Undrained lower bound solutions for end bearing capacity of shallow circular piles in non-homogeneous and anisotropic clays

The undrained bearing capacity of shallow circular piles in non-homogeneous and anisotropic clay is investigated by the lower bound (LB) finite element limit analysis (FELA) under two-dimensional (2D) axisymmetric condition using second-order cone programming, and the new solution of the problem is presented. Modified from the isotropic von Mises yield criterion, a cross-anisotropic undrained strength criterion of clays under the axisymmetric state of stress requiring three input shear strengths in triaxial compression, direct simple shear, and triaxial extension is employed in the 2D axisymmetric LB FELA. Parametric studies on the effects of pile embedment ratio, dimensionless strength gradient, anisotropic strength ratio, and pile roughness are investigated extensively, while the predicted failure mechanisms associated with these parameters are discussed and compared. Numerical results of undrained end bearing capacity of shallow circular piles are summarized in the form of design tables that are useful for design practice and represent a new contribution to the field of pile capacity considering the combined effects of undrained strength non-homogeneity and anisotropy.     

AUS: Anisotropic undrained shear strength model for clays

A total stress model applicable to clays under undrained conditions is presented. The model involves three strength parameters: the undrained shear strengths in triaxial compression, triaxial extension, and simple shear. The amount of physical anisotropy implied by the model is a function of the relative magnitude of these three strengths assuming a Mises-type plastic potential. Elastoplastic deformation characteristics below failure are accounted for by a hardening law requiring two additional parameters that can be related to the axial strains halfway to failure in triaxial compression and extension. Finally, elasticity is accounted for by Hooke law. The result is a relatively simple model whose parameters can all be inferred directly from a combination of in situ and standard undrained laboratory tests. The model is applied to a problem involving the horizontal loading of a monopile foundation for which full scale tests have been previously conducted. The model shows good agreement with the measured data.     

循环荷载下软黏土不排水强度弱化分析的动力有限元ABAQUS实现

在波浪循环荷载作用下饱和软黏土地基出现孔隙水压力升高,并导致不排水强度弱化,严重影响防波堤的承载性能。考虑静偏应力影响,基于最大孔隙水压力发展模型和正常固结软黏土不排水强度公式,推导出软黏土不排水强度随循环荷载作用次数和应力水平变化的动态折减规律。结合软黏土不排水强度动态折减规律和M-C屈服准则,在有限元软件ABAQUS上实现软黏土不排水强度循环弱化分析的数值开发和动力运算过程。运用该动力有限元方法对天津港防波堤地基软黏土的动、静三轴试验进行数值模拟运算。结果表明,最大孔隙水压力发展曲线以及循环荷载作用后不排水强度的数值预测结果与动三轴试验结果吻合良好。另外,动力有限元方法（DFEM）能够表示土体强度在循环荷载作用下的具体弱化过程。     

Effects of boundary conditions and partial drainage on cyclic simple shear test results—a numerical study

Owing to imperfect boundary conditions in laboratory soil tests and the possibility of water diffusion inside the soil specimen in undrained tests, the assumption of uniform stress/strain over the sample is not valid. This study presents a qualitative assessment of the effects of non‐uniformities in stresses and strains, as well as effects of water diffusion within the soil sample on the global results of undrained cyclic simple shear tests. The possible implications of those phenomena on the results of liquefaction strength assessment are also discussed. A state‐of‐the‐art finite element code for transient analysis of multi‐phase systems is used to compare results of the so‐called ‘element tests’ (numerical constitutive experiments assuming uniform stress/strain/pore pressure distribution throughout the sample) with results of actual simulations of undrained cyclic simple shear tests using a finite element mesh and realistic boundary conditions. The finite element simulations are performed under various conditions, covering the entire range of practical situations: (1) perfectly drained soil specimen with constant volume, (2) perfectly undrained specimen, and (3) undrained test with possibility of water diffusion within the sample. The results presented here are restricted to strain‐driven tests performed for a loose uniform fine sand with relative density D_r=40%. Effects of system compliance in undrained laboratory simple shear tests are not investigated here. Copyright © 2004 John Wiley & Sons, Ltd.     

原状和重塑海洋粘土经历动载后的静强度衰减

根据海洋粉质粘土原状和重塑土样的动三轴试验结果, 比较和分析了两种土样应力、应变、孔隙水压力和不排水抗剪强度行为, 得到了土样的静不排水抗剪强度衰减与波浪荷载作用下土样产生的动应变以及平均累积孔压之间的关系。 并将波浪荷载作用使土样内孔压升高, 有效应力降低, 形成拟超固结现象的理论, 应用到土样不排水抗剪强度衰减与平均累积孔压之间关系的分析;同时与重塑土样的超固结静态剪切试验结果进行比较, 得到了土样在波浪荷载作用后的归一化不排水抗剪强度与拟超固结比之间的关系式。 建议以少量原状土样, 配合大量重塑土样的动三轴试验结果, 实现对实际海洋粘土地基在波浪荷载作用后的静不排水抗剪强度衰化规律的评估。     

Anisotropic viscoplastic modeling of rate‐dependent behavior of clay

The objective of this study is to derive an effective stress‐based constitutive law capable of predicting rate‐dependent stress–strain, stress path and undrained shear strength and creep behavior. The flow rule used in the MIT‐E3 model and viscoplasticity theory is employed in the derivation. The model adopts the yield surface capable of representing the yield behavior of the Taipei silty clay and assumes that it is initially symmetric about the K₀‐line. A method is then developed to compute the gyration and expansion of the loading surface to simulate the anisotropic behavior due to the principal stress rotation after shear. There are 11 parameters required for the model to describe the soil behavior and six of them are exactly the same as those used in the Modified Cam‐clay model. The five additional parameters can be obtained by parametric studies or conventional soil tests, such as consolidation tests, triaxial compression and extension tests. Finally, verification of the model for the anisotropic behavior, creep behavior and the rate‐dependent undrained stress–strain and shear strength of the Taipei silty clay is conducted. Copyright © 2010 John Wiley & Sons, Ltd.     

各向异性弹黏塑性模型在ABAQUS中的研发

通过将Perzyna过应力理论与临界状态理论相结合,并引入Wheeler旋转硬化法则,提出一个能描述土体初始各向异性及应力诱发各向异性的三维弹黏塑性本构模型。模型考虑流变发生的下限,在三维应力空间,模型存在形状相似的静屈服面及动态加载面。采用缩放形式的幂函数。本构模型数值算法采用回映算法,借助ABAQUS软件UMAT子程序接口实现。并通过对三轴不排水蠕变试验的模拟,确定合适的积分步长。此后,分别对三轴不排水蠕变试验及常应变率三轴不排水剪切试验进行了模拟。模拟中通过设置不同参数值,可将模型退化为各向同性模型,并对这两种模拟结果进行了比较。模拟结果表明：(1) 对于三轴不排水蠕变,在低剪应力水平下,各向同性模型和各向异性模型模拟的结果相差不大,而在高剪应力水平下,各向异性模型模拟结果更接近试验结果;(2) 对于常应变率加载试验的模拟,模型合理反映了土体不排水强度随着加载速率的增大而增大现象。     

An experimental database for the development,calibration and verification of constitutive models for sand with focus to cyclic loading: part I—tests with monotonic loading and stress cycles

For numerical studies of geotechnical structures under earthquake loading, aiming to examine a possible failure due to liquefaction, using a sophisticated constitutive model for the soil is indispensable. Such a model must adequately describe the material response to a cyclic loading under constant volume (undrained) conditions, amongst others the relaxation of effective stress (pore pressure accumulation) or the effective stress loops repeatedly passed through after a sufficiently large number of cycles (cyclic mobility, stress attractors). The soil behaviour under undrained cyclic loading is manifold, depending on the initial conditions (e.g. density, fabric, effective mean pressure, stress ratio) and the load characteristics (e.g. amplitude of the cycles, application of stress or strain cycles). In order to develop, calibrate and verify a constitutive model with focus to undrained cyclic loading, the data from high-quality laboratory tests comprising a variety of initial conditions and load characteristics are necessary. The purpose of these two companion papers was to provide such database collected for a fine sand. The database consists of numerous undrained cyclic triaxial tests with stress or strain cycles applied to samples consolidated isotropically or anisotropically. Monotonic triaxial tests with drained or undrained conditions have also been performed. Furthermore, drained triaxial, oedometric or isotropic compression tests with several un- and reloading cycles are presented. Part I concentrates on the triaxial tests with monotonic loading or stress cycles. All test data presented herein will be available from the homepage of the first author. As an example of the examination of an existing constitutive model, the experimental data are compared to element test simulations using hypoplasticity with intergranular strain.     

Microplane constitutive model for porous isotropic rocks

The paper deals with constitutive modelling of contiguous rock located between rock joints. A fully explicit kinematically constrained microplane‐type constitutive model for hardening and softening non‐linear triaxial behaviour of isotropic porous rock is developed. The microplane framework, in which the constitutive relation is expressed in terms of stress and strain vectors rather than tensors, makes it possible to model various microstructural physical mechanisms associated with oriented internal surfaces, such as cracking, slip, friction and splitting of a particular orientation. Formulation of the constitutive relation is facilitated by the fact that it is decoupled from the tensorial invariance restrictions, which are satisfied automatically. In its basic features, the present model is similar to the recently developed microplane model M4 for concrete, but there are significant improvements and modifications. They include a realistic simulation of (1) the effects of pore collapse on the volume changes during triaxial loading and on the reduction of frictional strength, (2) recovery of frictional strength during shearing, and (3) the shear‐enhanced compaction in triaxial tests, manifested by a deviation from the hydrostatic stress–strain curve. The model is calibrated by optimal fitting of extensive triaxial test data for Salem limestone, and good fits are demonstrated. Although these data do not cover the entire range of behaviour, credence in broad capabilities of the model is lend by its similarity to model M4 for concrete—an artificial rock. The model is intended for large explicit finite‐element programs. Copyright © 2002 John Wiley & Sons, Ltd.     

An experimental database for the development,calibration and verification of constitutive models for sand with focus to cyclic loading: part II—tests with strain cycles and combined loading

For numerical studies of geotechnical structures under earthquake loading, aiming to examine a possible failure due to liquefaction, using a sophisticated constitutive model for the soil is indispensable. Such model must adequately describe the material response to a cyclic loading under constant volume (undrained) conditions, amongst others the relaxation of effective stress (pore pressure accumulation) or the effective stress loops repeatedly passed through after a sufficiently large number of cycles (cyclic mobility, stress attractors). The soil behaviour under undrained cyclic loading is manifold, depending on the initial conditions (e.g. density, fabric, effective mean pressure, stress ratio) and the load characteristics (e.g. amplitude of the cycles, application of stress or strain cycles). In order to develop, calibrate and verify a constitutive model with focus to undrained cyclic loading, the data from high-quality laboratory tests comprising a variety of initial conditions and load characteristics are necessary. It is the purpose of these two companion papers to provide such database collected for a fine sand. Part II concentrates on the undrained triaxial tests with strain cycles, where a large range of strain amplitudes has been studied. Furthermore, oedometric and isotropic compression tests as well as drained triaxial tests with un- and reloading cycles are discussed. A combined monotonic and cyclic loading has been also studied in undrained triaxial tests. All test data presented herein will be available from the homepage of the first author. As an example of the examination of an existing constitutive model, the experimental data are compared to element test simulations using hypoplasticity with intergranular strain.     

近海粘土设计参数与指标特性之间的关系分析

展示了近海粘土指标特性与设计参数之间相关关系的研究结果。该项研究的一个重要目的是建立一个按统一方法测定的高质量的土性测试指标数据库。该数据库由10个场地组成，包括大西洋、挪威北海、挪威海、里海和2个沿海陆上地点。数据库分析表明，前期固结压力pc?与液限指数IL之间存在良好的相关关系，但当液限指数小于0.5时，数据比较分散。同时还发现，前期固结压力与由三轴压缩、三轴拉伸及直剪试验测定的不排水抗剪强度之间均有很好的线性相关关系。由此，以pc?与IL之间的关系为基础，提出了使用这些线性关系式估算近海粘土原位不排水强度su的方法及建议。     

复合加载情况下双层地基极限承载力研究

在复合加载情况下精确求解层状非均质地基的极限承载力,具有很强的工程实用与理论参考价值。基于土体极限平衡理论与通用有限元软件ABAQUS,针对复合加载情况下上硬下软的双层不排水饱和软黏土地基的极限承载力,进行了大量的数值计算,得出了上层土临界深度Hcr的计算公式、竖向极限承载力Pv的计算公式以及复合加载情况下地基破坏时的破坏包络面方程。研究结果表明：上层土临界深度Hcr取决于土层间强度比Su1/Su2;竖向极限承载力Pv与破坏包络面取决于土层间强度比Su1/Su2、上层土深度H1与基础型式。     

Triaxial tests on the fluidic behavior of post-liquefaction sand

Liquefaction-induced ground deformation is a major cause of structural damage during earthquakes. However, a better understanding of seismic liquefaction is needed to improve earthquake hazard analyses and mitigate structural damage. In this paper, a dynamic triaxial test apparatus was employed to investigate the fluidic characteristics of post-liquefaction sand. The specimens were vibrated to the point of liquefaction by dynamic loading, and then the liquefied sand was further sheared by triaxial compression in an undrained manner. It was found that a non-Newtonian fluid model can accurately describe the shear stress and the shear strain rate of post-liquefaction sand during undrained triaxial compression. The apparent viscosity, a major parameter in a constitutive model of a non-Newtonian fluid, decreases with an increase in the shear strain rate.     

Mathematical modelling of monotonic and cyclic undrained clay behaviour

The proposed general analytical model describes the anisotropic, elasto-plastic, path-dependent, stress-strain-strength properties of inviscid saturated clays under undrained loading conditions. The model combines properties of isotropic and kinematic plasticity by introducing the concept of a field of plastic moduli which is defined in stress space by the relative configuration of yield surfaces. For any loading (or unloading) history, the instantaneous configuration is determined by calculating the translation and contraction (or expansion) of each yield surface. The stress-strain behaviour of clays can thus be determined for complex loading paths and in particular for cyclic loadings. The stress-strain relationships are provided for use in finite element analyses. The model parameters required to characterize the behaviour of any given clay can be derived entirely from conventional triaxial or simple shear soil test results. The model's extreme versatility is demonstrated by using it to formulate the behaviour of the Drammen clay under both monotonic and cyclic loading conditions. The parameters are determined by using solely the results from monotonic and cyclic strain-controlled simple shear experimental tests, and the model's accuracy is evaluated by applying it to predict the results of other tests such as (1) cyclic stress-controlled simple shear tests, (2) monotonic triaxial loading compression and unloading extension tests, and (3) cyclic stress- and strain-controlled triaxial tests on, this same clay. The theoretical predictions are found to agree extremely well with the experimental test results.     

Analysis of the vane test considering size and time effects

An analysis of the vane test using an Arbitrary Lagrangian–Eulerian formulation within a finite element framework is presented. This is suitable for soft clays for which the test is commonly used to measure in situ undrained shear strength. Constitutive laws are expressed in terms of shear stress–shear strain rates, and that permits the study of time effects in a natural manner. An analysis of the shear stress distributions on the failure surface according to the material model is presented. The effect of the constitutive law on the shear band amplitude and on the position of the failure surface is shown. In general, the failure surface is found at 1–1·01 times the vane radius, which is consistent with some experimental results. The problem depends on two dimensionless parameters that represent inertial and viscous forces. For usual vane tests, viscous forces are predominant, and the measured shear strength depends mainly on the angular velocity applied. That can explain some of the comparisons reported when using different vane sizes. Finally, the range of the shear strain rate applied to the soil is shown to be fundamental when comparing experimental results from vane, triaxial and viscosimeter tests. Appart from that, an experimental relation between undrained shear strength and vane angular velocity has been reproduced by this simulation. Copyright © 1999 John Wiley & Sons, Ltd.     

Undrained capacity of a surface circular foundation under fully three-dimensional loading

Circular foundations are widely employed in offshore engineering to support facilities and are generally subjected to fully three-dimensional loading due to the harsh offshore environmental load and complex operational loads. The undrained capacity of surface circular foundations on soil with varying strength profiles and under fully three-dimensional loading is investigated and presented in the form of failure envelopes that obtained from finite element analyses. The combined ultimate limit state of circular foundations is defined as the two-dimensional failure envelopes in resultant H-M loading space accounting for the vertical load and torsion mobilisation. The effects of vertical load and torsion mobilisation, soil shear strength heterogeneity and loading angle from moment to horizontal load on the shape of normalised H-M failure envelopes are explored. A series of expressions are proposed to describe the shape of failure envelopes obtained numerically, enabling essentially instantaneous generation of failure envelopes and optimisation of a circular foundation design based on constraint of any input variable through implementation in an automated calculation tool. An example application is ultimately provided to illustrate how the proposed expressions may be used in practice.     

A multisurface kinematic hardening model for the behavior of clays under combined static and undrained cyclic loading

In dynamic geotechnical problems, soils are often subjected to a combination of sustained static and fast cyclic loading. Under such loading conditions, saturated and normally consolidated clays generally experience a build-up of excess pore water pressure along with a degradation of stiffness and strength. If the strength of the soil falls below the static stress demand, a self-driven failure is triggered. In this paper, a constitutive model is presented for the analysis of such problems, based on a general multisurface plasticity framework. The hardening behavior, the initial arrangement of the surfaces, and the nonassociated volumetric flow rule are defined to capture important aspects of cyclic clay behavior. This includes nonlinear hysteretic stress-strain behavior, the effect of anisotropic consolidation, and the generation of excess pore water pressure during undrained cyclic loading along with a degradation of stiffness and strength. The model requires nine independent parameters, which can be derived from standard laboratory tests. A customized experimental program has been performed to validate the model performance. The model predictions show a good agreement with test results from monotonic and cyclic undrained triaxial tests, in particular with respect to the strain-softening response and the number of loading cycles to failure. A procedure for a general stress-space implicit numerical implementation for undrained, total stress-based finite element analyses is presented, including the derivation of the consistent tangent operator. Finally, a simulation of the seismic response of a submarine slope is shown to illustrate a possible application of the presented model.     

A simple critical-state-based double-yield-surface model for clay behavior under complex loading

The critical state concept has been widely used in soil mechanics. The purpose of this study is to apply this concept in the framework of multi-mechanism elastoplasticity. The developed model has two yield surfaces: one for shear sliding and one for compression. In this model, the location of the critical state line is explicitly considered and related to the actual material density to control the peak strength and the phase transformation characteristics. The stress reversal technique is incorporated into the model for describing clay behavior under complex loading including changes of stress direction. The determination of the model parameters is discussed; it requires only one drained or undrained triaxial test up to failure with an initial isotropic consolidation stage. The model is used to simulate drained and undrained tests under monotonic loading with different over-consolidation ratios on various remolded and natural clays, including true triaxial tests with different Lode’s angles. Drained and undrained tests under cyclic loadings are also simulated by using the set of parameters determined from monotonic tests. The comparison between experimental results and numerical simulations demonstrate a good predictive ability of this new simple model.     

基于有效固结应力法确定结构性黏性土不排水抗剪强度

由于结构性的存在使得很多天然黏性土的强度和变形特性不同于重塑土和非结构性土。首先回顾了适用于确定重塑土和非结构性土不排水抗剪强度的有效固结应力法,并推导了相应的方程。在此基础上,对于结构性黏性土,采用两段不同斜率（内摩擦角正切）和截距（黏聚力）的直线模拟其抗剪强度包络线,建立了确定其不排水抗剪强度的有效固结应力法方程;当有效应力小于结构屈服应力时,有效固结应力方程中有效应力部分需乘以0.8的修正系数;只要已知剪切前的有效应力,利用相应的有效固结应力法公式,可确定结构性土体的不排水抗剪强度。利用连云港结构性软黏土的等压固结三轴试验数据,验证了有效固结应力法的适用性。分析表明：对于连云港软黏土的不排水抗剪强度,有效固结应力法的计算结果与试验结果吻合较好;对于结构屈服应力,有效固结应力法的预测结果与试验数据点的拟合结果有一定偏差,但并不明显。     

纤维加筋砂土抗液化试验与数值模拟

砂土液化是导致重大地震灾害的主要原因之一。本研究探讨了天然纤维加筋砂土在循环荷载作用下的抗液化性能。在不排水条件下,对具有不同纤维含量的加筋砂土试样进行了一系列循环三轴试验,研究了饱和砂土的液化特性以及循环剪应变幅值、纤维含量对饱和砂土抗液化性能的影响。此外,通过模拟已完成的循环三轴试验,建立了二维有限元数值模型,并对具有不同纤维含量的加筋砂土进行了参数标定。研究结果表明:(1)增加循环剪应变幅值将促进超孔压累积,使得滞回曲线斜率和平均有效应力减小速度加快;(2)纤维的存在能够减缓超孔压的累积,随着纤维含量增加,加筋砂土抗液化能力得到明显提高;(3)标定后的本构模型参数能可靠地用于模拟纤维加筋砂土的液化响应。研究结果为饱和砂土抗液化问题与纤维加筋砂土的数值模拟提供了有价值的参考。