Cyclic shakedown of piles subjected to two‐dimensional lateral loading

Pile foundations are frequently subjected to cyclic lateral loads. Wave and wind loads on offshore structures will be applied in different directions and times during the design life of a structure. Therefore, the magnitude and direction of these loads in conjunction with the dead loads should be considered. This paper investigates a loading scenario where a monotonic lateral load is applied to a pile, followed by two‐way cycling in a direction perpendicular to the initial loading. This configuration is indicative of the complexity of loading that may be considered and is referred to in the paper as ‘T‐shaped’ loading. The energy‐based numerical model employed considers two‐dimensional lateral loading in an elasto‐plastic soil, with coupled behaviour between the two perpendicular directions by local yield surfaces along the length of the pile. The behaviour of the soil–pile system subjected to different loading combinations has been divided into four categories of shakedown previously proposed for cyclic loading of structures and soils. A design chart has been created to illustrate the type of pile behaviour for a given two‐dimensional loading scenario. Copyright © 2009 John Wiley & Sons, Ltd.     

Elastoplastic model with loading memory surfaces (LMS) for monotonic and cyclic behaviour of geomaterials

A new elastoplastic model called loading memory surface based on the critical state concept and the multi‐surface framework is proposed for geomaterials. The model uses a hypoelastic formulation and two plastic mechanisms. The formulations of the model are made in three‐dimensional stress–strain space and work under both monotonic and cyclic loadings. A newly introduced formalism makes it possible to obtain the cyclic response directly from the monotonic loading one. This formalism gives a three‐dimensional generalization of the well‐known Masing rule. The model has been validated against test results of Hostun sand under several conditions: monotonic and cyclic, drained and undrained, tests in compression and in extension, and at different confining pressures and different densities. Copyright © 2014 John Wiley & Sons, Ltd.     

Cyclic macro‐element for soil–structure interaction: material and geometrical non‐linearities

This paper presents a non‐linear soil–structure interaction (SSI) macro‐element for shallow foundation on cohesive soil. The element describes the behaviour in the near field of the foundation under cyclic loading, reproducing the material non‐linearities of the soil under the foundation (yielding) as well as the geometrical non‐linearities (uplift) at the soil–structure interface. The overall behaviour in the soil and at the interface is reduced to its action on the foundation. The macro‐element consists of a non‐linear joint element, expressed in generalised variables, i.e. in forces applied to the foundation and in the corresponding displacements. Failure is described by the interaction diagram of the ultimate bearing capacity of the foundation under combined loads. Mechanisms of yielding and uplift are modelled through a global, coupled plasticity–uplift model. The cyclic model is dedicated to modelling the dynamic response of structures subjected to seismic action. Thus, it is especially suited to combined loading developed during this kind of motion. Comparisons of cyclic results obtained from the macro‐element and from a FE modelization are shown in order to demonstrate the relevance of the proposed model and its predictive ability. Copyright © 2001 John Wiley & Sons, Ltd.     

黏土中两种不同直径单桩水平循环加载模型试验与分析

为探讨海上风机在风、浪等水平往复循环荷载下大直径单桩基础的循环弱化特性,设计了稳定输出长期循环荷载的机械加载装置,开展了软黏土中长期水平循环荷载下海上风电大直径单桩基础和传统长桩基础的模型试验对比研究。根据API给出的骨干曲线和Masing二倍准则构建循环荷载下的p-y（荷载-位移）曲线,并借鉴前人工作,采用累积塑性应变描述软黏土的不排水抗剪强度弱化,提出了分析大周数水平循环荷载下单桩基础循环弱化的理论方法。该方法将循环荷载次数、幅值等外界条件与桩周土体的循环弱化特性建立联系,以适应海洋环境复杂多变的水平循环荷载形式。通过模型试验和理论研究认为,大直径单桩基础因刚度较大,在同样的水平力循环荷载条件下,其抵抗循环荷载的能力明显优于传统长桩。在海上风机大直径单桩的设计中采用基于黏土残余强度的循环后稳定水平承载力更为合理。     

Discrete element method simulations of the seismic response of shallow foundations including soil‐foundation‐structure interaction

A novel three‐dimensional particle‐based technique utilizing the discrete element method is proposed to analyze the seismic response of soil‐foundation‐structure systems. The proposed approach is employed to investigate the response of a single‐degree‐of‐freedom structure on a square spread footing founded on a dry granular deposit. The soil is idealized as a collection of spherical particles using discrete element method. The spread footing is modeled as a rigid block composed of clumped particles, and its motion is described by the resultant forces and moments acting upon it. The structure is modeled as a column made of particles that are either clumped to idealize a rigid structure or bonded to simulate a flexible structure of prescribed stiffness. Analysis is done in a fully coupled scheme in time domain while taking into account the effects of soil nonlinear behavior, the possible separation between foundation base and soil caused by rocking, the possible sliding of the footing, and the dynamic soil‐foundation interaction as well as the dynamic characteristics of the superstructure. High fidelity computational simulations comprising about half a million particles were conducted to examine the ability of the proposed technique to model the response of soil‐foundation‐structure systems. The computational approach is able to capture essential dynamic response patterns. The cyclic moment–rotation relationships at the base center point of the footing showed degradation of rotational stiffness by increasing the level of strain. Permanent deformations under the foundation continued to accumulate with the increase in number of loading cycles. Copyright © 2011 John Wiley & Sons, Ltd.     

海上风电桩基础竖向承载力循环弱化简化分析

提出了一个考虑循环衰减作用的软黏土弹塑性损伤弱化模型,在此模型基础上建立了一个基于剪切位移法的单桩竖向承载力简化计算方法,并利用大型有限元软件进行了不同循环荷载水平下单桩竖向承载力的计算。为了证明简化方法的准确性与有效性,将计算结果与有限元计算结果进行对比,二者的吻合度较高。先期循环荷载能引起单桩竖向承载力弱化,并且弱化程度随先期循环荷载水平的增加而增加。最后将简化方法应用于某海上风电场桩基础承载力的计算中,结果表明,提出的简化方法可应用于实际工程问题的分析。     

水平循环荷载下风电机桩基础离心模型试验研究

在近海风力发电工程中桩基是常用的基础型式,海上风力发电机桩基础一般建立于复杂软土地基、承受着海上风浪、潮流等近似水平向的循环荷载作用,而风力发电机组运行对基础的承载力和变形有严格的要求。因此,研究水平循环荷载下桩土系统变形规律和相互作用机制具有重要的意义。针对典型的近海风机单桩基础,选取典型的饱和砂性土地基,通过离心模型试验的方法研究了水平循环荷载下的风机桩基础的受力变形规律。试验结果表明,水平向循环作用下,桩周围土体中变形主要呈现为挤压或塌陷产生的沉降和水平向变形,变形主要集中在桩周围较小的范围内;变形呈现逐渐累积特性,其大小随着循环次数的增加而增加;桩身弯矩峰值出现在埋深上1/3处,多次循环后的弯矩大小和分布变化不大;桩周围土体中不同位置产生不同的超静孔隙水压力,孔隙水压力发展对土体变形有一定影响     

波浪荷载作用下斜向抗拔桩的承载特性分析

针对浮式海洋结构采用的桩基础,考虑土的循环软化效应,将软土的循环强度与Mohr-Coulomb屈服准则相结合,基于拟静力弹塑性分析建立了循环波浪载荷作用下斜向抗拔桩循环承载性能的计算模型,确定了斜向上载荷作用下抗拔桩的循环承载力,并与单调加载作用下的斜向抗拔桩的极限承载力进行了对比,进一步探讨了桩长、桩径、桩体模量及载荷循环次数等因素对斜向抗拔桩循环承载力的影响。研究结果表明：循环波浪荷载的作用导致了斜向抗拔桩土体循环强度的分布不均匀,从而降低了地基的循环承载力。斜向抗拔桩的动态极限承载力随循环次数的增加而降低,随桩长、桩径及桩体模量的增大而增大。     

Continuum large cracking in a rate‐dependent plastic–damage model for cyclic‐loaded concrete structures

Formulation and algorithmic treatment of a rate‐dependent plastic–damage model modified to capture large tensile cracking in cyclic‐loaded concrete structures are presented in detail for a three‐dimensional implementation. The plastic–damage model proposed by Lee and Fenves in 1998 was founded based on isotropic damaged elasticity in combination with isotropic multi‐hardening plasticity to simulate cracking and crushing of concrete under cyclic or dynamic loadings. In order that the model can capture large crack opening displacements, which are inevitable in plain concrete structures, the excessive increase in plastic strain causing unrealistic results in cyclic behaviors is prevented when the tensile plastic–damage variable controlling the evolution of tensile damage is larger than a critical value. In such a condition, the crack opening/closing mechanism becomes similar to discrete cracking. The consistent tangent operator required to accelerate convergence rate is also formulated for the large cracking state including viscoplasticity. The validation and performance of the modified algorithm implemented in a special finite element program is exemplified through several single‐element tests as well as three structural applications. The last example examines the model in the seismic fracture analysis of Koyna dam as a benchmark problem and the resulting crack profile is compared with the available experiment. The numerical experimentations well demonstrate that the developed model whose modification is necessary to properly simulate the cyclic behavior of plain concrete subjected to large tensile strains is robust and reasonably accurate. Copyright © 2012 John Wiley & Sons, Ltd.     

Three‐dimensional analysis of the seismic behaviour of micropiles used in the reinforcement of saturated soil

This paper includes a numerical study of the behaviour of micropiles used for the reinforcement of saturated soil. Analysis is carried out using the (u–p) formulation (displacement for the solid phase and pore‐pressure for the fluid phase) implemented in a three‐dimensional finite element program. The soil behaviour is described by means of a cyclic elastoplastic constitutive relation which was developed within the framework of the bounding surface concept. The paper is composed of three parts. The first one is concerned with a presentation of the numerical model; the second includes analysis of the seismic behaviour of a single micropile; the last part deals with the group effect under seismic loading. Copyright © 2001 John Wiley & Sons, Ltd.     

考虑循环弱化的饱和黏土简化非线性模型

随着海洋工程建设的快速发展,海洋环境中的地基稳定性逐渐成为学者和工程师关注的热点问题,建立一个简化的饱和黏土循环加载模型对于长期循环荷载下海上构筑物的设计具有重要意义。针对饱和黏土的循环弱化特性,在Hardin-Drnevich等效非线性模型的基础上,建立了考虑循环弱化的饱和黏土简化非线性模型来描述循环加载下饱和黏土的应力-应变关系,模型中引入了由循环加载期间产生的累积塑性变形控制的强度和模量衰减比公式。通过参数分析,说明了形状参数 与n以及残余衰减比与衰减系数等参数的意义和作用。通过对文献中单向循环试验和双向循环试验结果的模拟,验证了该简化模型可以较好地描述循环加载时饱和黏土应力应变滞回圈的演变规律以及循环加载后饱和黏土的强度和刚度弱化现象。简化模型大大提高了计算效率,与传统的土体弹塑性模型相比更加便于工程应用。     

A macro‐element for a circular foundation to simulate 3D soil–structure interaction

This paper presents a non‐linear interface element to compute soil–structure interaction (SSI) based on the macro‐element concept. The particularity of this approach lies in the fact that the foundation is supposed to be infinitely rigid and its movement is entirely described by a system of global variables (forces and displacements) defined in the foundation's centre. The non‐linear behaviour of the soil is reproduced using the classical theory of plasticity. Failure is described by the interaction diagram of the ultimate bearing capacity of the foundation under combined loads. The macro‐element is appropriate for modelling the cyclic or dynamic response of structures subjected to seismic action. More specifically, the element is able to simulate the behaviour of a circular rigid shallow foundation considering the plasticity of the soil under monotonic static or cyclic loading applied in three directions. It is implemented into FedeasLab, a finite element Matlab toolbox. Comparisons with experimental monotonic static and cyclic results show the good performance of the approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Three‐dimensional shakedown solutions for anisotropic cohesive‐frictional materials under moving surface loads

Previous work on three‐dimensional shakedown analysis of cohesive‐frictional materials under moving surface loads has been entirely for isotropic materials. As a result, the effects of anisotropy, both elastic and plastic, of soil and pavement materials are ignored. This paper will, for the first time, develop three‐dimensional shakedown solutions to allow for the variation of elastic and plastic material properties with direction. Melan's lower‐bound shakedown theorem is used to derive shakedown solutions. In particular, a generalised, anisotropic Mohr–Coulomb yield criterion and cross‐anisotropic elastic stress fields are utilised to develop anisotropic shakedown solutions. It is found that shakedown solutions for anisotropic materials are dominated by Young's modulus ratio for the cases of subsurface failure and by shear modulus ratio for the cases of surface failure. Plastic anisotropy is mainly controlled by material cohesion ratio, the rise of which increases the shakedown limit until a maximum value is reached. The anisotropic shakedown limit varies with frictional coefficient, and the peak value may not occur for the case of normal loading only. Copyright © 2013 John Wiley & Sons, Ltd.     

Formulation of a three‐dimensional constitutive model for unsaturated soils incorporating mechanical–water retention couplings

Wheeler, Sharma and Buisson proposed an elasto‐plastic constitutive model for unsaturated soils that couples the mechanical and water retention behaviours. The model was formulated for isotropic stress states and adopts the mean Bishop's stress and modified suction as stress state variables. This paper deals with the extension of this constitutive model to general three‐dimensional stress conditions, proposing the generalized stress–strain relationships required for the numerical integration of the constitutive model. A characteristic of the original model is the consideration of a number of elasto‐plastic mechanisms to describe the complex behaviour of unsaturated soils. This work presents the three‐dimensional formulation of these coupled irreversible mechanisms in a generalized way including anisotropic loading. The paper also compares the results from the model with published experiments performed under different loading conditions. The response of the model is very satisfactory in terms of both mechanical and water retention behaviours. Copyright © 2013 John Wiley & Sons, Ltd.     

A viscoplastic subloading soil model for rate‐dependent cyclic anisotropic structured behaviour

This paper presents a new purely viscoplastic soil model based on the subloading surface concept with a mobile centre of homothety, enabling the occurrence of viscoplastic strains inside the yield surface and avoiding the abrupt change in stiffness of the traditional overstress viscoplastic models. This is required for overconsolidated soils. The model is formulated to reproduce the soil rate‐dependent behaviour under cyclic loading (changes in loading direction) and incorporates both initial and induced anisotropy, as well as destructuring. The model shows good qualitative response to some imposed three‐dimensional stress paths under quasi‐inviscid (elastoplastic) behaviour. Some of the main time‐dependent aspects of soil behaviour that the model is capable of reproducing were also illustrated. The capability of the model to adequately reproduce the results from an undrained triaxial test performed on stiff overconsolidated clays from the Lisbon region (Formação de Benfica), with an unloading–reloading deviatoric stress cycle at constant mean stress, that incorporates a series of staggered fast loading and creep stages, was evaluated. The model was able to reproduce well the main observed aspects of the time‐dependent stress–strain response and pore pressure evolution of a stiff overconsolidated clay under complex loading. The revised and generalised viscoplastic subloading surface concept is viable and can be applied to a consistent extension to viscoplasticity, including in the interior of the yield surface, of existing elastoplastic models formulated for soils and other materials. Copyright © 2016 John Wiley & Sons, Ltd.     

Assessment of soil–pile–structure interaction influencing seismic response of mid-rise buildings sitting on floating pile foundations

The role of the seismic soil–pile–structure interaction (SSPSI) is usually considered beneficial to the structural system under seismic loading since it lengthens the lateral fundamental period and leads to higher damping of the system in comparison with the fixed-base assumption. Lessons learned from recent earthquakes show that fixed-base assumption could be misleading, and neglecting the influence of SSPSI could lead to unsafe design particularly for structures founded on soft soils. In this study, in order to better understand the SSPSI phenomena, a series of shaking table tests have been conducted for three different cases, namely: (i) fixed-base structure representing the situation excluding the soil–structure interaction; (ii) structure supported by shallow foundation on soft soil; and (iii) structure supported by floating (frictional) pile foundation in soft soil. A laminar soil container has been designed and constructed to simulate the free field soil response by minimising boundary effects during shaking table tests. In addition, a fully nonlinear three dimensional numerical model employing FLAC3D has been adopted to perform time-history analysis on the mentioned three cases. The numerical model adopts hysteretic damping algorithm representing the variation of the shear modulus and damping ratio of the soil with the cyclic shear strain capturing the energy absorbing characteristics of the soil. Results are presented in terms of the structural response parameters most significant for the damage such as foundation rocking, base shear, floor deformation, and inter-storey drifts. Comparison of the numerical predictions and the experimental data shows a good agreement confirming the reliability of the numerical model. Both experimental and numerical results indicate that soil–structure interaction amplifies the lateral deflections and inter-storey drifts of the structures supported by floating pile foundations in comparison to the fixed base structures. However, the floating pile foundations contribute to the reduction in the lateral displacements in comparison to the shallow foundation case, due to the reduced rocking components.     

On generalization of constitutive models from two dimensions to three dimensions

In this paper, a study is made of the generalization of constitutive models for geomaterials from two‐dimensional stress and strain states to three‐dimensional stress and strain states. Existing methods of model generalization are reviewed and their deficiencies are highlighted. A new method is proposed based on geometries of the model imprints on two normal planes. Using the proposed method, various three‐dimensional failure criterions suitable for geomaterials are implemented directly into a two‐dimensional model and the generalized model is identical to its original form for the axially symmetric condition. To demonstrate the application of the proposed method, the Modified Cam Clay model is extended using the Matsuoka–Nakai failure criterion. Simulations of soil behaviour for loading in the principal stress space are presented and analysed. Copyright © 2008 John Wiley & Sons, Ltd.     

复合加载条件下沉箱基础稳定性的三维效应

联合采用swipe加载模式与固定位移比加载模式,对于吸力式沉箱基础在水平荷载H与力矩M的复合加载条件下的稳定性进行比较系统的三维有限元分析,主要探讨了基础埋深与直径之比、地基土不排水强度的非均质性对于基础在H-M荷载空间内的破坏包络轨迹的影响,揭示了地基在不同荷载分量组合条件下的失稳破坏机制,并与平面应变假定下得到的结果进行了比较。计算结果表明：平面应变与三维情况下基础的破坏包络面形状有较大差异,分析基础稳定性时,必须考虑其三维效应。在三维情况下,非均质土中埋深与直径之比较小的基础的破坏包络面仍然会向负方向倾斜,已有的包络面方程明显高估这种情况下沉箱基础在正向水平荷载与力矩联合作用下的承载力,从而导致基础设计偏于不安全。     

Rotational kinematic hardening model for three‐dimensional stress reversals in sand

A kinematic hardening mechanism has previously been proposed to capture the behavior of soil during large stress reversals in the triaxial plane. This mechanism is now extended to the principal stress space. It incorporates rotation and intersection of yield surfaces to achieve a consistent and physically rational fit with experimentally observed soil behavior during large three‐dimensional stress reversals. An existing elasto‐plastic model with isotropic hardening is used as the basic framework to which the rotational kinematic hardening mechanism has been added. The new combined model preserves the behavior of the isotropic hardening model under monotonic loading conditions, and the extension from isotropic to rotational kinematic hardening under three‐dimensional conditions is accomplished without introducing new material parameters. The framework of the model is presented here with some comparisons between theoretical and experimental directions of strain increment vectors to indicate the potential of the model. Copyright © 2008 John Wiley & Sons, Ltd.