soil yielding. Unlike pile foundations, the nonlinear Winkler model is not widely used for modeling cyclic soil–footing–structure interaction (SFSI) problems. Nonetheless, it has some important features that make it more attractive than conventional finite element approaches, and is a recommended approach in the FEMA 356 design guideline. This paper explores the strengths and limitations of the FEMA 356 nonlinear Winkler modeling approach, when used in predicting the cyclic response of various recent SFSI experiments. The results of the study show that the model is capable of satisfactorily predicting all the different cyclic response quantities apart from permanent horizontal displacements. This should therefore be noted when using the approach in design.     

RC pile–soil interaction analysis using a 3D‐finite element method with fibre theory‐based beam elements

To evaluate the overall response of a structural system including its foundation and surrounding soil, an equivalent finite element model with reduced degrees of freedom using fibre theory‐based beam element was proposed. The proposed model was based on investigations of the subgrade soil reaction of a single‐layer model, and was verified for the cyclic behaviour of a laterally loaded single RC pile in terms of the load–displacement relationship, pile deformation, and soil pressures on the pile surface. Also investigated was the effect of the interfacial element between pile and soil on the behaviour of the laterally loaded pile. Copyright © 2006 John Wiley & Sons, Ltd.     

无限层弹性地基中常轴力桩基的地震反应分析

根据Ｗｉｎｋｌｅｒ地基模型，对桩基础通过特性分析建立了合理的力学模型。在动力分析的基础上，给出了桩基础横向自振特性及在常轴力与横向地震载荷作用下的强迫反应解析解。文中的解析公式为桩基础动力分析提供了一种新的解析方法。     

Winkler model for dynamic response of composite caisson–piles foundations: Seismic response

A simplified method with a dynamic Winkler model to study the seismic response of composite caisson–piles foundations (CCPF¹) is developed. Firstly, with the dynamic Winkler model, the kinematic response of the CCPF subjected to vertically propagating seismic S-wave is analyzed by coupling the responses of caisson part and pile part. Secondly, a simplified model for the foundation–structure system is created with the structure simplified as a lumped mass connected to the foundation with an elastic column, and through the Fast Fourier Transformation (FFT) this model is enabled to solve transient seismic problems. Thirdly, the proposed method for the seismic response of CCPF-structure systems is verified by comparison against 3D dynamic finite element simulation, in which the Domain Reduction Method (DRM²) is utilized. Lastly, the mechanism and significance of adding piles in improving the earthquake resistance of the foundation and structure is analyzed through an example with different soil conditions. Discovered in this study is that adding piles under the caisson is an efficient way to increase seismic resistant capability of the soil–foundation–structure system, and the main mechanism of that is the elimination of the pseudo-resonance.     

基于动力BNWF法的冻土-桩相互作用模型研究

基于水平循环荷载作用下不同负温冻土环境中单桩动力特性模型试验结果,在已有分析桩-土-结构相互作用的动力BNWF模型的基础上,提出改进的冻土-桩基动力相互作用非线性反应分析模型。在该模型中,利用改进的双向无拉力多段屈服弹簧考虑桩侧冻土的水平非线性力学特性,同时兼顾桩侧与冻土间的竖向非线性摩擦效应、桩尖土的挤压与分离作用以及远场土体阻尼对桩基动力特性的影响。其中桩侧水平多段屈服弹簧参数根据冻土非线性p-y关系获得,该关系曲线以三次函数曲线段及常值函数段共同模拟,并由室内冻土压缩试验结果确定。最后基于改进的动力BNWF模型,提取动位移荷载作用下该桩顶力-位移滞回曲线及桩身不同埋深处的弯矩动响应数值分析结果,并与相应的模型试验结果对比,二者具有较好的拟合度,表明本文所提出的改进模型在分析冻土-桩动力相互作用时有较好的适用性。     

考虑水平力作用的弹性地基梁位移及内力解析解

考虑水平力作用下弹性地基梁受力特点,针对Winkler地基模型不能考虑梁底面间与地基切向相互作用的不足,在地基与梁体接触面上引入一系列各自独立的水平弹簧。假定弹簧反力与梁底和地基间的切向相对位移成正比,根据弹性力学基本原理,结合小变形条件下梁体几何方程和线弹性本构关系,建立力学分析模型,导出基本微分方程组并利用微分算子级数法进行求解,获得了考虑水平力作用时地基梁位移及内力解析解。最后通过实例分析,验证了该解析解的正确性和合理性,并对切向地基反力系数等影响因素进行了探讨。其结果可为工程设计提供借鉴参考。     

无缝桥抗震性能的对比研究

本文以一座三跨总长60 m的整体桥为案例桥,分别试设计了同跨径的半整体桥、延伸桥面板桥和常规连续梁桥。通过Midas/Civil软件建立四种桥型的有限元模型,并对其进行了E1和E2反应谱分析和时程分析,对比了四种桥型的结构反应峰值（墩顶位移、桥墩及桩基剪力与弯矩、台底位移、桥台桩基剪力与弯矩）。计算结果表明:当桥梁存在15°的斜交角,整体桥、半整体桥在地震动沿平行于桥台长边方向及其垂直方向输入时更不利,而延伸桥面板桥和常规连续梁桥在地震动沿顺桥向和横桥向输入时更不利。四种桥型在地震作用下:整体桥抗震性能最优异,但其台底位移、桥台桩基的剪力和弯矩最大;半整体桥台底位移、桥台桩基的剪力和弯矩最小,其墩顶位移、桥墩及桩基的剪力和弯矩仅比整体桥大;延伸桥面板桥和常规连续梁桥的墩-梁相对位移远大于整体桥和半整体桥,不适用于地震基本烈度高的区域。     

Soil–pile interaction during the passage of rayleigh waves: An analytical solution

A simple analytical solution is presented to calculate the single-pile response when excited by the passage of Rayleigh seismic waves. Closed-form expressions for the horizontal and vertical displacement distributions are presented for piles with finite or infinite length. The analytical results for both free-head and fixed-head piles are obtained through a dynamic Winkler model, with realistic frequency-dependent ‘springs’ and ‘dashpots’. The results of the presented method are in excellent agreement with results of a rigorous solution. It is shown that in vertical motion, the differences between pile and soil displacements are far more significant than in horizontal motion, and therefore, further work is needed to investigate the importance of pile-soil-pile interaction (group effects), because of the vertical component of Rayleigh seismic waves.     

Torsional vibrations of elastic foundations embedded in an elastic half-space

This paper examines the axisymmetric torsional vibrations of an elastic pile and a hemispherical foundation embedded in a homogeneous elastic half-space. The embedded foundation–half-space system is decomposed into an extended half-space and a fictitious foundation. The deformations of the fictitious system are specified by an admissible function containing a set of generalized coordinates. The Lagrangian equations of motion are used to determine these coordinates associated with the assumed displacement function. Numerical results are presented for torsional impedance of an elastic pile and a hemisphere to illustrate the effects of relative flexibility and geometry. By employing certain simplifications on the pile–half-space system an approximate closed form solution is presented for the torsional impedance of an elastic pile.     

液化场地桩-土地震相互作用p-y曲线分析方法研究

目前,我国尚缺乏液化场地桩-土-桥梁结构地震相互作用分析的合理数值模型与简化分析方法。鉴于此,直接针对振动台试验,基于非线性文克尔地基梁模型,考虑桩周参振土的质量惯性力、上部结构的惯性力、土体辐射阻尼等效应,建立了液化场地桩-土-桥梁结构地震相互作用的p-y曲线分析模型,并给出相应的简化方法。针对振动台试验进行了0.1g El Centro波输入下的分析,验证了桩-土地震相互作用分析方法的正确性,并且推荐了计算参数的合理选取方法,可用于液化场地桩-土地震相互作用的分析。提出的液化场地桩-土地震相互作用p-y曲线简化分析方法,为实际桥梁桩基抗震设计与分析提供一定参考。     

Intensity measures for the seismic response of pile foundations

In this study the efficacy of various ground motion intensity measures for the seismic response of pile foundations embedded in liquefiable and non-liquefiable soils is investigated. A soil-pile-structure model consisting of a two-layer soil deposit with a single pile and a single degree-of-freedom superstructure is used in a parametric study to determine the salient features of the seismic response of the soil-pile-structure system. A suite of ground motion records scaled to various levels of intensity are used to investigate the full range of pile behaviour, from elastic response to failure. Various intensity measures are used to inspect their efficiency in predicting the seismic demand on the pile foundation for a given level of ground motion intensity. It is found that velocity-based intensity measures are the most efficient in predicting the pile response, which is measured in terms of maximum curvature or pile-head displacement. In particular, velocity spectrum intensity (VSI), which represents the integral of the pseudo-velocity spectrum over a wide period range, is found to be the most efficient intensity measure in predicting the seismic demands on the pile foundation. VSI is also found to be a sufficient intensity measure with respect to earthquake magnitude, source-to-site distance, and epsilon, and has a good predictability, thus making it a prime candidate for use in seismic response analysis of pile foundations.     

强震状态下黄土中桩基动力性状分析

传统通过p-y曲线法分析强震状态下黄土中桩基动力性状时未进行桩基结构模拟,获取的强震状态下黄土中桩基动力的相关动力参数不准确。本文提出新的强震状态下黄土中桩基动力性状分析方法,依据HS硬化模型设计HSS本构模型,通过模型获取强震状态下黄土中桩基动力的相关参数,以此为基础采用PLAXIS软件构建黄土中桩基有限元模型;通过两种模型从耦合荷载作用下的桩基桩身水平位移响应、桩身内力响应两方面对强震状态下黄土桩基动力性状展开实验分析。实验结果表明,所提方法可对强震状态下黄土中桩基动力性状进行准确分析。