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.     

Seismic response of single-column bent on pile: evidence of beneficial role of pile and soil inelasticity

While seismic codes do not allow plastic deformation of piles, the Kobe earthquake has shown that limited structural yielding and cracking of piles may not be always detrimental. As a first attempt to investigate the consequences of pile yielding in the response of a pile-column supported bridge structure, this paper explores the soil–pile-bridge pier interaction to seismic loading, with emphasis on structural nonlinearity. The pile–soil interaction is modeled through distributed nonlinear Winkler-type springs and dashpots. Numerical analysis is performed with a constitutive model (Gerolymos and Gazetas 2005a, Soils Found 45(3):147–159, Gerolymos and Gazetas 2005b, Soils Found 45(4):119–132, Gerolymos and Gazetas 2006a, Soil Dyn Earthq Eng 26(5):363–376) materialized in the OpenSees finite element code (Mazzoni et al. 2005, OpenSees command language manual, p 375) which can simulate: the nonlinear behaviour of both pile and soil; the possible separation and gapping between pile and soil; radiation damping; loss of stiffness and strength in pile and soil. The model is applied to the analysis of pile-column supported bridge structures, focusing on the influence of soil compliance, intensity of seismic excitation, pile diameter, above-ground height of the pile, and above or below ground development of plastic hinge, on key performance measures of the pier as is: the displacement (global) and curvature (local) ductility demands and the maximum drift ratio. It is shown that kinematic expressions for performance measure parameters may lead to erroneous results when soil-structure interaction is considered.     

Natural vibration frequency and damping of slender structures founded on monopiles

Offshore wind turbine (OWT) is a typical example of a slender engineering structure founded on large diameter rigid piles (monopiles). The natural vibration characteristics of these structures are of primary interest since the dominant loading conditions are dynamic. A rigorous analytical solution of the modified SSI eigenfrequency and damping is presented, which accounts for the cross coupling stiffness and damping terms of the soil–pile system and is applicable but not restrictive to OWTs. A parametric study was performed to illustrate the sensitivity of the eigenfrequency and damping on the foundation properties, the latter being expressed using the notion of dimensionless parameters (slenderness ratio and flexibility factor). The application of the approximate solution that disregards the off diagonal terms of the dynamic impedance matrix was found to overestimate the eigenfrequency and underestimate the damping. The modified SSI eigenfrequency and damping was mostly affected by the soil–pile properties, when the structural eigenfrequency was set between the first and second eigenfrequency of the soil layer. Caution is suggested when selecting one of the popular design approaches for OWTs, since the dynamic SSI effects may drive even a conservative design to restrictive frequency ranges, nonetheless along with advantageous – from a designers perspective – increased damping.     

Capacity evaluation of statnamic tested long piles

A procedure that uses the structural damping (SD) concept for estimating the capacity of a pile based on the Statnamic (STN) pile load test results, formerly used by the authors for short piles, is extended in this paper for the STN tested long piles. Similar to segmental unloading point method procedures for long piles, the shaft length is divided into several segments and each segment is assumed to behave as a mass of a single degree of freedom. The SD concept is then applied to each segment to consider the displacement related soil damping instead of the velocity dependent damping. Instrumented strain gauge data at different levels of the shaft are required for the interpretation method. Three case studies are presented in this paper to study the validity and applicability of the present method. The predicted results are also compared to the available test or analytical data.     

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.     

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.     

阻尼耗能在结构弹塑性地震反应中的作用

本文用计算分析的方法研究了结构在弹塑悸地震反应过程中的阻尼耗能与塑性耗能的数量关系问题。     

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。     

Damping formulation for nonlinear 1D site response analyses

Measurements and observations of ground shaking during large earthquakes have demonstrated the predominant role of site effects in the response of infrastructure during a seismic event. Despite significant efforts to model the hysteretic response and nonlinearity of soils due to medium and large ground motions, the most widely accepted nonlinear site response methods are not able to represent simultaneously the changes of stiffness and energy dissipation (damping) observed in both laboratory tests and during earthquake events. This paper presents two new soil damping formulations implemented in nonlinear one-dimensional site response analysis for small and large strains. The first formulation introduces an approach to construct a frequency-independent viscous damping matrix which reduces the over-damping at high frequencies, and therefore, the filtering at those frequencies. The second formulation introduces a reduction factor that modifies the extended Masing loading/unloading strain–stress relationship to match measured modulus reduction and damping curves simultaneously over a wide range of shear strains. A set of examples are introduced to illustrate the effect of using the two proposed formulations, separately and simultaneously, in nonlinear site response analyses.     

考虑波流影响的深水群桩基础桥墩地震反应分析

用基于ABAQUS软件为平台的平行计算技术,对考虑波流影响的地基土-群桩-桥墩体系进行三维非线性地震反应数值模拟,土体和墩台以八节点等参单元离散,桩以梁单元离散,采用土体黏塑性记忆型嵌套面本构模型描述土的动力特性,采用动力塑性损伤模型描述混凝土的动力特性;基于Morison公式,采用Stokes五阶波浪理论描述表面波流,波浪力以分布力的形式施加于桥墩之上,分析了考虑和不考虑波流作用时不同地震动作用下群桩基础桥墩的地震反应特性,结果表明:波流作用对桩体加速度反应的影响很小,但对桩体相对位移和弯矩的影响显著,波流作用使桩体弯矩和顺流向的相对位移增大、逆流向的相对位移减小,其影响幅度随流速的增大而增大,波流作用与输入地震动特性密切相关。考虑波流作用对深水大型桥梁群桩基础桥墩地震反应的影响是有必要的。     

大直径扩底灌注桩的抗震性能研究

深入分析土-大直径扩底灌注桩体系动力相互作用机理是地震工程的重要研究内容。本文采用快速拉格朗日FLAC~(3D)有限差分程序建立地震荷载作用下扩底桩-土和等直径桩-土动力相互作用体的三维数值模型,分析大直径扩底桩与普通等直径桩地震反应的差异。桩周土采用Mohr-Coulomb弹性模型以考虑土体的非线性,桩体采用线弹性模型,桩与桩周土之间采用"切割模型"法设置桩土间接触面。输入5·12汶川地震波,对两种桩基的地震反应进行了数值计算与分析。结果表明:扩底桩的抗震性能优于等直径桩;与具有显著差异的加速度时程曲线相比,扩底桩对位移动力响应并不敏感。     

Quasi-3D analysis: Validation by full 3D analysis and field tests on single piles and pile groups

A quasi-3D method for the analysis of single piles and pile groups is presented. The method includes an equivalent linear constitutive model for nonlinear analysis, an 8-node pile element that simulates the effects of pile volume and energy transmitting boundaries which are especially important for the analysis of high frequency loading of machine foundations. The quasi-3D formulation and equivalent linear model result in orders of magnitude decreases in computational time. The accuracy and reliability of the approximate approach was validated by comparing results with 3D analytical results from MIT and by data from field tests on single piles and pile groups from Taiwan. The computed results compared very favorably with the analytical and field test data.     

Morison方程中动水阻力项对桥梁桩柱地震反应的影响

深水桥梁地震反应计算时,当采用Morison公式考虑水的作用时,增加了一个附加惯性项和一个附加阻尼项,其中附加阻尼项是非线性的。由于非线性附加阻尼项的存在,给采用反应谱方法求解桥梁的地震反应带来不便。讨论了非线性阻尼项对一般桥梁桩、墩结构地震反应的贡献,得到的结论是阻尼项的贡献很小,可以忽略。从而水中桥梁地震反应的计算就得到了很大的简化。     

Evidence of beneficial role of inclined piles: observations and summary of numerical analyses

The behaviour under seismic loading of inclined piles embedded in two idealized soil profiles, a homogeneous and a non-homogenous “Gibson” soil, is analysed with 3D finite elements. Two structures, modeled as single-degree-of-freedom oscillators, are studied: (1) a tall slender superstructure (H _st = 12 m) whose crucial loading is the overturning moment, and (2) a short structure (H _st = 1 m) whose crucial loading is the shear force. Three simple two-pile group are studied: (a) one comprising a vertical pile and a pile inclined at 25°, (b) one consisting of two piles symmetrically inclined at 25°, and (c) a group of two vertical piles. The influence of key parameters is analysed and non-dimensional diagrams are presented to illustrate the role of raked piles on pile and structure response. It is shown that this role can be beneficial or detrimental depending on a number of factors, including the slenderness of the superstructure and the type of pile-to-cap connection.     

Dynamic nonlinear response of pile foundations under vertical vibration—Theory versus experiment

The influence of nonlinearity on the dynamic response of cast-in-situ reinforced concrete piles subjected to strong vertical excitation was studied. Forced vibration test of single piles (L/d=10, 15, 20) and 2×2 pile groups (s/d=2, 3, 4 for each L/d) were conducted in the field for two different embedded conditions of pile cap. From the measured nonlinear response curves, the effective pile–soil system mass, stiffness and damping were determined and the nonlinear response curves were back-calculated using the theory of nonlinear vibration. The test results were compared with the continuum approach of Novak with dynamic interaction factor approach using both linear and linear-equivalent numerical methods. Reasonable match between the measured and predicted response was found for linear-equivalent methods by introducing a weak boundary-zone around the pile to approximately account for the nonlinear behaviour of pile–soil system. The test data were used to establish the empirical relationship in order to estimate the extent of soil separation around the pile with soil under vertical vibration.     

Response of a RC pile group in liquefiable soil: A shake-table investigation

Soil liquefaction induced by earthquakes frequently cause costly damage to pile foundations. However, various aspects of the dynamic behavior and failure mechanisms of piles in liquefiable soils still remain unclear. This paper presents a shake-table experiment conducted to investigate the dynamic behavior of a reinforced-concrete (RC) elevated cap pile foundation during (and prior to) soil liquefaction. Particular attention was paid to the failure mechanism of the piles during a strong shaking event. The experimental results indicate that decreasing the frequency and increasing the amplitude of earthquake excitation increased the pile bending moment as well as the speed of the excess pore pressure buildup in the free-field. The critical pile failure mode in the conducted testing configuration was found to be of the bending type, which was also confirmed by a representative nonlinear numerical model of the RC pile. The experimental results of this study can be used to calibrate numerical models and provide insights on seismic pile analysis and design.     

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.     

Energy dissipation models for RC members and structures

The unloading parameters of hysteretic models for RC members are given in terms of their shear-span-to-depth ratio and the viscous damping used to model other energy dissipation sources. They reflect the energy dissipation in full post-yield load cycles in 534 tests of rectangular or circular members. Pre-yield hysteretic energy dissipation—ignored if the model is elastic till yielding—amounts in the tests to a mean viscous damping around 8.5% and can be considered in nonlinear response-history analysis through a new model which combines constant elastic stiffness in virgin loading with hysteretic energy dissipation both before and after yielding. Models with linear behavior till yielding and hysteretic energy dissipation only after it come closer to the results of the new model if viscous damping is 5%.     

Discussion of ‘Modelling viscous damping in nonlinear response history analysis of buildings for earthquake excitation’ by Anil K. Chopra and Frank McKenna

This discussion deals with recommendations in the paper on appropriate damping formulations for use in nonlinear response history analysis of buildings. Concern over potentially excessive damping forces and moments should extend beyond the damping moments produced by the stiffness proportional part of Rayleigh damping that corresponds to rotational springs used to explicitly model plastic hinges. The key to an appropriate damping formulation for nonlinear analysis is a realistic mechanism that allows all damping forces and moments to be meaningfully assessed. Then features can be added to keep these forces and moments within reasonable bounds. Copyright © 2016 John Wiley & Sons, Ltd.