Validation of discrete element method by simulating a 2D assembly of randomly packed elliptical rods

This paper aims at establishing the predictive capability of the discrete element method (DEM) by validating the simulated responses of granular systems against experimental observations at both the macroscale and the microscale. A previously published biaxial shearing test on a 2D assembly of randomly packed elliptical rods was chosen as the benchmark test. In carrying out the corresponding DEM simulations herein, the contact model was derived and then validated using finite element analysis; the associated parameters were calibrated experimentally. The flexible (membrane) boundary was modeled by a bonded-particle string with experimentally calibrated parameters. An iteration procedure was implemented to replicate the initial packing and also to satisfy the boundary conditions in the experiment. Overall, the DEM simulation is found effective in reproducing the stress–strain–volumetric response, the statistical observation on the fabric anisotropy and the strain localization. Furthermore, the closer the numerical packing is to the experimental one, the closer the response is reproduced, demonstrating the significance of the initial packing reconstruction. Still, there are some minor differences between the experiment and simulation, reflecting the limitations associated with the particle number and the measurement resolution used in the experiment when reproducing the initial packing.     

基于广义塑性力学的黄土湿陷变形本构关系

分析了黄土湿陷变形的塑性特性,基于广义塑性力学原理建立了湿陷变形的增量本构关系。将增湿含水量作为内应力,应用常规三轴浸水试验拟合得出了湿陷体积屈服面和剪切屈服面,并且给出了黄土湿陷变形的起始屈服面。该模型能够反映湿陷性黄土在不同湿陷作用,即水和力的不同组合作用下的湿陷变形特性,考虑了湿陷体积变形和湿陷剪切变形以及球应力和偏应力对它们的交叉影响。     

考虑颗粒破碎影响的粗粒土本构关系

粗粒土在较大的应力条件下容易产生颗粒破碎现象,而现有的大多数模型都没有考虑剪切过程中的颗粒破碎。模型将塑性功引入土体受力变形过程的能量方程中,推导得到土体流动法则。采用直线型屈服轨迹和非相关联流动法则,利用不排水应力路径计算得到硬化函数,建立了一个考虑颗粒破碎的粗粒土本构模型。对比分析表明：该模型对粗粒土在各种围压下的应力-应变和体应变计算结果与试验曲线吻合较好。     

超固结土热黏弹塑性本构关系

热黏弹塑性本构模型是描述土在温度（热）和时间（黏）耦合作用下的应力-应变关系的本构模型。在一些新型岩土工程诸如高放核废料地质处置、地热资源开发与贮存的建设中,需要同时考虑温度和时间对土的影响,所以建立一个热黏弹塑性本构模型具有理论和实际意义。将温度变化对黏土体积和强度参数的影响引入笔者之前提出的超固结土等向应力-应变-时间关系,建立了一个等向应力条件下的应力-应变-时间-温度关系。随后,基于该关系推导了屈服面硬化定律,并将其与超固结土统一硬化模型的屈服方程和流动法则结合,建立了超固结土的热黏弹塑性本构模型。最后,使用新模型预测室内试验,证明新模型能够反映时间和温度对土体积、一维压缩曲线和前期固结压力的耦合影响。     

A generalized rigid particle contact model for fracture analysis

Rigid particle models taking directly into consideration the physical mechanisms and the influence of the material meso‐structure have recently been developed for fracture studies of quasi‐brittle material such as concrete. The formulation of a generalized contact model for rigid particle simulations is presented in which the contact discretization is a model parameter. The contact model performance for different discretizations is evaluated for uniaxial tensile tests, for uniaxial compression tests and for a notched beam in mode I. Copyright © 2005 John Wiley & Sons, Ltd.     

A constitutive model for coal-fouled ballast capturing the effects of particle degradation

Rail tracks undergo degradation owing to particle breakage and fouling of ballast by various fines including coal and subgrade soil. As the ballast becomes fouled, its strength and drainage capacity are compromised, sometimes resulting in differential settlement and reduced track stability. This paper demonstrates a continuum mechanics based framework to evaluate the detrimental effect of fines on the strength, deformation and degradation of coal-fouled ballast under monotonic loading. An elastoplastic constitutive model that considers the effect of fines content and energy consumption associated with particle breakage during shearing is presented. This multiphase constitutive model is developed within a critical state framework based on a kinematic-type yield locus and a modified stress-dilatancy approach. A general formulation for the rate of ballast breakage and coal particle breakage during triaxial shearing is presented and incorporated into the plastic flow rule to accurately predict the stress–strain response of coal-fouled ballast at various confining pressures. The behaviour of ballast at various levels of fouling is analysed and validated by experimental data.     

Mechanical trapping of fine particles in a medium of mono‐sized randomly packed spheres

Mechanical trapping (or straining) of fine particles is a key mechanism in many filtration systems. For example, the performance of rapid sand filters depends in part on mechanical trapping of larger fine particles, while relying on adsorptive processes to trap very small fine particles and microbes. The ability to trap these particles is directly related to the construction of the packed bed used for filtration in this system. Thus, the ability to model the effect of the inner structure of the packed bed can lead to more efficient design for improved filtration. Because of its significant efficiency, gravitational sphere packing is employed in this work to simulate a bed of mono‐sized randomly packed spheres. The simulated bed provides a way to visualize the pore network and estimate the pore size distribution associated with the void space between particles. Furthermore, by subsequently introducing fine particles into the bed, we evaluate the mass‐rate of fine particles passing through and possibly saturating the packed bed. Results show that fine particles between 15% and 25% of the coarse particle size can be physically strained within the randomly packed bed. These results differ significantly from the results obtained assuming a periodically spaced bed. The technique therefore provides an efficient yet accurate alternative for understanding how fine particles pass through a coarse particulate medium. Copyright © 2014 John Wiley & Sons, Ltd.     

考虑孔隙变形的孔隙介质本构关系初探

孔隙存在是孔隙介质材料结构的本质特征,它决定了孔隙介质的本构关系呈现更为复杂的性质。首先给出了孔隙介质的视应力、视应变、骨架实际应力和骨架实际应变的定义,并在理想孔隙介质的物质模型假定下讨论了理想孔隙介质的本构关系,表明即使孔隙介质的骨架结构满足虎克弹性体本构关系的假定,即假定骨架的实际应力与实际应变之间呈现线性关系,但由于孔隙的存在,孔隙介质的视应力与视应变之间还是呈现非线性,说明应力与变形之间的非线性是孔隙介质的固有特性。     

基于广义塑性理论的尾砂本构模型在ABAQUS中的二次开发

建立尾砂的本构模型是开展尾矿坝数值模拟和安全评价的重要基础,而目前尾砂的本构模型研究多集中于非线性弹性模型,如Duncan-Chang模型,关于弹塑性模型的研究较少。结合尾砂的应力-应变特性,提出了一种适用于描述尾砂力学特性的改进广义塑性模型。基于用户自定义材料子程序UMAT,将提出的模型在ABAQUS中二次开发实现,应力积分采用Runge-Kutta显式积分。通过三轴试验模拟验证,偏差应力曲线表明,有限元计算结果可以反映围压对应力-应变关系的影响,抗剪强度随应变逐渐硬化,达到峰值强度,随后发生应变软化,抗剪强度有所下降。体应变曲线结果表明,广义塑性模型可以很好地描述体应变曲线的体缩-体胀发展过程,与试验曲线吻合较好。同时有限元数值模拟结果和理论值误差很小,且和试验结果拟合较好。该研究成果可进一步用于尾矿坝的应力变形计算和安全评价。     

A state-dependent hyperelastic-plastic constitutive model considering shear-induced particle breakage in granular soils

Acta Geotechnica - An elastic–plastic constitutive model considering particle breakage for simulation of crushable granular soils behavior is proposed. In the model, elastic strain rates are...     

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。     

考虑颗粒破碎效应的堆石料静动力本构模型

为合理反映颗粒破碎对堆石料力学特性的影响,基于试验结果分析,得出了堆石料在压缩和剪切作用下的颗粒破碎特性规律。通过引入压缩破碎和剪切破碎的相关参数,借鉴已有本构模型的合理定义,吸收临界状态理论和边界面理论的优点,发展了考虑颗粒破碎和状态相关的堆石料静动力统一弹塑性本构模型,并阐述了模型参数的确定方法。该模型不仅能够反映堆石料在静力荷载作用下的低压剪胀、高压剪缩、应变软化和硬化等特性,还能够反映在循环荷载作用下应力-应变的滞回特性和残余变形的累积效应。最后为验证模型的合理性,分别对堆石料的静力三轴和循环三轴试验进行了数值模拟预测,结果表明：模型预测与试验数据吻合良好,所提出的本构模型能够合理地描述颗粒破碎对堆石料静动力变形特性的影响。     

基于颗粒流程序的黏弹塑性本构模型开发与应用

在深入研究西原体模型黏弹塑性特征的基础上,推导出不同塑性条件下的流变特性方程,并将其推广到离散单元法中,研究了颗粒间力与位移关系的数值积分方案,总结出颗粒流程序中接触本构模型开发方法,并基于二维颗粒流程序(PFC2D)开发出具有黏弹塑性特征的西原体接触本构模型。通过两个互相接触的固定球体之间的应力松弛试验,分3种情况验证了模型编制的准确性。利用取自张家洼铁矿巷道内的岩石试样,通过单轴和三轴压缩试验获取计算参数,并进行了单轴压缩蠕变试验的模拟,通过与室内蠕变试验结果的对比,验证了PFC2D中自定义西原体模型用于岩石流变特性研究的可行性。利用西原体模型与线弹性模型对D型深埋巷道进行分析计算和破坏模式研究,结果显示,西原体模型预测结果与Hoek-Brown准则理论结果更为接近。在围岩蠕变作用下,巷道两帮变形量大于顶板和底板,破坏程度更为严重,计算结果与现场监测数据基本吻合。根据巷道长期稳定性的要求,提出着重支护两帮的治理建议。     

Numerical modeling of changes in anisotropy during liquefaction using a generalized constitutive model

A constitutive model with rotation hardening was generalized from the triaxial compression state to a general stress state. With the generalized model, numerical simulations of cyclic and monotonic undrained triaxial tests were conducted to reproduce the phenomenon of continuous, orderly and rapid changes in anisotropy during liquefaction. The simulated results demonstrated that when sand enters the liquefaction stage, the yield surface in the stress space rotates quickly, causing continuous and rapid changes in anisotropy. Through comparison of the simulated and experimental results, the generalized constitutive model was shown to be able to capture the fundamental behaviors of sand demonstrated by the experimental data, and the rotational hardening rule adopted in the generalized model was proven suitable for describing the continuous, orderly and rapid changes in anisotropy that occur during liquefaction.     

An anisotropic elastic‐decohesive constitutive relation for sea ice

Thermodynamic growth or melt and mechanical redistribution due to lead opening or ridge formation shape the thickness distribution of the Arctic ice cover and impact the overall strength of pack ice. Specifically, the deformation and strength of ice are not isotropic but vary with the thickness and lead orientation. To reflect these facts, we develop an anisotropic, elastic‐decohesive constitutive model for sea ice together with a model to describe an oriented, ice thickness distribution. The tight connection between the mechanical response and the thickness distribution is an improvement over a previous model that only depended on the average ice thickness. The model describes mechanical responses anisotropically in both the elastic and failure regimes. In the elastic regime, the constitutive relation implicitly reflects strong and weak directions of the pack ice depending on the distribution of thin ice (including open water) and thicker ice (e.g., multi‐year ice or ridges). In the failure regime, the model predicts both failure initiation and the lead orientation. Evolution from initial failure to complete failure when traction‐free crack surfaces are formed is also modeled. Crack or lead width is determined during the evolution. Various examples of failure surfaces are presented to describe the behavior of modeled ice when the thickness distribution varies. The model predictions are also illustrated and compared with previous modeling efforts by examining regions of ice under idealized loading. Copyright © 2015 John Wiley & Sons, Ltd.     

考虑循环软化特性的饱和软土弹塑性本构关系研究

将软化指数关系与非等向硬化模量场理论相结合,研究了可描述循环荷载作用下饱和软土软化特性的增量弹塑性模型。该模型借助硬化模量的插值和映射中心的移动,在偏应力空间中构造硬化模量的演化规则;通过在弹塑性模量插值函数中引入初始弹塑性模量软化系数,模拟循环荷载作用下软土的刚度软化特性;通过引入硬化模量调整系数,增强循环加载时应力-应变曲线的滞回特性;再通过引入反映应变累积速率和大小的模型参数,描述循环加载时软土的应变累积特性。利用Idriss提出的指数关系式近似拟合软化系数随应力循环次数的变化关系,并通过引入循环应力参数建立了循环软化系数与静应力水平和循环应力水平的关系。阐述了确定模型参数的方法,并利用模型预测了相关试验结果,通过预测结果与试验结果的对比,验证了该模型描述循环荷载作用下软土软化特性的可行性。     

Sensitivity of incipient particle motion to fluid flow penetration depth within a packed bed

A discrete element method is applied to a three‐dimensional analysis related to sediment entrainment on a micro‐scale. Sediment entrainment is the process by which a fluid medium accelerates particles from rest and advects them upward until they are either transported as bedload or suspended by the flow. Modelling of the entrainment process is a critically important aspect for studies of erosion, pollutant resuspension and transport, and formation of bedforms in environmental flows. Previous discrete element method studies of sediment entrainment have assumed the flow within the particle bed to be negligible and have only allowed for the motion of the topmost particles. At the same time, micro‐scale experimental studies indicate that there is a small slip of the fluid flow at the top of the bed, indicating the presence of non‐vanishing fluid velocity within the topmost bed layers. The current study demonstrates that the onset of particle incipient motion, which immediately precedes particle entrainment, is highly sensitive to this small fluid flow within the topmost bed layers. Using an exponential decay profile for the inner‐bed fluid flow, the discrete element method calculations are repeated with different fluid penetration depths within the bed for several small particle Reynolds numbers. For cases with slip velocity corresponding to that observed in previous experiments with natural sediment, the predicted particle velocity is found to be a few percent of the fluid velocity at the top of the viscous wall layer, which is a reasonable range of velocities for observation of incipient particle motion. This method for prescribing the fluid flow within the particle bed allows for the current discrete element method to be extended in future studies to the analysis of sediment entrainment under the influence of events such as turbulent bursting. Additionally, predictions for the slip velocities and fluid flow profile within the bed suggest the need for further experimental studies to provide the data necessary for additional improvement of the discrete element method models.     

A technique for estimating permeability of a randomly fractured rock mass

Extensive field and laboratory testing programs were performed to develop a relationship between the permeability of a fractured limestone and the core recovery values. The studied limestone does not encompass any jointing system but is consistently and randomly fractured. Nineteen in situ falling head permeability tests were carried out to measure permeability of the fractured rock mass at a representative study area. Analysis of test results has led to the formulation of an empirical equation that estimates the permeability of the rock mass in terms of its solid core recovery value and the permeability of the fractures filling material. Unlike the existing equations for estimating the permeability of rock masses, the proposed equation is simple and utilizes parameters that can be easily determined in regular geotechnical field and laboratory investigations. A technique is also presented to estimate the permeability of a rock layer, the quality of which significantly changes with depth, using the proposed equation that utilizes a single value of core recovery. Analysis of well-documented pumping test results supported the validity of the proposed equation and technique.     

考虑颗粒破碎对特征孔隙比影响的堆石体亚塑性本构模型

颗粒破碎是影响堆石体强度和变形特性的主要问题之一。相比于砂土,堆石料在较低的应力水平下就会发生严重的颗粒破碎,因此,在进行堆石体力学特性及本构模型研究时必须考虑颗粒破碎的影响。同时,堆石体在受力过程中孔隙比是变化的,而传统本构模型不能使用一组参数模拟不同孔隙比的同种材料。因此,以能够考虑应力水平和土体孔隙比影响的Gudehus-Bauer亚塑性本构模型为基础,考虑堆石体有别于砂土的孔隙比变化特征,提出了考虑堆石破碎的亚塑性本构模型。亚塑性理论是目前可最大限度地减少人为假定的一种本构理论,颗粒材料在不同特征应力路径下,破碎造成的过度变形量不同;但相同应力水平、不同特征应力路径下孔隙比已不满足Gudehus-Bauer亚塑性本构模型中提出的等比例变化规律。据此,结合考虑颗粒破碎的临界状态理论和堆石体常规三轴试验和循环加载试验结果,提出了考虑颗粒破碎堆石体特征孔隙比的表达式,并将其引入到Gudehus-Bauer亚塑性本构模型中,建立了考虑颗粒破碎的堆石体亚塑性本构模型,提出了模型参数的确定方法。与堆石体试验结果对比表明,该本构模型可以较好地模拟其力学与变形特性。