粒状材料颗粒破碎的力学特性描述

基于粒状材料的颗粒破碎对材料剪胀特性的影响以及描述特征状态应力比的幂函数表达式,提出相应的屈服面和屈服面的表达式,并对屈服面随参数的变化规律进行分析。分析结果表明:通过选取适当的参数,屈服面能够完全回归到修正剑桥模型屈服面的形式。最后,结合适当的等向压缩条件和统一硬化参数,将屈服面应用到砂土的本构模型,能够很好地预测试验结果,合理描述砂土颗粒破碎的力学特性。     

砂土三维多重机构边界面模型

以土的临界状态和边界面塑性理论为基础,引入状态参数,考虑砂土的剪胀特性,提出一个新型三维多重机构边界面模型。模型将复杂的宏观变形行为分解为一个宏观体应变机构和一系列空间分布的虚拟一维微观剪切机构。每个微观剪切机构包含一个微观剪应力–应变关系和一个微观应力–剪胀关系。利用三轴压缩试验中的应力条件,建立典型宏微观参数之间的关系。模型包含13个参数,多数可通过具有明确物理意义的土性参数来确定。通过对砂土三轴压缩试验和空心圆柱扭剪试验结果的数值模拟,表明模型不但能够合理反映在排水或不排水条件下砂土的硬化及软化特性,而且能在不增加任何参数条件下预测应力主轴旋转产生的变形累积特性和应变增量主轴与应力主轴之间的非共轴特性。     

常压至高压下砂土强度、变形特性试验研究

 砂土材料常压至高压下的强度、变形特性是构建砂土模型的首要问题。开展3种粒组砂土8 MPa围压范围内的等向压缩试验以及0.2～6.4 MPa围压范围内的三轴剪切试验,将砂土常压至高压范围内的力学特性进行系统分析,以获得能够将常压至高压范围内的强度、变形特性进行统一描述的力学参数。通过研究发现：(1) 砂土在高压下出现一定量的颗粒破碎,改变了砂土的剪切耗能机制,使得砂土三轴压缩剪切由剪胀软化特征向剪缩硬化特征转变;(2) 砂土材料的三轴压缩剪切峰值应力比受砂土粒径、围压共同影响,M-C强度准则在高压条件下不再适用;而残余应力比则基本不受粒径、围压的影响,是典型的无黏性摩擦型岩土力学参数,应作为砂土基本力学特性指标;(3) 砂土材料在常压至高压范围内的剪切过程中存在较明显的临界状态现象,临界状态曲线与等向压缩曲线形态相同均呈指数衰减型并在高压条件下产生交叉,两者共同构成砂土材料的状态区间能够体现常压至高压范围内的剪胀与剪缩特征。     

土的统一硬化模型及其发展

土的统一硬化模型是以修正剑桥模型为理论基础,以采用统一硬化参数使其简明反映土的剪胀性、以采用变换应力方法使其合理反映土的三维特性为标志性特征,可针对不同类型土的特性,通过对统一硬化参数作适当调整,来建立与其相应的模型。统一硬化模型被发展为黏土和砂土的统一硬化模型、统一硬化超固结土模型、统一硬化K0超固结土模型、考虑砂土软化的模型、考虑土的材料各向异性的模型等十余种模型。这些模型能分别描述土的剪缩、剪胀、硬化、软化、超固结性、初始应力各向异性、材料各向异性、结构性、蠕变压缩和渐进状态等特性以及大应力条件下颗粒破碎和循环加载条件下土的变形特性等。     

一个考虑颗粒破碎的堆石料弹塑性本构模型

基于广义塑性理论建立了一个考虑堆石料颗粒破碎的弹塑性本构模型。模型采用随平均应力增加而减小的峰值摩擦角和特征点摩擦角来反映堆石料因颗粒破碎而表现出的峰值应力比与剪胀应力比的非线性,在此基础上确定塑性流动和加载方向向量;运用指数型压缩函数建立依赖于体积应变和平均应力的压缩参数 λ ,并构造随平均应力与剪应力水平而变化的塑性模量表达式。模型共有 8 个参数,均可通过等向或单向压缩和三轴压缩试验确定。为验证本文模型的合理性,依据试验资料确定了 3 种不同堆石料的本构模型参数,并对典型三轴压缩试验进行了模拟。 3 种材料的模型预测结果与试验数据均吻合良好,表明本文模型可合理反映了颗粒破碎对堆石料强度与变形特性的影响。     

考虑状态相关的砂土非正交弹塑性本构模型

砂土的力学特性具有显著的状态相关性，主要体现为不同应力状态与密实状态下砂土的变形特性具有显著差异。合理的状态相关硬化规律与剪胀规律描述是反映砂土状态相关变形特性的基础。提出了能够有效描述砂土等向压缩规律与临界状态规律的微分表达式，并基于等向压缩硬化规律建立了状态相关因子ω，发展了砂土状态相关的硬化参数H，旨在合理确定塑性应变增量的大小；在利用非正交塑性流动法则确定塑性应变增量的方向的过程中，引入了状态变量ψ对分数阶次μ的影响，从而考虑了塑性应变增量方向的状态相关性，合理地描述了砂土的状态相关剪胀性。进一步，结合引入了状态变量的Hooke定律，确定了弹性应变增量，从而发展得出能够描述砂土状态相关特征的非正交弹塑性本构模型。通过合理预测Toyoura砂的常规三轴排水及不排水试验结果，验证了所建模型能够有效捕获砂土的状态相关力学特性。     

考虑砂土颗粒破碎的柱孔扩张问题弹塑性分析

目前对砂土中圆孔扩张问题的研究均未考虑到砂土颗粒的破碎以及剪胀特性,且为了方便后续求解,很多学者对剪应力,剪切模量等计算参数做了简化,使得最终的求解结果无法准确反映实际情况。针对上述问题,采用考虑颗粒破碎和剪胀特性的砂土临界本构模型,在塑性区联合相关流动法则和拉格朗日分析法,将传统的欧拉描述下的柱孔扩张问题转换为基于拉格朗日描述的带初值的一阶非线性常微分方程组,最终通过数值方法得到砂土中柱孔扩张问题的半解析精确解,并通过算例分析了土体初始应力对扩孔结果的影响。结果表明,颗粒破碎和初始应力对孔周应力和塑性区半径影响巨大,两者共同作用使得土体在扩孔期间表现出不同的剪胀/剪缩特性;此外,高初始应力下的孔周土体在扩孔期间难以到达临界状态。     

考虑砂土颗粒破碎的柱孔扩张问题弹塑性分析

目前对砂土中圆孔扩张问题的研究均未考虑到砂土颗粒的破碎以及剪胀特性,且为了方便后续求解,很多学者对剪应力,剪切模量等计算参数做了简化,使得最终的求解结果无法准确反映实际情况。针对上述问题,采用考虑颗粒破碎和剪胀特性的砂土临界本构模型,在塑性区联合相关流动法则和拉格朗日分析法,将传统的欧拉描述下的柱孔扩张问题转换为基于拉格朗日描述的带初值的一阶非线性常微分方程组,最终通过数值方法得到砂土中柱孔扩张问题的半解析精确解,并通过算例分析了土体初始应力对扩孔结果的影响。结果表明,颗粒破碎和初始应力对孔周应力和塑性区半径影响巨大,两者共同作用使得土体在扩孔期间表现出不同的剪胀/剪缩特性;此外,高初始应力下的孔周土体在扩孔期间难以到达临界状态。     

考虑颗粒破碎的砂土高应力一维压缩特性颗粒流模拟

以Toyoura砂室内高应力一维压缩试验结果为基础,利用二维颗粒流方法中的接触黏结模型生成簇颗粒单元来模拟实际砂土的颗粒破碎特性。高应力一维压缩数值试验中,数值试样由887个簇颗粒单元组成。数值试验与室内试验结果对比表明:数值试验得到的压缩曲线形状及颗粒破碎屈服应力大小均与Toyoura砂室内试验结果一致,说明数值试验能够较好地再现实际砂土在高应力一维压缩条件下的颗粒破碎特性。与室内试验相比,利用数值试验不仅能得到宏观的颗粒破碎现象,而且还能通过分析内部接触力的变化和对黏结破裂位置的追踪来研究颗粒破碎的细观演化规律,从而可进一步探讨颗粒破碎的细观力学机制。最后,就细观参数、加荷速率、簇颗粒数量及试样平均粒径等因素变化对数值试验结果的影响进行了分析。     

不同应力路径下钙质砂力学特性的排水三轴试验研究

钙质砂的力学性质既有强度低、易破碎的特点,又有应力路径依附性的特性。为了研究不同应力路径对钙质砂的颗粒破碎和力学性质的影响,对不同固结压力的钙质砂进行了5种应力路径下的排水三轴压缩试验。结果表明:不同应力路径对钙质砂的应力–应变关系、抗剪强度和颗粒破碎特性有较大的影响。相同固结压力下,等轴向应力试验的剪胀现象最为明显,颗粒破碎率最小,峰值内摩擦角最大;等围压试验的剪胀现象最不明显,颗粒破碎率最大,峰值内摩擦角最小;等平均主应力试验的这些性质介于上述两种试验之间。等主应力比和等向固结试验在加载过程中主要表现为试样的体积压缩,因此与另外3种应力路径试验差别很大。不同应力路径对钙质砂应力–应变关系和强度的影响,除了砂土具有应力路径依附性的特性外,主要来自于应力路径和固结压力的不同产生的颗粒破碎程度不一致造成的影响,使得在不同的应力路径试验中钙质砂的力学性质表现出更大的差异。     

Evaluation of shear strength and mechanical properties of granulated coal ash based on single particle strength

The authors have been studying the mechanical properties of granulated coal ash formed by the milling process with a small amount of cement added, with particles almost equivalent in size to sand or fine gravel. The use of granulated coal ash has many advantages, such as the suppression of leaching of heavy metals and the possibility of outdoor curing. In addition, since granulated coal ash is produced artificially, their particle strength can be understood easily. Another advantage is that it is possible to control the particle strength, something which cannot be performed in natural sands. The present research was carried out in order to investigate the possibility of putting such advantages to good use.Single particle crushing tests were carried out on various kinds of granulated coal ash to evaluate the crushing characteristics of each individual grain. Also, the characteristics of the individual particle, such as shape, were investigated. Next, one-dimensional compression tests were conducted to investigate their compression characteristics. Finally, drained monotonic triaxial compression tests were performed under different confining pressures. The effects of the confining pressure on the shear characteristics, as well as their relation to shear strength, were examined with the single particle crushing strength taken into account.Contrary to observations in natural sands, the single particle crushing strength of granulated coal ash did not depend on particle size. Regarding compression characteristics, granulated coal ash compressed very easily because the crushing strength of a single particle was low. Therefore, the yield stress of granulated coal ash was found to be smaller than that of natural sands. Moreover, the crushing strength affected the shear characteristics, i.e., as the crushing strength increased, the shear stiffness became higher and the compressive volumetric strain became smaller. Therefore, crushing strength can be a useful parameter in evaluating the shear characteristic of granulated coal ash.     

循环三轴应力路径下钙质砂颗粒破碎演化规律

钙质砂广泛分布于中国南海区域,是吹填造陆的重要材料。钙质砂颗粒容易破碎,使得其力学特性相比于普通的陆源硅质砂有显著差异。对取自中国南海西沙群岛某岛礁的钙质砂开展了三轴排水循环剪切试验,研究了围压、循环应力比、循环振次对钙质砂颗粒破碎发展过程的影响。在试验所采用的围压范围内,钙质砂在固结过程中产生的颗粒破碎较少,但是在随后的循环剪切过程中产生了显著的颗粒破碎。在循环剪切作用下,钙质砂的颗粒破碎形式主要是尖角的磨损,剪切后试样的颗粒中出现了一些碎屑和微细颗粒,大颗粒的棱角有一定程度的磨圆,但粒径无明显减小。在常围压下的等幅循环剪切中,颗粒破碎程度随着循环剪切次数的增大而增加,增长速率逐渐降低,可以采用对数曲线来描述相对破碎指数的发展过程。再考虑围压和循环应力比的影响规律,初步建立了一个描述颗粒破碎演化过程的数学模型。     

Undrained Monotonic and Cyclic Shear Behaviour of Sand Under Low and High Confining Stresses

Monotonic and cyclic loading tests have been carried out on a silica sand over a wide range of stresses in order to compare non-crushing and crushing behaviour. Samples were sieved at several stages of testing to theoretically determine the increase in particle surface area and hence degree of crushing. Undrained shear behaviour was compared for crushing and non-crushing regions above 3 MPa. Samples consolidated to 0.1 MPa demonstrated strong dilative behaviour, while above the yield stress of 3 MPa dilation was suppressed and considerable particle crushing occurred. Shearing caused a marked increase in particle crushing particularly after the phase transformation point. Crushing at the steady state was similar for isotropic and anisotropically consolidated sands. At high confining pressures the cyclic strength curves were similar to those for loose sands except for confining pressure dependency due to particle crushing. For low confining stresses cyclic strength increased with initial stress ratio, while for high confining stresses it decreased with initial shear stress ratio. In the cyclic tests there was no significant crushing for 0.1 MPa. Crushing was seen to increase rapidly after the phase transformation point, where high strains developed and where particle rotation and translation contributed to the crushing process.     

双向耦合循环剪切条件下饱和砂土体应变发展规律试验研究

砂土的剪胀与循环应力路径密切相关。针对饱和南京细砂,利用空心圆柱扭剪仪(HCA)进行了一系列均等固结条件下轴向–扭转耦合循环剪切排水试验,研究了复杂应力路径下饱和砂土的剪胀性及其体应变量化方法。研究表明:双向耦合循环剪切条件下饱和砂土的剪胀由一个完全可逆的循环体应变分量和一个不可逆的累积体应变分量构成,循环应力路径对累积体应变发展规律影响显著;以等效循环应力比ESR作为表征复杂应力路径下动应力大小的指标,饱和砂土累积体应变与ESR值具有事实上的唯一性关系,累积体应变随ESR的增加而线性累积;通过引入参数ESR,提出了双向耦合剪切条件下饱和砂土累积体应变规准化方法。验证性试验表明新的体应变增量模型的预测值与试验结果的吻合度较高,而基于循环直剪试验结果建立的Byrne模型对双向耦合剪切条件下饱和南京细砂的体应变预测偏小。     

Hypoplastic model for crushable sand

A constitutive model for granular materials which considers grain crushing effects is developed in the framework of hypoplasticity. As grain crushing occurs the behaviour of granular material can usually be significantly affected. Several empirical relations between peak strength, uniformity coefficient and stiffness of sand depending on stress level or amount of grain crushing have been derived in the past. In this paper, such relations are employed to improve a basic hypoplastic constitutive model based on the changes of stress level or grain size distribution. In the proposed modified hypoplastic model only two additional physical parameters, namely uniformity coefficient and mean grain size are incorporated. The validation of the modified model for three different sands under triaxial test response with cell pressures up to 30?MPa is presented and shows a significantly better correspondence with regard to the original basic hypoplastic model.     

A new probabilistic approach for predicting particle crushing in one-dimensional compression of granular soil

This paper presents a new probability-based method for the prediction of particle crushing in the one-dimensional compression of granular soil. The method is comprised of a joint-probability particle crushing criterion that takes into account the statistical particle-scale stress distribution information derived from the Discrete Element Method (DEM) simulations and Weibull׳s distribution of particle crushing strength. A normalized tensile stress index f and a diameter index I_d are introduced to quantify the statistical particle-scale data. The method is further implemented in DEM simulations and verified by comparing the simulation results with the experimental data of oedometer tests of sands.     

DEM analysis of energy dissipation in crushable soils

It is well known that particle crushing plays a critical role in the mechanical behavior of granular soils. Understanding energy dissipation under the influence of particle breakage is of key importance to the development of micromechanics-based constitutive models for sands. This paper reports the original results of the energy input/dissipation of an idealized crushable soil using 3D DEM simulations. Particle breakage is modeled as the disintegration of the synthetic agglomerate particles which are made up of parallel-bonded elementary spheres. A parametric study is performed to fully investigate the effects of initial specimen density and crushability on the energy allocation of the crushable soil.The simulation results show that the initial specimen density and the crushability strongly affect the energy allocation of the soil both at small and large strains. The major roles of particle breakage, which itself only dissipates a negligible amount of input energy, are to advance changes in the soil fabric and to promote the interparticle friction dissipation. Particularly, at small strains, particle breakage disrupts the strain energy buildup, and thus, reduces the mobilized shear strength and dilatancy of a granular soil. At large strains, where particle breakage is greatly reduced, steady energy dissipation by interparticle friction and mechanical damping is observed. Furthermore, it is found that shear bands develop in most dense crushable specimens at large strains, but they are only weakly correlated to the anisotropy of the accumulated friction dissipation.     

Viscous Properties of Granular Materials Having Different Particle Shapes in Direct Shear

The viscous properties of air-dried relatively poorly-graded granular materials having different particle shapes were evaluated by performing a series of direct shear (DS) tests. The applied loading histories include repeated step changes in the shear displacement rate (s) or repeated sustained loading stages during otherwise monotonic loading (ML) at a constant s under constant vertical stress. Test results of an angular gravelly soil (i.e., Chiba gravel-a) obtained from the present study and those of a wide variety of poorly-graded granular materials (i.e., glass beads and natural sands including Toyoura, Hostun, Silica No. 6a, Ticino, Silver Leighton Buzzard, Ottawa, Albany and Monterey sands) previously obtained by the authors are analysed. The viscous properties of granular materials can be adequately described by three basic parameters: i.e., the rate-sensitivity coefficient, the residual rate-sensitivity coefficient (or their ratio, i.e., the viscosity-type parameter) and the decay parameter. These parameters, as well as the viscosity type (i.e., Isotach, Combined, TESRA and P&N), are strongly affected by particle shape as quantified in terms of the degree of particle angularity while being rather independent of particle size. The creep deformation that takes place by sustained loading increases with an increase in the shear stress level, and it also increases with changes in the viscosity type associated with an increase in mainly the particle angularity and partly the coefficient of uniformity. The various viscous property types and transitions among them can be described by a single general equation incorporating these parameters. A non-linear three component model incorporating this general equation can simulate very well all of the various viscous responses observed in the DS tests referred to in the paper.