超固结黏土中不排水柱孔扩张弹塑性解及应用

为求得超固结黏土中考虑K₀影响的柱孔不排水扩张精确解，该文基于黏土和砂土模型(CASM)屈服准则，采用经典的应力剪胀关系，充分考虑土体静止土压力参数K₀和重度超固结比，运用非相关联流动法则进行应力空间转换，进而建立超固结黏土中考虑K₀影响情况下柱孔不排水扩张问题的一阶偏微分方程组求解模型。根据弹塑性边界已知的应力和位移条件，通过数值求解方法确定柱孔扩张模型的精确解。对比修正剑桥模型(MCC)解，基于SMP准侧改进的修正剑桥模型(SMP-MCC)解及黏土和砂土统一硬化模型(CSUH)解进行参数分析表明：当土体OCR≤2时，该文方法较好地模拟土体单元屈服应力和破坏应力；当土体OCR>2时，该文方法克服了超固结黏土高估屈服应力和破坏应力；当K₀由1.0变化到2.5时，归一化极限扩孔压力由5.4变化到3.2，归一化极限超静孔隙水压力由2.4变化到1.0。并通过现场实测数据验证了该文方法的实用性与正确性。     

砂土统一本构模型研究及其三维数值实现

基于广义塑性理论与临界状态概念,研究提出了一个统一三维砂土本构模型,通过一组参数实现了砂土由压缩至剪切过程中状态参量的统一表述。基于ABAQUS提供的用户自定义材料子程序UMAT接口,利用Fortran语言编程实现了该三维弹塑性本构关系模型在软件中的二次开发。分别利用Toyoura砂、Fuji River砂以及Tokachi砂的剪切试验数据与数值模拟结果进行对比,结果表明:提出的有限元计算模型可以有效反映加载过程中不同围压和砂土初始密度对应力-应变曲线的影响,能够准确描述密砂的剪胀特性与应变软化特性以及松砂的剪缩特性与应变硬化特性,从而更加真实地反映三维应力状态下土的变形和强度特性。研究成果进一步扩展了ABAQUS在岩土工程中的应用范围,能够为岩土工程领域的数值分析计算提供更加快捷的解决方案。     

砂土强度和剪胀性的颗粒力学分析

砂土强度和剪胀性一直是土力学强度和变形研究的难点和重点,对其进一步认识的关键取决于对砂土颗粒状微观结构的洞察。砂土的颗粒性和散碎性使其适合采用颗粒力学来研究。该文从颗粒力学角度出发,利用平面离散元模拟砂土变形,建立并标定了砂土单元实验的一个颗粒力学模型。在此基础上,通过颗粒力学参数影响分析,研究了砂土无侧限双轴试验的三种表观强度指标(临界状态强度、峰值强度和特征应力强度)、剪胀性及剪切模量的颗粒力学影响因素。研究结果表明:砂土临界状态强度仅受砂土颗粒摩擦系数的影响,是材料属性,符合临界状态土力学理论;砂土峰值强度和特征应力强度不但与砂土颗粒摩擦系数相关,还与围压水平和相对密实度有关。峰值强度不受砂土颗粒自身刚度性质的影响,而特征应力强度受颗粒刚度性质的影响较大,但后者的影响规律不是简单的正比或反比的关系。砂土剪切模量主要受其颗粒自身刚度性质的影响,就目前研究来看,它与砂土相对密实度的关系并不显著。用颗粒力学方法对剪胀性的深入研究比较困难,主要是因为诸多颗粒力学参数(砂土颗粒摩擦系数和刚度、砂土样品的孔隙率及围压水平)均与之相关。该文尝试研究了砂土剪胀性与其颗粒转角的关系。最后,用该文标定的颗粒力学模型,研究了无重地基极限承载力普朗德尔-瑞斯纳问题,通过颗粒力学计算结果与普朗德尔-瑞斯纳解的对比,深化了对砂土地基极限承载力的理解,也为计算颗粒力学方法在岩土工程尺度上的应用提供了参考。     

基于非共轴理论的各向异性砂土应变局部化分析

针对各向异性砂土应变局部化分析中本构模型存在的不足,采用非共轴理论进行改进。传统塑性位势理论采用各向同性假设,导致其模型不能描述非共轴特性和不能较好描述各向异性的不足,为克服传统塑性势理论的局限性,引入非共轴塑性理论建立了砂土的三维非共轴临界状态各向异性本构模型。考虑细观组构张量和应力张量的几何关系,改进模型即可描述主应力轴旋转条件下砂土材料状态的改变,材料状态变化直接导致模型的硬化规律和剪胀性发生变化,从而描述了原生各向异性的影响。非共轴修正后模型可以描述应力诱发各向异性和非共轴特性,结合分叉理论模型可以对不同沉积角度随围压变化的应变局部化特性进行分析。Toyoura砂的单剪试验和平面应变试验验证表明模型改进效果较好。     

不同应力路径下石灰岩碎石力学特性的大型三轴试验研究

为了解不同应力路径下,昆明新机场石灰岩碎石填料的力学特性及该填料力学特性受水影响的程度,采用大型三轴试验机,对该填料进行不同应力路径下的三轴试验及等σ′₃压缩应力路径下的干湿对比试验。结果表明:Δσ′₁≥0 时,围压和应力比k (即小主应力增量与大主应力增量的比值)增大,试件峰值应力及初始模量亦增大,但剪胀逐渐受到抑制;石灰岩碎石的剪胀及剪缩特性与应力路径有很强的相关性;石灰岩碎石的强度非线性特征显著,围压减小的应力路径下,试件剪切强度比等σ′₃应力路径下略低;水对石灰岩碎石的剪切强度、初始模量及剪胀性有较大影响。该文的试验成果可为构建考虑应力路径影响的高填方粗颗粒填料本构模型提供试验基础。     

三维各向异性砂土UH模型

为了全面地描述砂土在三维空间不同方向上的本构特性,应当综合考虑各向异性和中主应力的影响。该文在砂土UH（统一硬化）模型的基础上,采用各向异性的变换应力方法,发展了三维各向异性砂土UH模型。该方法通过调整不同方向应力分量的相对大小,将各向异性砂土等效为各向同性砂土,并且在变换应力空间将偏平面上的破坏或屈服包线变成圆形。用各向异性的变换应力张量代替真实应力张量,能够方便地得到同时考虑各向异性和中主应力影响的砂土UH模型。与试验数据的对比表明,三维各向异性UH模型能够合理地预测真三轴应力状态下各向异性砂土的应力-应变关系。     

饱和砂土基于相变状态的不排水本构模型

饱和砂土基于相变状态的改进本构模型能较好地描述砂土不排水情况下的应力-应变关系。通过改进模型中相变状态参量的计算方法,将e-lgp°表达式加以改进,通过详细的阐述,提出e_pt-lgp的关系式,并通过三轴压缩试验的数据对提出的关系式加以验证。应用新的关系式计算不排水条件下试样的相变孔隙比e_pt,进而计算出模型中的相变状态参量。改进后的不排水本构模型的计算结果与不排水三轴压缩的试验结果能较好地吻合,即验证了本构模型的有效性,也验证了e_pt-lgp关系式的合理性,使原有的边界面本构模型更好地描述不排水的情况下、不同密度和围压状态下饱和砂土的力学行为。     

反映粗粒料应力路径相关性的一种应变硬化模型

粗粒料已成为山区高填方工程的主要填筑材料,建立能较全面反映其力学特性的本构模型,对高填方工程的模拟分析及安全评价具有重要意义。在已有大型三轴试验研究的基础上,通过将硬化土模型与修正剑桥模型相结合同时引入对数形式的非线性强度参数关系式,建立了一种简便实用的弹塑性本构模型。该模型不仅能考虑应力水平对粗粒料应力-应变关系、体变特性、强度特性的影响,还能较好地反映粗粒料的应力路径相关性,模拟复杂应力状态下的粗粒料的变形特性,并且相关参数通过常规三轴试验即可测定。最后通过与不同应力路径试验结果进行对比,证明了模型的合理性。     

等压固结条件下湘江饱和砂土动力特性研究

在大量的动三轴试验基础上,研究了等压固结条件下湘江饱和砂土振动孔隙水压力、应力应变滞回圈以及应力路径的发展变化规律。研究结果表明:孔压发展变化过程与土体的剪胀、剪缩密切相关;孔压与轴向动应变之间的变化关系显示饱和砂土具有明显的各向异性;从孔压与滞回圈面积累积之和的关系看,孔压的增长伴随着能量的损失;对于围压较大的情形,用ExpAssoc函数进行拟合效果较好。隧振次增加应力应变滞回圈也在发生变化,第一阶段滞回圈呈倒置的帽子形,第二阶段呈菱角形状。在振动初始阶段,应力路径基本上呈倾斜的直线变化;随孔压的增加,加载和卸载两条应力路径逐渐分开,呈纺锤形。     

非饱和黏性土的三剪次加载面模型研究

基于非饱和土三剪强度准则和次加载面模型，构建了适用正常固结非饱和黏性土的Bishop和Fredlund应力变量法三剪次加载面模型，将2个模型计算结果与非饱和黏土的单调静三轴试验及循环动三轴试验结果做了对比，结果表明，Fredlund应力变量法本构模型要更接近试验结果。在静三轴试验的土体变形后期，Fredlund和Bishop应力变量法的模型计算结果与试验数据的应力偏差分别为2%和10%;在动三轴试验的土体振动后期，Fredlund和Bishop应力变量法与试验结果的应变偏差分别为4.2%和7.5%。另外，对所提模型的真三轴分析结果可知，静真三轴试验的中间主应力影响系数和基质吸力的增大均会使得土体的抗剪强度增加，随着基质吸力增大，不同模拟结果依次的应力偏差均为11%左右；随着中间主应力影响系数增大，不同模拟结果之间的应力偏差大致为4%。动真三轴试验的最小主应力或中间主应力越大，非饱和黏性土的棘轮效应和抗剪强度也越大，不同中间主应力模拟结果之间的应变偏差为3.3%,不同最小主应力模拟结果之间的应变偏差为8.5%。     

A constitutive model for the uplift behavior of anchors in cohesionless soils

Abstract

A series of triaxial tests has been performed to establish the stress‐strain curves for I‐Lan sand and Taipei silty sand. A constitutive model for the continuous strain hardening‐softening and volumetric dilatancy of these two soils is proposed, based on the results of triaxial tests. Using this model, a numerical program is then established, with FLAC software, to analyze the uplift behavior of model anchors in sand and field anchors in silty soil.

It was found from triaxial tests, that the peak friction angle increases with relative density of soil and decreases with confining pressure. A non‐associated flow rule between plastic strain increment and stress tensor was found. As accumulative plastic strain, relative density and confining pressure were changed, the mobilized friction angle and mobilized dilatancy angle also changed. All parameters needed for the proposed model can be expressed as functions of relative density and confining pressure. This model can calculate the stress‐ strain curves of cohesionless soils determined from triaxial tests accurately.

The load‐displacement behaviors determined from anchor tests are compared with those calculated from this numerical program, the numerical results are in good agreement with the test results not only for model anchors in sand but also for different types of field anchors in silty soil.     

An experimental study of failure and softening in sand under three-dimensional stress condition

This paper describes an experimental study of failure and softening behaviour in dense Toyoura sand. A true triaxial apparatus equipped with three pairs of rigid loading platens is used to test sand sample under three-dimensional stress condition. The testing results demonstrate that the rigid boundary around the sand samples cannot prevent formation of shear localization. Shear localization are observed to emerge in the hardening or the softening regime in the loading depending on the magnitude of intermediate principal stress. Uniform deformation for the whole strain range is obtained only in triaxial compression tests. The peak stress state obtained from tests of sand samples of the same initial density can be described with good approximation by the Matsuoka–Nakai criterion.     

考虑主应力轴旋转Gudehus-Bauer亚塑性模型的改进

基于非线性连续介质力学的基本原理,提出了一个考虑主应力轴旋转改进的Gudehus-Bauer亚塑性模型。新改进的Gudehus-Bauer亚塑性模型强调应力增量的大小和方向不仅与当前应力状态有关,而且还取决于当前应变增量的大小和方向。模型中4个参数可由休止角,最大孔隙比以及最小孔隙比估计出来;而其它4个参数可由等向压缩实验、三轴压缩实验以及密砂的侧向压缩实验确定。最后,通过算例把改进后模型数值模拟结果与有关实验资料做了比较,结果表明改进的Gudehus-Bauer亚塑性模型可以考虑主应力轴旋转对砂土强度和变形特性的影响。     

Experimental evaluation and extension of a simple critical state model for sand

This paper presents an experimental evaluation of a simple critical state model and its extension in modelling the stress-strain behaviour of sand under a wide range of confining pressures and initial void ratios under both drained and undrained loading conditions. The critical state model concerned is known as CASM developed by Yu [1,2] and CASM is a relatively simple model as it only requires seven model constants, five of which are the same as those used in the modified Cam clay model. All these constants have clear physical meanings and can be easily determined from the results of triaxial tests as demonstrated in this paper. A key advantage of CASM over many other existing critical state models lies on its unified nature as it can be used to model the behaviour of both clay and sand. In addition, the paper also shows how CASM can be further extended in order to simulate a particular undrained behaviour of loose sand, which is the reappearance of hardening after the material experiences a peak shear stress followed by a softening response.     

Triaxial compression tests of QH-E lunar soil simulant under constant mean principal stress path using discrete element method simulations

In this paper, discrete element method (DEM) simulations are applied to investigate the triaxial compression tests of QH-E lunar soil simulant (developed by Tsinghua University, China) under constant mean principal (P) stress path. The P stress path is achieved by controlling the loading speed and direction of the axial stress and confining stress in the DEM simulations, the strain softening and dilatancy characteristics of QH-E lunar soil simulant both at low and conventional P stress levels are discussed. The results show that the deviatoric stress–strain curve is divided into hardening, softening descending, and residual strain stages, and the shear strength and residual strength increase with the increase of P stress, which are similar to the conventional triaxial compression tests. The volumetric strain versus shear strain curve shows a good linear relationship both at the linear shear dilatancy and residual shear dilatancy stages, but the slope of the linear dilatancy stage is larger than that of the residual dilatancy stage. Furthermore, it is found that the variations of shear dilatancy characteristic parameters with regard to P stress also show a good linear relationship, and the values of these parameters increase with the increase of P stress.     

Parameter identification for a macroscopic granular soil model applied to dense Berlin Sand

The present paper outlines the macroscopic stress-strain behaviour of cohesionless soils by the example of dense Berlin Sand. Granular materials as sand show very complex stress-strain relations depending on the stress state and the load history. Examination of these relations is performed at a representative elementary volume (REV) consisting of a sufficient amount of particles. In triaxial tests quasi-static loads are applied to axisymmetric samples, representing the REV, with simultaneous measurement of the response of the granular structure. Within the constitutive equations of the elasto-plastic model, the elastic response is described by a materially non-linear elasticity law. Plastic deformations are considered in the context of a single-surface yield function with isotropic hardening properties. Non-associated flow is realized with an additional plastic potential function. Isotropic behaviour is assumed and the study is restricted to small strains. The parameter identification for the model under study is shown for dense Berlin Sand on the basis of triaxial tests. Received: 2 July 1999     

Internal-variable constitutive model for rate-independent plasticity with hardening saturation surface

Summary An elastic-plastic material model with internal variables and thermodynamic potential, not admitting hardening states out of a saturation surface, is presented. The existence of such a saturation surface in the internal variables space — a consequence of the boundedness of the energy that can be stored in the material's internal micro-structure — encompasses, in case of general kinematic/isotropic hardening, a one-parameter family of envelope surfaces in the stress space, which in turn is enveloped by a limit surface. In contrast to a multi-surface model, noad hoc rules are required to avoid the intersection between the yield and bounding/envelope surface. The flow laws of the proposed model are studied in case of associative plasticity with the aid of the maximum intrinsic dissipation theorem. It is shown that the material behaves like a standard one as long as its hardening state either is not saturated, or undergoes a desaturation from a saturated hardening state, whereas, for saturated hardening states not followed by desaturation, it conforms to a combined yielding law in which the static internal variable rates obey a nonlinear hardening rule similar to that of analogous models of the literature. Additionally, the material is shown to behave as a perfectly plastic material for a class of (critical) saturated hardening states for which the stress state is on the limit surface. For nonassociative material models, it is shown that, under a special choice of the plastic and saturation potentials and through a suitable parameter identification, the well-known Chaboche model is reproduced. A few numerical examples are presented to illustrate the associative material response under monotonic and cyclic loadings.Dedicated to Prof. Dr. Dr. h. c. Franz Ziegler on the occasion of his 60th birthday