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.     

Nonlinear FE model updating and reconstruction of the response of an instrumented seismic isolated bridge to the 2010 Maule Chile earthquake

Nonlinear finite element (FE) modeling has been widely used to investigate the effects of seismic isolation on the response of bridges to earthquakes. However, most FE models of seismic isolated bridges (SIB) have used seismic isolator models calibrated from component test data, while the prediction accuracy of nonlinear FE models of SIB is rarely addressed by using data recorded from instrumented bridges. In this paper, the accuracy of a state‐of‐the‐art FE model is studied through nonlinear FE model updating (FEMU) of an existing instrumented SIB, the Marga‐Marga Bridge located in Viña del Mar, Chile. The seismic isolator models are updated in 2 phases: component‐wise and system‐wise FEMU. The isolator model parameters obtained from 23 isolator component tests show large scatter, and poor goodness of fit of the FE‐predicted bridge response to the 2010 Mw 8.8 Maule, Chile Earthquake is obtained when most of those parameter sets are used for the isolator elements of the bridge model. In contrast, good agreement is obtained between the FE‐predicted and measured bridge response when the isolator model parameters are calibrated using the bridge response data recorded during the mega‐earthquake. Nonlinear FEMU is conducted by solving single‐ and multiobjective optimization problems using high‐throughput cloud computing. The updated FE model is then used to reconstruct response quantities not recorded during the earthquake, gaining more insight into the effects of seismic isolation on the response of the bridge during the strong earthquake.     

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。     

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.     

Seismic response of masonry-infilled steel frames via multi-scale finite-element analyses

Effects of masonry infills on the seismic vulnerability of steel frames is studied through multi-scale numerical modelling. First, a micro-modelling approach is utilized to define a homogenized masonry material, calibrated on experimental tests, which is used for modelling the nonlinear response of a one-story, single span, masonry-infilled portal under horizontal loads. Based on results of the micro-model, the constitutive behavior of a diagonal strut macro-element equivalent to the infill panel is calibrated. Then, the diagonal strut is used to model infill panels in the macro-scale analysis of a multi-span multi-story infilled moment-resisting (MR) steel frame. The seismic vulnerability of the MR frame is evaluated through a nonlinear static procedure. Numerical analyses highlight that infills may radically modify the seismic response and the failure mechanism of the frame, hence the importance of the infill correct modelling.     

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.     

Generalized cyclic p–y curve modeling for analysis of laterally loaded piles

Owing to their simplicity and reasonable accuracy, Beam on Nonlinear Winkler Foundation (BNWF) models are widely used for the analysis of laterally loaded piles. Their main drawback is idealizing the soil continuum with discrete uncoupled springs representing the soil reactions to pile movement. Static p–y curves, obtained from limited full-scaled field tests, are generally used as a backbone curve of the model. However, these empirically derived p–y curves could not incorporate the effects of various pile properties and soil continuity. The strain wedge method (SWM) has been improved to assess the nonlinear p–y curve response of laterally loaded piles based on a three-dimensional soil–pile interaction through a passive wedge developed in front of the pile. In this paper, the SWM based p–y curve is implemented as the backbone curves of developed BNWF model to study the nonlinear response of single pile under cyclic lateral loading. The developed nonlinear model is capable of accounting for various important soil–pile interaction response features such as soil and pile yielding, cyclic degradation of soil stiffness and strength under generalized loading, soil–pile gap formation with soil cave-in and recompression, and energy dissipation. Some experimental tests are studied to verify the BNWF model and examine the effect of each factor on the response of laterally loaded pile embedded in sand and clay. The experimental data and computed results agree well, confirming the model ability to predict the response of piles under one-way and two-way cyclic loading. The results show that the developed model can satisfactorily simulate the pile stiffness hardening due to soil cave in and sand densification as observed in the experiment. It is also concluded from the results that the gap formation and soil degradation have significant effects on the increase of lateral pile-head deflection and maximum bending moment of the pile in cohesive soils.     

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.     

Model tests and numerical analyses on horizontal impedance functions of inclined single piles embedded in cohesionless soil

Horizontal impedance functions of inclined single piles are measured experimentally for model soil-pile systems with both the effects of local soil nonlinearity and resonant characteristics.Two practical pile inclinations of 5° and 10° in addition to a vertical pile embedded in cohesionless soil and subjected to lateral harmonic pile head loadings for a wide range of frequencies are considered.Results obtained with low-to-high amplitude of lateral loadings on model soil-pile systems encased in a laminar shear box show that the local nonlinearities have a profound impact on the horizontal impedance functions of piles.Horizontal impedance functions of inclined piles are found to be smaller than the vertical pile and the values decrease as the angle of pile inclination increases.Distinct values of horizontal impedance functions are obtained for the ’positive’ and ’negative’ cycles of harmonic loadings,leading to asymmetric force-displacement relationships for the inclined piles.Validation of these experimental results is carried out through three-dimensional nonlinear finite element analyses,and the results from the numerical models are in good agreement with the experimental data.Sensitivity analyses conducted on the numerical models suggest that the consideration of local nonlinearity at the vicinity of the soil-pile interface influence the response of the soil-pile systems.     

Dynamic characteristics of lateral load-deflection relationships of flexible piles

Most offshore platforms are supported on long and large-diameter piles with variable wall-thickness along the length, and soil properties varying with depth. The design and analyses of these piles are made by modelling the soil-pile system with a beam-on-Winkler foundation. Therefore, evaluation of appropriate soil-pile springs for use in such analyses is a matter of concern. Fundamental characteristics of dynamic lateral load-deflection relationships for piles were studied analytically considering the soil-pile-structure interaction under seismic loading conditions. The soil layer was assumed homogeneous, linearly elastic with hysteretic type material damping, and overlying a rigid base. A superstructure with multi-degrees of freedom was supported by a single vertical pile hinged at the rigid base. Parametric studies were carried out to identify the influence of the system parameters on the behaviour of the dynamic lateral load-deflection relationships of piles. The lateral load-deflection relationships vary considerably with depth and are influenced not only by the dynamic properties of soil but also by the structural properties of a pile and loading conditions. These lateral load-deflection relationships can be used to define the soil-pile springs for the seismic response analysis of a soil-pile-structure system, and the results can be extended to problems with soil profiles with layering and non-linearity.     

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.     

端承桩在分层地基中的横向地震反应分析

本文对分层弹性地基中端承桩基础按Ｗｉｎｋｌｅｒ（温克尔）地基土模型，通过特性分析，建立了合理的力学模型，经过动力分析，给出了端承桩基础横向自由振动特性及在横向动力载荷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端承桩基础在横向动力载荷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。     

Analysis of bridge structures crossing strike-slip fault rupture zones: A simple method for generating across-fault seismic ground motions

This article presents a simple and effective method for generating across-fault seismic ground motions for the analysis of ordinary and seismically isolated bridges crossing strike-slip faults. Based on pulse models available in the literature, two simple loading functions are first proposed to represent the coherent (long-period) components of ground motion across strike-slip faults. The loading functions are then calibrated using actual near-fault ground-motion records with a forward-directivity velocity pulse in the fault-normal direction and a fling-step displacement in the fault-parallel direction. The effectiveness of the proposed method is demonstrated by comparing time history responses and seismic demands of ordinary and seismically isolated bridges obtained from nonlinear response history analyses using the actual ground-motion records and the calibrated loading functions. A comprehensive methodology is also presented for selecting the input parameters of the loading functions based on empirical equations and practical guidelines. Finally, an analysis procedure for bridge structures crossing strike-slip faults is introduced based on the proposed method for generating across-fault ground motions and the parameter selection methodology for the loading functions.     

液化场地桥梁足尺桩抗震简化分析方法

采用国际VELACS项目中离心机试验标定的内华达砂的动力计算参数,建立液化场地足尺桩-土动力相互作用分析的三维有限元模型;获得不同幅值的正弦波作用下桩-土动力相互作用的p-y曲线,修正并发展一种可用于液化场地桩-土动力相互作用分析的宏单元模型,并基于非线性文克尔地基梁模型建立桥梁足尺桩抗震分析的数值模型与简化方法,通过有限元分析结果验证该简化方法的正确性。     

Physical parameters identification for full-scale ten-story reinforced concrete building with degrading tri-linear model by modal iterative error correction method

To assess the post-earthquake seismic safety of buildings, it is crucial to predict seismic response, and it is necessary to set the appropriate physical parameters of the response analysis model. Numerous methods have been proposed to identify physical parameters. However, most of them are limited to linear systems, and previous researches on nonlinear systems have difficulties in practical applications. In this paper, a nonlinear response analysis model is identified for a full-scale ten-story reinforced concrete building with the degrading tri-linear stiffness model by the modal iterative error correction (MIEC) method, and the accuracy of this technique is discussed by comparing with the shaking table test.     

Modelling of raked pile foundations in liquefiable ground

Raked piles are believed to behave better than vertical piles in a laterally flowing liquefied ground. This paper aims at numerically simulating the response of raked pile foundations in liquefying ground through nonlinear finite element analysis. For this purpose, the OpenSees computer package was used. A range of sources have been adopted in the definition of model components whose validity is assessed against case studies presented in literature. Experimental and analytical data confirmed that the backbone force density–displacement (p–y) curve simulating lateral pile response is of acceptable credibility for both vertical and raked piles. A parametric investigation on fixed-head piles subject to lateral spreading concluded that piles exhibiting positive inclination impart lower moment demands at the head while those inclined negatively perform better at liquefaction boundaries (relative to vertical piles). Further studies reveal substantial axial demand imposed upon negatively inclined members due to the transfer of gravity and ground-induced lateral forces axially down the pile. Extra care must be taken in the design of such members in soils susceptible to lateral spreading such that compressive failure (i.e. pile buckling) is avoided.     

Predicting torsion‐induced lateral displacements for pushover analysis: Influence of torsional system characteristics

The increasing popularity of simplified nonlinear methods in seismic design has recently led to many proposals for procedures aimed at extending pushover analysis to plan asymmetric structures. In terms of practical applications, one particularly promising approach is based on combining pushover analysis of a 3D structural model with the results of linear (modal) dynamic analysis. The effectiveness of such procedure, however, is contingent on one fundamental requirement: the elastic prediction of the envelope of lateral displacements must be conservative with respect to the actual inelastic one. This paper aims at verifying the above assumption through an extensive parametric analysis conducted with simplified single‐storey models. The main structural parameters influencing torsional response in the elastic and inelastic range of behaviour are varied, while devoting special attention to the system stiffness eccentricity and radius. The analysis clarifies the main features of inelastic torsional response of different types of building structures; in this manner, it is found that the above‐mentioned method is generally suitable for structures characterized by moderate to large torsional stiffness, whereas it cannot be recommended for extremely torsionally stiff structures, as their inelastic torsional response almost always exceeds the elastic one. Copyright © 2010 John Wiley & Sons, Ltd.     

A model to simulate special concentrically braced frames beyond brace fracture

Special concentrically braced frames (SCBFs) are commonly used as the lateral‐load resisting system in buildings. SCBFs primarily sustain large deformation demands through inelastic action in the brace, including compression buckling and tension yielding; secondary yielding may occur in the gusset plate and framing elements. The preferred failure mode is brace fracture. Yielding, buckling, and fracture behavior results in highly nonlinear behavior and accurate analytical modeling of these frames is required. Prior research has shown that continuum models are capable of this level of simulation. However, those models are not suitable for structural engineering practice. To enable the use of accurate yet practical nonlinear models, a research study was undertaken to investigate modeling parameters for line‐element models, which is a more practical modeling approach. This portion of the study focused on methods to predict brace fracture. A fracture modeling approach simulated the nonlinear, cyclic response of SCBFs by correlating onset of fracture to the maximum strain range in the brace. The model accounts for important brace design parameters including slenderness, compactness, and yield strength. Fracture data from over 40 tests was used to calibrate the model and included single‐brace component, single story frame, and full‐scale multistory frame specimens. The proposed fracture model is more accurate and simpler than other, previously proposed models. As a result, the proposed model is an ideal candidate for practical performance simulation of SCBFs. Copyright © 2012 John Wiley & Sons, Ltd.     

Developing fragility curves for a pile-supported wharf

This study proposes a procedure for developing seismic fragility curves for a pile-supported wharf. A typical pile-supported wharf, as commonly used in the ports of Taiwan, is chosen for demonstration. For a structural model of the wharf, the deck is modeled by shell elements and the Winkler model is used for the pile–soil system, in which the piles and soils are represented by beam elements and springs, respectively. A pushover analysis with lateral loads distributed according to the fundamental modal shape of the wharf structure is conducted to deduce the capacity curve of the wharf. The procedure for developing fragility curves can be explicitly performed using the spreadsheet platform in Microsoft EXCEL. First, quantitative criteria for damage states are established from the sequence of development of plastic zones. Then a nonlinear static procedure called the Spectrum Capacity Method (CSM) is used to efficiently construct a response matrix of the wharf to 24 earthquake events with differing levels of peak ground acceleration (PGA). Based on the damage criteria and the response matrix, the fragility curves of the wharf can be thus constructed through simple statistical analysis. Shifted lognormal cumulative distribution functions are also employed to better approximate the fragility curves for practical applications.     

基于不同参数的基础隔震结构非线性概率密度演化

为了研究不同设计参数条件下基础隔震结构非线性响应的概率密度演化特征,采用两质点模型来模拟基础隔震结构,隔震层与上部结构分别采用Bouc-Wen模型与刚度退化的Bouc-Wen模型来描述其非线性特征,运用概率密度演化理论,进行隔震结构非线性随机地震响应的概率密度演化分析。采用基于物理的随机地震动模型生成人工地震动,提出基础隔震结构非线性随机地震响应的概率密度演化分析的基本步骤。通过改变基础隔震结构的设计参数,同时考虑激励的随机性,研究基础隔震结构非线性随机地震响应的概率密度演化规律。结果表明,基础隔震结构的阻尼比、周期比和屈重比取合理范围,能使隔震结构上部和下部的位移可控。