A hypoplastic macroelement for single vertical piles in sand subject to three-dimensional loading conditions

This paper presents a novel macroelement for single vertical piles in sand developed within the hypo-plasticity theory, where the incremental nonlinear constitutive equations are defined in terms of generalized forces, displacements and rotations. Inspired from the macroelement for shallow foundations of Salciarini and Tamagnini (Acta Geotech, 4(3):163–176, 2009), the new element adopts the “intergranular displacement” mutuated from Niemunis and Herle (Mech Cohes Frict Mater, 2:279–299, 1997) to reproduce the behavior under cyclic loading. Analytical and numerical strategies are provided to calibrate the macroelement’s parameters. Comparisons with experimental results show the performance of the macroelement that while being simple and computational fast is suitable for finite element calculations and engineering design.     

砂土地基斜桩水平承载特性p-y曲线法

基于Reese建议的砂土p-y曲线,提出了适用于斜桩水平承载特性分析的修正p-y曲线及相应的有限元分析方法。根据桩前土体受力特点,假设桩前浅层土体达到极限破坏状态时桩侧被动破坏区为一个三维楔形体,采用极限平衡分析方法导出了斜桩桩侧极限土抗力表达式,对比研究了斜桩倾角、桩-土界面摩擦系数等因素对极限土抗力的影响规律,并给出了斜桩初始地基反力模量确定方法。在此基础上,修正Reese提出的直桩p-y曲线,提出了砂土地基中斜桩p-y曲线确定方法。利用虚功原理,导出了斜桩水平承载特性分析的有限单元列式,编制相应的分析程序,通过算例验证了方法的合理性和有效性。最后,采用修正的p-y曲线法对一离心机模型试验进行了模拟分析,结果表明,计算与试验结果吻合得很好     

A macroelement formulation for shallow foundations on cohesive and frictional soils

The scope of this paper is to present a macroelement model for shallow foundations encompassing the majority of combinations of soil and foundation–soil interface conditions that are interesting for practical applications. The basic idea of the formulation is to raise the common assumption that the surface of ultimate loads of the foundation is identified as a yield surface in the space of force parameters which the footing is subjected to. Instead, each non‐linear mechanism participating in the global response of the system is modelled independently and the surface of ultimate loads is retrieved as the combined result of all active mechanisms. This allows formulating each mechanism by respecting its particular characteristics and offers the possibility of activating, modifying or deactivating each mechanism according to the context of application. The model comprises three non‐linear mechanisms: (a) the mechanism of sliding at the soil–footing interface, (b) the mechanism of soil yielding in the vicinity of the footing and (c) the mechanism of uplift as the footing may get detached from the soil. The first two are irreversible and dissipative and are combined within a multi‐mechanism plasticity formulation. The third mechanism is reversible and non‐dissipative. It is reproduced with a phenomenological non‐linear hyperelastic model. The model is validated with respect to the existing results for shallow foundations under quasi‐static loading tests. It is shown that although the ultimate surface of the foundation is not explicitly used in the formulation of the model, the obtained force states by the model are always contained within it. Copyright © 2010 John Wiley & Sons, Ltd.     

轴向荷载对斜桩水平承载特性影响试验及理论研究

斜群桩受水平荷载作用时,群桩中的基桩受到径向荷载、轴向荷载和弯矩的共同作用。为研究轴向荷载对斜桩水平承载特性的影响,完成了3根单桩以及1组1×2斜桩的大尺寸模型试验。试验结果表明：轴向拉力作用会降低斜桩的水平刚度和极限承载力;而轴向压力作用则会使其水平刚度和极限承载力提高。基于桩侧浅层土体楔形破坏假定,推导了考虑轴向荷载影响的斜桩水平极限土抗力计算公式,提出了桩侧土抗力的p-y曲线方法,并通过模型试验及现场试验验证其合理性。     

竖向荷载作用下斜桩荷载传递性状试验研究

通过模型试验研究了竖向荷载作用下砂土中斜桩的荷载传递性状,分析了桩身倾角及长径比对斜桩桩身轴力、弯矩、剪力、桩侧摩阻力及端阻比的影响。试验结果表明：在桩顶竖向荷载作用下,斜桩桩身轴力均小于相应直桩桩身轴力,桩身倾角越大,轴力沿深度衰减得越快,桩长径比越大,轴力沿深度衰减得也越快;斜桩桩身最大弯矩随桩身倾角及长径比的增加而增加,最大弯矩出现的深度与桩身倾角无关,只与长径比相关;不论桩身倾角及长径比的大小,斜桩桩身最大剪力均出现在桩顶截面处,桩身最大剪力随着桩身倾角的增加而增大;桩身倾角越大,斜桩最大摩阻力越大,长径比越大,斜桩最大摩阻力越小,斜桩最大摩阻力出现在桩顶下1/4～1/5桩长处;斜桩端阻比随着桩顶竖向荷载的增加而增大,随着桩身倾角及长径比的增加而减小。     

Vertical stress distributions around batter piles driven in cross‐anisotropic media

This work presents analytical solutions to compute the vertical stresses for a cross‐anisotropic half‐space due to various loading types by batter piles. The loading types are an embedded point load for an end‐bearing pile, uniform skin friction, and linear variation of skin friction for a friction pile. The cross‐anisotropic planes are parallel to the horizontal ground surface. The proposed solutions can be obtained by utilizing Wang and Liao's solutions for a horizontal and vertical point load acting in the interior of a cross‐anisotropic medium. The derived cross‐anisotropic solutions using a limiting approach are in perfect agreement with the isotropic solutions of Ramiah and Chickanagappa with the consideration of pile inclination. Additionally, the present solutions are identical to the cross‐anisotropic solutions by Wang for the batter angle equals to 0. The influential factors in yielded solutions include the type and degree of geomaterial anisotropy, pile inclination, and distinct loading types. An example is illustrated to clarify the effect of aforementioned factors on the vertical stresses. The parametric results reveal that the stresses considering the geomaterial anisotropy and pile batter differ from those of previous isotropic and cross‐anisotropic solutions. Hence, it is imperative to take the pile inclination into account when piles are required to transmit both the axial and lateral loads in the cross‐anisotropic media. Copyright © 2008 John Wiley & Sons, Ltd.     

A simplified analysis method for piled raft and pile group foundations with batter piles

A simplified method of numerical analysis has been developed to estimate the deformation and load distribution of piled raft foundations subjected to vertical, lateral, and moment loads, using a hybrid model in which the flexible raft is modelled as thin plates and the piles as elastic beams and the soil is treated as springs. Both the vertical and lateral resistances of the piles as well as the raft base are incorporated into the model. Pile–soil–pile, pile–soil–raft and raft–soil–raft interactions are taken into account based on Mindlin's solutions for both vertical and lateral forces. The validity of the proposed method is verified through comparisons with several existing methods for single piles, pile groups and piled rafts. Workable design charts are given for the estimation of the lateral displacement and the load distribution of piled rafts from the stiffnesses of the raft alone and the pile group alone. Additionally, parametric studies were carried out concerning batter pile foundations. It was found that the use of batter piles can efficiently improve the deformation characteristics of pile foundations subjected to lateral loads. Copyright © 2002 John Wiley & Sons, Ltd.     

A hypoplastic constitutive model for clays

This paper presents a new constitutive model for clays. The model is developed on the basis of generalized hypoplasticity principles, which are combined with traditional critical state soil mechanics. The positions of the isotropic normal compression line and the critical state line correspond to the Modified Cam clay model, the Matsuoka–Nakai failure surface is taken as the limit stress criterion and the non‐linear behaviour of soils with different overconsolidation ratios is governed by the generalized hypoplastic formulation. The model requires five constitutive parameters, which correspond to the parameters of the Modified Cam clay model and are simple to calibrate on the basis of standard laboratory experiments. This makes the model particularly suitable for practical applications. The basic model may be simply enhanced by the intergranular strain concept, which allows reproducing the behaviour at very small strains. The model is evaluated on the basis of high quality laboratory experiments on reconstituted London clay. Contrary to a reference hypoplastic relation, the proposed model may be applied to highly overconsolidated clays. Improvement of predictions in the small strain range at different stress levels is also demonstrated. Copyright © 2005 John Wiley & Sons, Ltd.     

A Winkler model approach for vertically and laterally loaded piles in nonhomogeneous soil

An investigation is made to present analytical solutions provided by a Winkler model approach for the analysis of single piles and pile groups subjected to vertical and lateral loads in nonhomogeneous soils. The load transfer parameter of a single pile in nonhomogeneous soils is derived from the displacement influence factor obtained from Mindlin's solution for an elastic continuum analysis, without using the conventional form of the load transfer parameter adopting the maximum radius of the influence of the pile proposed by Randolph and Wroth. The modulus of the subgrade reaction along the pile in nonhomogeneous soils is expressed by using the displacement influence factor related to Mindlin's equation for an elastic continuum analysis to combine the elastic continuum approach with the subgrade reaction approach. The relationship between settlement and vertical load for a single pile in nonhomogeneous soils is obtained by using the recurrence equation for each layer. Using the modulus of the subgrade reaction represented by the displacement influence factor related to Mindlin's solution for the lateral load, the relationship between horizontal displacement, rotation, moment, and shear force for a single pile subjected to lateral loads in nonhomogeneous soils is available in the form of the recurrence equation. The comparison of the results calculated by the present method for single piles and pile groups in nonhomogeneous soils has shown good agreement with those obtained from the more rigorous finite element and boundary element methods. It is found that the present procedure gives a good prediction on the behavior of piles in nonhomogeneous soils. Copyright © 2011 John Wiley & Sons, Ltd.     

A hypoplastic model for mechanical response of unsaturated soils

A new constitutive model is developed for the mechanical behaviour of unsaturated soils based on the theory of hypoplasticity and the effective stress principle. The governing constitutive relations are presented and their application is demonstrated using several experimental data from the literature. Attention is given to the stiffening effect of suction on the mechanical response of unsaturated soils and the phenomenon of wetting‐induced collapse. All model parameters have direct physical interpretation, procedures for their quantification from test data are highlighted. Quantitative predictions of the model are presented for wetting, drying and constant suction tests. Copyright © 2008 John Wiley & Sons, Ltd.     

Surface displacements due to batter piles driven in cross‐anisotropic media

This article derives the closed‐form solutions for estimating the vertical surface displacements of cross‐anisotropic media due to various loading types of batter piles. The loading types include an embedded point load for an end‐bearing pile, uniform skin friction, and linear variation of skin friction for a friction pile. The planes of cross‐anisotropy are assumed to be parallel to the horizontal ground surface. The proposed solutions are never mentioned in literature and can be developed from Wang and Liao's solutions for a horizontal and vertical point load embedded in the cross‐anisotropic half‐space. The present solutions are identical with Wang's solutions when batter angle equals to 0^°. In addition, the solutions indicate that the surface displacements in cross‐anisotropic media are influenced by the type and degree of material anisotropy, angle of inclination, and loading types. An illustrative example is given at the end of this article to investigate the effect of the type and degree of soil anisotropy (E/E′, G′/E′, and ν/ν′), pile inclination (α), and different loading types (a point load, a uniform skin friction, and a linear variation of skin friction) on vertical surface displacements. Results show that the displacements accounted for pile batter are quite different from those estimated from plumb piles, both driven in cross‐anisotropic media. Copyright © 2007 John Wiley & Sons, Ltd.     

Thermal analysis of energy piles in sand

The present work investigates the behaviour of geothermal energy piles in sand subjected to thermal loading and the resulting soil-structure interaction, numerically using the finite element software Abaqus and user-defined material subroutines for soil. The stress-strain response of sand has been simulated using CASM constitutive model based on critical-state soil mechanics. Detailed parametric sensitivity studies have been carried out to understand the effects of different end conditions of the pile, relative densities of the soil, coefficients of lateral earth pressure of the ground, lengths and diameters of the pile, thermal loads, coefficients of friction at the pile-soil interface, critical-state friction angles of soil, thermal conductivity of soil, specific heat of soil and thermal conductivity of the pile on the stress response of soil, deformation of the pile and soil, and strains in the pile. The results show that negative shear stress is generated in the soil at the pile-soil interface. In the pile with both ends restrained the lateral earth pressure coefficient in soil increases due to high radial strain generation. Moreover, the lateral earth pressure coefficient in soil increases with the increase in the thermal load, the coefficient of friction at the pile-soil interface and the critical-state friction angle of the soil.     

一种改进的粘土亚塑性本构模型

简要地介绍了Herle和Kolymbas针对黏土建立的亚塑性本构模型的方法。结合黏土的特性以及对响应包络线的分析,详细地列出了HK模型几个尚未解决的问题,并对该模型3个参数分别进行了改进,建立了改进后的HK亚塑性公式以及参数的确定方法。改进后的模型继承了HK模型参数少、易确定以及公式简洁等特点,使HK模型不仅具有严密的数学和力学基础,而且具有较好的实际意义。     

考虑物态变化的粗粒土亚塑性本构模型

建立了可描述粗粒土单调和循环力学特性的一个亚塑性本构模型。基于亚塑性理论的基本框架,引入临界状态参数,建立了一个新的粗粒土亚塑性模型,给出了数学公式及参数确定方法。采用该模型对粗粒土单调和循环加载试验进行了模拟和预测。该模型无需判断加卸载、参数较少、易于三维化,能够较全面地描述单调和循环荷载作用下粗粒土的主要力学特性,如强度与围压的非线性关系,胀缩规律与围压相关、卸载体缩、体变随加载过程累积等主要体变特性等。     

Skin friction features of drilled CIP piles in sand from pile segment analysis

Numerical pile segment analysis is conducted in this study with an advanced soil model to investigate the skin friction behaviour of a drilled Cast‐In‐Place (CIP) pile installed in sand. Although the interface between the sand and pile is considered rough, thin elements adjacent to the pile are used to include effects of localized shear. Unit weights of fluid concrete and accompanied changes in stress are considered as the effects of pile installation. Changes in effective stresses are the most prominent effect due to pile installation with a change in direction of the major principal stress from the vertical to the radial direction. Shear behaviour of the sand at the interface during the early shear stage is related to the contractive tendency of the sand at small strain levels. Changes in the stress field around the pile with little changes in volumetric strain take place during the early shear stage. Stress redistributions during the early shear stage depend on the direction of the major principal stress before shear. Results of the pile segment analyses for drilled CIP piles show good agreement with design methods. Parametric studies are used to characterize the effects of sand density and pile diameter on the skin friction behaviour of drilled CIP piles. Copyright © 2007 John Wiley & Sons, Ltd.     

砂土中单桩抗拔极限承载力的计算

桩侧极限摩阻力是砂土中单桩抗拔极限承载力的主要组成部分,作为计算桩侧极限摩阻力的关键参数--土侧压力系数K的取值合理与否直接影响到单桩抗拔极限承载力计算的准确度。首先,基于密砂和松砂中的桩在上拔破坏时桩侧土压力分别呈被动和主动状态,同时考虑桩侧摩阻力和桩身表面粗糙度的影响,分别推导了不同相对密实度砂土中的土侧压力系数。然后,利用所得到的土侧压力系数并考虑桩侧单位摩阻力发挥的临界深度,按沿桩-土界面发生圆柱状剪切破坏模式建立了砂土中单桩抗拔极限承载力的计算方法。最后,利用该方法对已有的抗拔桩试验结果进行分析和比较,结果表明计算值与实测值吻合较好。     

Three dimensional elasto‐plastic interface for embedded beam elements with interaction surface for the analysis of lateral loading of piles

This paper presents a numerical formulation for a three dimensional elasto‐plastic interface, which can be coupled with an embedded beam element in order to model its non‐linear interaction with the surrounding solid medium. The formulation is herein implemented for lateral loading of piles but is able to represent soil‐pile interaction phenomena in a general manner for different types of loading conditions or ground movements. The interface is formulated in order to capture localized material plasticity in the soil surrounding the pile within the range of small to moderate lateral displacements. The interface is formulated following two different approaches: (i) in terms of beam degrees of freedoms; and (ii) considering the displacement field of the solid domain. Each of these alternatives has its own advantages and shortcomings, which are discussed in this paper. The paper presents a comparison of the results obtained by means of the present formulation and by other well‐established analysis methods and test results published in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

A hypoplastic model for granular soils incorporating anisotropic critical state theory

It is well known that soil is inherently anisotropic and its mechanical behavior is significantly influenced by its fabric anisotropy. Hypoplasticity is increasingly being accepted in the constitutive modeling for soils, in which many salient features, such as nonlinear stress-strain relations, dilatancy, and critical state failure, can be described by a single tensorial equation. However, within the framework of hypoplasticity, modeling fabric anisotropy remains challenging, as the fabric and its evolution are often vaguely assumed without a sound basis. This paper presents a hypoplastic constitutive model for granular soils based on the newly developed anisotropic critical state theory, in which the conditions of fabric anisotropy are concurrently satisfied along with the traditional conditions at the critical state. A deviatoric fabric tensor is introduced into the Gudehus-Bauer hypoplastic model, and a scalar-valued anisotropic state variable signifying the interplay between the fabric and the stress state is used to characterize its impact on the dilatancy and strength of the soils. In addition, fabric evolution during shearing can explicitly be addressed. Modifications have also been undertaken to improve the performance of the undrained response of the model. The anisotropic hypoplastic model can simulate experimental tests for sand under various combinations of principle stress direction, intermediate principal stress (or mode of shearing), soil densities, and confining pressures, and the associated drastic effect of different principal stress orientations in reference to the material axes of anisotropy can be well captured.     

砂土中螺纹桩承载特性的模型试验研究

通过室内模型试验,研究砂土中螺纹桩的竖向承载特性,比较分析螺纹桩与普通直桩承载性能的差异以及螺距对螺纹桩承载力的影响。静载荷试验后进行一系列土工试验,研究桩周土的物理力学性质。试验结果表明,在相同条件下螺纹桩的极限承载力约是普通直桩极限承载能力的1～4倍,极限状态下的平均桩侧阻力是普通直桩的3~4倍;在一定范围内,随着螺距的减小,螺纹桩的桩侧阻力可以得到有效的发挥,极限承载能力和控制沉降的能力逐渐增强。     

Group interaction on vertically loaded piles in saturated poroelastic soil

The pile-to-pile interaction was obtained for vertically loaded piles embedded in homogeneous poroelastic saturated soil. Deduced from Biot’s theory, the fundamental functions of the quasi-static development for the force, displacement and pore pressure were acquired in cylindrical coordinates. The pile–soil system was decomposed into extended soil and fictitious piles, and the compatibility condition was set up between the axial strain of the fictitious piles and the corresponding average strain over the extended soil. This approach results in the governing equations, which consist of the Fredholm integral equations of the second kind and the basic unknowns of the axial forces along the fictitious pile shaft. The axial force and settlement along the pile shaft were calculated based on the axial forces of the fictitious piles. The interaction between the piles was investigated under different consolidation conditions through a two-pile model, and two pile interaction factors were obtained. Stemming from the two-pile analysis, numerical analyses on the settlement of the pile groups were conducted to probe pile interaction with consolidation. The conventional solutions for the single-phase soil-pile problem seem to underestimate the interaction factor if the consolidation effect is taken into account as pile settlement continues. The pile-to-pile interaction can also aggravate the percentage of consolidation settlement (PCS), and as the pile number increases, the value of the PCS will also increase. Several key factors, such as the pile stiffness, pile slenderness ratio and pile spacing, are investigated to better understand the impact of consolidation on pile analysis.