考虑颗粒破碎的粗粒土剪胀性统一本构模型

粗粒土作为无黏性散粒状材料具有状态依赖特性,土体的剪切特性受密度和应力水平影响。易破碎是粗粒土的另一个特点,颗粒破碎影响粗粒土的剪胀、内摩擦角、峰值强度和渗透系数。为了能够准确地描述粗粒土的应力-应变关系,采用初始状态参量描述粗粒土的内部状态,根据三轴试验数据建立考虑颗粒破碎耗能的应力-应变关系,采用相关联流动法则推导考虑颗粒破碎的粗粒土剪胀性“统一本构模型”,并建立初始状态参量与模型参数之间的关系。所建立的统一本构模型既考虑了颗粒破碎对剪胀、内摩擦角的影响,又考虑了剪切特性对土体初始状态的依赖。采用变异粒子群算法拟合试验曲线,确定模型参数。模型计算结果能够很好地拟合试验曲线。采用同一组参数对假定的初始状态进行模拟计算,计算结果表明,模型能够模拟不同初始密度和应力水平下粗粒土变形的一般规律。     

干密度对粗粒料力学特性的影响

粗粒料的力学特性不仅取决于应力状态,还与粗粒料本身的松密程度密切相关,即与粗粒料的材料状态相关。通过不同初始干密度的粗粒料常规大型三轴各向等压固结排水剪切试验研究了干密度对粗粒料力学特性的影响。试验结果表明：粗粒料应力-应变曲线的形态取决于密度和围压的共同作用,破坏状态之前密度和围压共同决定了粗粒料的强度和变形,而当应变足够大处于渐进状态或临界状态时,粗粒料的应力和体积应变受初始干密度的影响逐渐减小直至消失。对于软化型曲线,相变状态的应力小于渐进状态的应力,而渐进状态的应力小于破坏状态的应力。无论围压大小如何,随着初始干密度的增大,应力-应变曲线的硬化性逐渐减弱,而软化性则逐渐增强。     

基于分数阶微积分的粗粒料静动力边界面本构模型

分数阶微分理论在土体静力黏弹性本构模型中得到了广泛应用,然而,其在动力弹塑性模型中的应用尚不多见。为此,基于分数阶微积分理论分析了粗粒料在循环荷载下的变形特性,提出了粗粒料在循环荷载下的分数阶应变率;并以此为基础,进一步建立了粗粒料受静动力荷载作用下的边界面塑性力学本构模型。所提出模型包含10个参数,均可以运用常规三轴试验获得。为了验证所提出模型,选取了几种已有不同文献中的不同粗粒料试验数据进行了模拟,发现,所提出的模型可以较好地模拟粗粒料在静动力加载下的应力-应变行为,对于循环荷载下的长期变形也能较好地预测。     

一种适用于饱和黏土循环动力分析边界面塑性模型的隐式积分算法

修正了传统隐式回映算法,建立了适用于饱和黏土循环动力分析的边界面塑性模型的完全隐式积分格式。该模型基于无弹性域概念和临界状态理论,采用各向同性、运动硬化准则、旋转的边界面,并引入表征土体结构损伤和重塑程度的损伤变量以反映循环载荷作用下饱和黏土的各向异性、刚度、强度软化及塑性变形累积等特征。针对等压固结 和偏压固结 的饱和高岭黏土的不排水三轴试验进行模拟,采用不同的应变增量步长进行计算,并与试验数据对比,结果表明,修正隐式回映算法应用于该类边界面模型的合理性、积分格式的精确性和稳定性;另外,结合有限元软件自动时间步长的增量迭代解法,对饱和黏土应力控制的不排水动三轴试验进行预测,结果表明,修正的适用于该边界面的塑性模型隐式回映算法可以得到比较合理的数值分析结果,能够反映饱和黏土的循环刚度的退化和强度的弱化等动力特性。     

砂土多机构边界面塑性模型及其试验验证

根据Iai多重剪切机构塑性模型及边界面塑性模型的特点,建立了一个砂土多机构边界面塑性模型。该模型将土复杂的变形机理分解为体积机理和一系列简单的剪切机理。用边界面弹塑性模型模拟多重剪切机构塑性模型中虚拟单剪机构,避免了Iai多重剪切机构塑性模型在利用修正Masing准则模拟虚拟单剪应力-应变关系时确定比例参数的复杂性。根据大量试验资料,建立了液化面参数与归一累积剪切功的关系,能够用较少的参数很好地建立有效应力路径。由于多重机理的特性,该模型能够模拟复杂荷载作用下主应力轴偏转的影响。试验结果表明,应用该模型的计算结果与试验结果有较好的一致性。     

颗粒级配对粗粒土强度与变形特性影响的研究

采用三维颗粒流软件PFC3D的内置FISH语言,进行二次开发,模拟粗粒土级配,建立一个研究高铁填方路基粗粒土变形特性的颗粒流模型。通过粗粒土三轴试验,标定了表征粗粒土细观力学性质的模型参数,并验证了模型的有效性。考虑粗粒土曲率系数和不均匀系数对颗粒级配的影响,模拟并研究了5种不同级配下粗粒土在3种不同围压下的变形特性。试验结果表明,曲率系数对粗颗粒土变形特性影响较大,当其有效粒径与中值粒径及限制粒径的差距过大时,粗粒土中颗粒填充及致密性将变差,变形增大,强度降低。以较大曲率系数与较大不均匀系数组合的粗粒土受力性能较好,但此种级配的粗粒土压缩性大。级配良好且不均匀系数较大,其应力链分布越均匀,颗粒的挤压效果越显著,力的传递和分配也越均匀。     

基于CPTu的状态相关边界面模型标定研究

对土工结构进行数值分析时,需要引入土的有效应力本构模型,以预测土体变形或液化破坏。然而,由于土单元初始状态的不确定性和缺乏适当的试验结果,模型参数标定经常成为实际工程应用的障碍。在现有边界面模型中引入状态相关的剪胀性概念,使得土体破坏时处于临界状态。基于现场孔压静力触探试验（piezocone penetration test,简称CPTu）的测试数据,提出了模拟单调和循环荷载下土体液化和破坏的边界面模型的参数标定方法。取现场残余强度为室内试验的临界状态,用于标定临界状态线相关参数。基于现有CPTu数据的抗液化强度图,以及震级比例系数与液化等效循环次数之间的联系,建立了土体液化应力比与等效循环次数的关系,在此基础上简要介绍了标定卸载体积模量参数的方法。最后基于CPTu实测地层数据,具体说明了模型相关参数的标定过程。     

粗粒筑坝材料的动力变形特性

结合室内大型动三轴试验资料,对粗粒料的动力变形特性进行研究后认为,在复杂的高应力条件下振动过程中试验粗粒料由于体积缩小而变得更为密实,其动应力-应变关系与Hardin-Drnevich模型的双曲骨架曲线假定有明显差异,其阻尼特性也不符合Hardin假定;提出了反映试验过程中材料振动硬化特性的幂函数型动应力-应变关系模型和基于试验资料的粗粒料阻尼比估算公式;粗粒料的动残余变形特性与其初始密度、静应力状态、动荷载、振动持续时间等因素密切相关,建立了考虑初始固结围压影响的粗粒料残余应变与动剪应力之间的关系模型。可为强震区超高土石坝的深入研究提供可靠的理论依据。     

粗粒土大三轴试验研究综述

自然界中广泛分布粗粒土,其具有压实密度大、良好透水性、抗剪强度高、沉降变形小、不易产生地震液化等优良的工程特性,已被广泛运用于土石坝工程建设中。本文在阅读大量参考文献的基础上概括和总结了粗粒土大三轴试验研究进展情况,包括抗剪强度、变形特性、应力-应变关系特性、试验中的若干问题,并结合已有认识,提出了笔者一些自己的思考,指出了今后关于粗粒土的研究方向。     

粗粒含量对砾类土直剪过程中强度与变形特性影响的离散元模拟研究

粗粒含量对砾类土的工程力学特性具有重要的影响。本文对4组不同粗粒含量的强风化玄武岩砾类土进行了大型直剪试验,并获取相关的强度与变形参数,基于离散单元法颗粒流理论,采用粒间作用为平行黏结模型的圆球模拟土颗粒,建立了4种不同粗粒含量砾类土直剪的离散单元模拟的计算模型,并进一步校正了颗粒单元细观参数,模拟了不同粗粒含量砾类土100kPa垂直压力时的应力应变关系、垂直变形以及剪切带上的土颗粒运动与颗粒间作用力传递的影响特性,分析了粗粒含量对砾类土宏观及细观力学性质的影响机理。结果表明:砾类土表现出的粗粒含量越大强度越高的本质是由于随粗粒含量增加时,土颗粒间平均刚度增加及颗粒间的咬合作用使得摩擦系数增加,采用平行黏结模型能较好的拟合峰值前剪应力-剪位移曲线,但是峰后曲线段尤其对软化现象的适应性不是十分理想; 垂直位移-剪位移模拟值与试验值存在一定的偏差; 随着粗粒含量的增加,最大剪应力时粗颗粒对力链的控制表现得愈明显,相应的剪切带厚度约为剪切盒高度的1/3～1/5,并随粗粒含量增加而增大。     

A unified bounding surface plasticity model for unsaturated soils

A unified constitutive model for unsaturated soils is presented in a critical state framework using the concepts of effective stress and bounding surface plasticity theory. Consideration is given to the effects of unsaturation and particle crushing in the definition of the critical state. A simple isotropic elastic rule is adopted. A loading surface and a bounding surface of the same shape are defined using simple and versatile functions. The bounding surface and elastic rules lead to the existence of a limiting isotropic compression line, towards which the stress trajectories of all isotropic compression load paths approach. A non‐associated flow rule of the same general form is assumed for all soil types. Isotropic hardening/softening occurs due to changes in plastic volumetric strains as well as suction for some unsaturated soils, enabling the phenomenon of volumetric collapse upon wetting to be accounted for. The model is used to simulate the stress–strain behaviour observed in unsaturated speswhite kaolin subjected to three triaxial test load paths. The fit between simulation and experiment is improved compared to that of other constitutive models developed using conventional Cam‐Clay‐based plasticity theory and calibrated using the same set of data. Also, the model is used to simulate to a high degree of accuracy the stress–strain behaviour observed in unsaturated Kurnell sand subjected to two triaxial test load paths and the oedometric compression load path. For oedometric compression theoretical simulations indicate that the suction was not sufficiently large to cause samples to separate from the confining ring. Copyright © 2005 John Wiley & Sons, Ltd.     

Constitutive model for cyclic behaviour of cohesionless sands

This paper presents a constitutive model for describing the stress-strain response of sands under cyclic loading. The model, formulated using the critical state theory within the bounding surface plasticity framework, is an upgraded version of an existing model developed for monotonic behaviour of cohesionless sands. With modification of the hardening law, plastic volumetric strain increment and unloading plastic modulus, the original model was modified to simulate cyclic loading. The proposed model was validated against triaxial cyclic loading tests for Fuji River sand, Toyoura sand and Nigata sand. Comparison between the measured and predicted results suggests that the proposed modified model can capture the main features of cohesionless sands under drained and undrained cyclic loading.     

Cavity expansion analyses of crushable granular materials with state‐dependent dilatancy

Crushability is one of the important behaviors of granular materials particularly under high stress states, and affects both the deformability and strength of the materials that are in essence associated with state‐dependent dilatancy. In this presentation, first, a new critical state model is proposed to take into account the three different modes of compressive deformation of crushable granular materials, i.e. particle rearrangement, particle crushing and pseudo‐elastic deformation. Second, the governing equations for cavity expansion in crushable granulates are introduced, in which the state‐dependent dilatancy as well as the bounding surface plasticity model are used. Then, the procedure to obtain semi‐analytical solutions to cavity expansion in the material is described in detail, in which a commercial differential equation solver is employed. Finally, cavity expansion analyses are carried out on Toyoura sand, a well‐documented granular material, to demonstrate the effects of crushability and state‐dependent dilatancy. The study shows that particle crushing does occur at both high stress and critical states and affects the stress fields and the deformation behavior of the material surrounding the cavity in association with state‐dependent dilatancy. This leads to conclusion that particle crushing and state‐dependent dilatancy have to be taken into account when cavity expansion theory is used to interpret cone penetration tests and pressuremeter tests. Copyright © 2011 John Wiley & Sons, Ltd.     

Constitutive modelling of granular materials using a contact normal-based fabric tensor

This paper presents a fabric tensor-based bounding surface model accounting for anisotropic behaviour (e.g. the dependency of peak strength on loading direction and non-coaxial deformation) of granular materials. This model is developed based on a well-calibrated isotropic bounding surface model. The yield surface is modified by incorporating the back stress which is proportional to a contact normal-based fabric tensor for characterising fabric anisotropy. The evolution law of the fabric tensor, which is dependent on both rates of the stress ratio and the plastic strain, rules that the material fabric tends to align with the loading direction and evolves towards a unique critical state fabric tensor under monotonic shearing. The incorporation of the evolution law leads to a rotational hardening of the yield surface. The anisotropic critical state is assumed to be independent of the initial values of void ratio and fabric tensor. The critical state fabric tensor has the same intermediate stress ratio (i.e. b value) and principal directions as the critical state stress tensor. A non-associated flow rule in the deviatoric plane is adopted, which is able to predict the non-coaxial flow naturally. The stress–strain relation and fabric evolution of model predictions show a satisfactory agreement with DEM simulation results under monotonic shearing with different loading directions. The model is also validated by comparing with laboratory test results of Leighton Buzzard sand and Toyoura sand under various loading paths. The comparison results demonstrate encouraging applicability of the model for predicting the anisotropic behaviour of granular materials.

     

A high strain‐rate constitutive model for sand and its application in finite‐element analysis of tunnels subjected to blast

The paper presents a constitutive model for simulating the high strain‐rate behavior of sands. Based on the concepts of critical‐state soil mechanics, the bounding surface plasticity theory and the overstress theory of viscoplasticity, the constitutive model simulates the high strain‐rate behavior of sands under uniaxial, triaxial and multi‐axial loading conditions. The model parameters are determined for Ottawa and Fontainebleau sands, and the performance of the model under extreme transient loading conditions is demonstrated through simulations of split Hopkinson pressure bar tests up to a strain rate of 2000/s. The constitutive model is implemented in a finite‐element analysis software Abaqus to analyze underground tunnels in sandy soil subjected to internal blast loads. Parametric studies are conducted to examine the effect of relative density and type of sand and of the depth of tunnel on the variation of stresses and deformations in the soil adjacent to the tunnels. Copyright © 2012 John Wiley & Sons, Ltd.     

A two-mechanism soil–structure interface model for three-dimensional cyclic loading

A three-dimensional (3D) soil–structure interface model is proposed within the two-mechanism constitutive theory and bounding surface theory originally established for soils. The proposed model has two main characteristics: first, the model is formulated based on two different and superposed deformation mechanisms. The first mechanism is due to the stress ratio increment, and the second is due to the normal stress increment. Each mechanism induces a shear strain component and a normal strain component. The proposed model can be reduced to the conventional single-mechanism interface model. Second, the plastic modulus and stress dilatancy are defined using the bounding surface theory. The plastic flow rule under cyclic loading is modified and assumed to be dependent on both the stress state of the mapping point and the stress reversal loading direction. The proposed model was validated against the available 3D interface tests and was found to satisfactorily reflect the salient features of the interfaces under monotonic and cyclic loading paths with different normal boundaries. The problem in which the elastic normal stiffness in conventional single-mechanism interface models is often underestimated to enhance the simulation performance under varying normal stress conditions is solved by incorporating the second mechanism. And the effect of the second mechanism on the modeling behavior is discussed. The modified plastic flow direction accurately simulates the 3D cyclic shear response, and the difference between the model simulation and test result increases with the number of cycles by use of the plastic flow direction defined in conventional bounding surface theory.     

On the modeling of the state dependency of granular soils

Experimental studies have revealed that principal elements of the mechanical behavior of granular soils like the angles of internal peak friction and dilatancy are highly influenced by the combined effect of soil density and mean principal effective stress. In the literature, various empirical correlations between these elements and some parameters indicating soil state have been suggested. Herein, by using two well-known empirical expressions for state dependent peak friction and dilatancy angles, proper constitutive equations are derived and implemented in a stress ratio-based bounding surface plasticity framework. It is shown that the modified model is capable of simulating sand response in either loose or dense states using a unique set of parameters.     

硬化土模型体积屈服机制及其本构积分算法研究

剪切-体积双屈服机制的硬化土（Hardening-Soil）模型能够相对准确地反映土体复杂应力路径的影响在岩土工程中已得到广泛的应用,国内的相关研究对于其体积屈服机制的理解上普遍存在着偏差,相关文献对于其内部控制参数解法的描述并不正确,无法体现该模型准确模拟单轴压缩及K0固结特性等方面的优势。笔者从对其体积屈服和硬化内部控制参数的物理意义的着手,解释了该模型体积屈服机制的工作过程,并进一步给出了其内部控制参数的显式解析算法及推导过程。针对于该模型的非线性弹性-多屈服机制塑性所导致的数值求解复杂性,给出了其基于改进欧拉中点法的本构积分算法,结合相关研究的参考试验及数值计算结果进行了验证。     

A kinematic hardening constitutive model for sands: the multiaxial formulation

This paper explores the possibility of using well-accepted concepts—Mohr-Coulomb-like strength criterion, critical state, existence of a small strain elastic region, hyperbolic relationship for representing global plastic stress–strain behaviour, dependence of strength on state parameter and flow rules derived from the Cam-Clay Model—to represent the general multiaxial stress–strain behaviour of granular materials over the full range of void ratios and stress level (neglecting grain crushing). The result is a simple model based on bounding surface and kinematic hardening plasticity, which is based on a single set of constitutive parameters, namely two for the elastic behaviour plus eight for the plastic behaviour, which all have a clear and easily understandable physical meaning. In order to assist the convenience of the numerical implementation, the model is defined in a ‘normalized’ stress space in which the stress–strain behaviour does not undergo any strain softening and so certain potential numerical difficulties are avoided. In the first part the multiaxial formulation of the model is described in detail, using appropriate mixed invariants, which rationally combine stress history and stress. The model simulations are compared with some experimental results for tests on granular soils along stress paths lying outside the triaxial plane over a wide range of densities and mean stresses, using constitutive parameters calibrated using triaxial tests. Furthermore, the study is extended to the analysis of the effects induced by the different shapes of the yield and bounding surfaces, revealing the different role played by the size and the curvature of the bounding surface on the simulated behaviour of completely stress- and partly strain-driven tests. Copyright © 1999 John Wiley & Sons, Ltd.