基于统一标定的势接触力计算

传统的离散元类数值方法存在处理角-角接触时接触力方向不确定、三维情形时接触计算极其复杂等问题。Munjiza提出的基于势的接触力计算方法很好地解决了这一问题,但同时存在势的物理意义不明确,计算出的接触力与物理直观不符、相同嵌入量计算的接触力大小不一致等问题。在已有研究的基础上,提出了一种基于统一标定的势接触力计算方法,该方法重新定义了势函数,即三角形单元内一点的势与该点到3条边的最短距离成正比。采用这种势函数定义可以对嵌入量进行统一表征。在相同的嵌入量下,计算的接触力大小是一致的,同时保留基于势的接触力计算方法所有优点。新定义的势函数,解决了原有势函数所存在的重大缺陷,只要重叠区域不变,计算的总接触力是不变的,接触力计算具有局部特性,而与划分的三角形单元的整体形状和大小无关,即新的接触力计算方法,具有更好的网格鲁棒性。该方法使得基于势的接触力计算方法建立在坚实的物理基础之上,意义重大。     

三维距离势离散单元法

通过定义距离势函数,提出一种适用于空间任意凸多面体单元的三维距离势函数离散单元法。该方法采用归一化的计算方式,将势函数表征为接触体间的距离函数,并基于此建立接触力计算方程,明确了势函数的物理意义,使接触力计算更加合理,无需对各种可能的接触形式进行差异化处理。新方法克服了原有势函数物理意义不明、接触力计算受单元形式影响等重要缺陷,并突破了四面体单元的限制,可采用空间任意凸多面体单元。通过若干算例说明新方法的正确性和有效性。数值模拟结果表明新方法能够很好处理空间任意多面体单元复杂接触变换过程,准确处理复杂非连续介质的运动过程。     

粗粒料多边形表征及二维FEM/DEM分析

考虑到颗粒形状对粗粒料的力学特性有重大影响,提出了一种新的表征颗粒形状的方法,即在椭圆上随机选取一系列点连接成多边形颗粒,表征狭长扁平的颗粒。新方法较圆上取点的方法能代表更多类型的颗粒形状,适用范围更广。提出了一种新的粗粒料投放算法,即先缩小颗粒,然采用随机算法将缩小的颗粒投放至给定区域,对颗粒划分好网格后,将颗粒放大到原来的大小,然后采用有限元-离散元(FEM/DEM)方法计算稳定后即生成了相应的试样。通过将上述颗粒生成及投放算法与FEM/DEM结合,应用于粗粒料的数值模拟。分析表明,FEM/DEM是研究粗粒料力学性质的较好方法,对复杂的颗粒形状也可简单建模,且因在颗粒内部划分了有限元网格,复杂的接触判断及接触力计算转化为标准统一的三角形和三角形之间的接触判断及接触力计算,所有的计算均可标准化、统一化。同时因为颗粒是可以变形的,依然保留了连续介质力学中应力和应变的概念,无须像PFC那样需通过测量圆来间接表示某点的应力、应变。最后,通过粗粒料的侧限压缩试验的数值模拟,展现了文中提出的一整套解决方案在模拟粗粒料方面的巨大潜力。     

考虑颗粒棱角影响的直剪试验的离散元模拟

为了研究颗粒棱角对颗粒材料力学行为的影响,建立了具有不同棱角度的对称多面体颗粒,采用了一种简单并适合任意颗粒形状的接触本构模型,对三维离散元开源程序YADE进行了修改,研究了颗粒棱角度在模拟直剪试验中的影响以及接触力各向异性在剪切过程中的演化规律。研究结果表明,颗粒棱角度越小,颗粒间相互咬合自锁的作用越小,颗粒受剪更易转动,致使颗粒体系的剪切强度和剪胀性下降;竖向加载力越大,颗粒棱角度的影响越明显;法向接触力的各向异性在剪切过程中表现为先增后减最后趋向稳定的趋势;法向接触力的各向异性变化程度随颗粒棱角度的增大而增大。     

基于局部单元劈裂的FEM/DEM自适应分析方法

为了模拟岩体中裂纹的萌生、扩展,Munjiza提出了有限元法/离散元法(FEM/DEM)耦合分析方法。因为裂纹是沿单元边界进行扩展的,亦即裂纹扩展具有网格依赖性,为获得较好的裂纹扩展形态,需要划分密集的初始网格。为解决上述难题,基于FEM/DEM耦合分析方法,提出了基于局部单元动态劈裂的FEM/DEM自适应分析方法,以克服裂纹扩展形态对网格的依赖性。该方法在最初建模时无需划分很密的初始网格,随着荷载的施加,对裂纹尖端附近的局部单元进行动态劈裂,为裂纹的后续扩展提供了更多可能的扩展方向,使得裂纹扩展不必沿着初始网格的单元边界扩展,即可以沿着单元内部进行扩展,裂纹扩展形态更为平滑,与实际情况更为接近。同时相对原FEM/DEM耦合分析方法一开始就划分很密的网格而言,新方法可以划分较为稀疏的初始网格,计算成本降低。最后,通过巴西劈裂算例与原FEM/DEM耦合分析方法对比,分析表明,新方法在一定程度上克服了裂纹扩展形态对初始网格的依赖性。     

颗粒流强度折减法和重力增加法的边坡安全系数研究

将强度折减法和重力增加法的思路引入离散单元法,对土坡安全系数的评价作尝试性研究。运用颗粒流软件,采用强度折减法和重力增加法对边坡进行稳定分析。结果表明颗粒流计算得到的结果与有限元和条分法计算结果比较接近,为计算边坡稳定开辟了一条新的途径。采用颗粒流求解边坡的安全系数不需要条分,也即不需要对条间力做假定,同时不需要假定滑移面的位置和形状,颗粒根据所受到的接触力调整其位置,最终从抗剪强度最弱面发生剪切破坏。最后对强度折减法的不等比例折减提出了不同观点,为今后的研究提供思路。     

Discrete element analysis of the influence of bolt pattern and spacing on the force-displacement response of bolted steel mesh

Steel wire mesh held by a pattern of bolts can be used to stabilize a rock slope. Knowledge of the force-displacement response of steel mesh is essential in the design of this support system. Laboratory tests have been used to test mesh that is held to rigid steel frames. These testing conditions differ from how steel mesh is held in the field by bolts. The existing laboratory test data may underestimate the deformation and overestimate the load-bearing capacity of the steel mesh. This paper focuses on the response of the high tensile strength steel mesh held by commonly used bolt patterns. Discrete element models were used to study the force-displacement response of the steel mesh pinned by bolts. The influences of different bolt patterns and varying ratios of bolt spacing on the effectiveness of steel wire mesh were analyzed. Relationships between the resistance force of steel mesh and bolt density at various mesh deformations were developed. These relationships can help engineers choose the bolt spacing and provide an estimate of the resistance force that a steel mesh can mobilize at a desired deformation limit for a given bolt pattern.     

Application of the third medium method for frictionless contact problems in geomechanics

Traditional approaches in contact mechanics demand complicated search algorithms at the interface between the contacting bodies. Recently, a new contact method based on the concept of a third medium has been developed, which overcomes the drawbacks of conventional contact mechanics techniques. This new scheme is based on a space filling mesh, in which the contacting bodies can move and interact. The ability and accuracy of this method in predicting displacements, as well as the contact forces, is validated by solving selected numerical examples. The potential merits of this method for analysing geotechnical problems by the finite element method are addressed.     

Revisiting the existence of an effective stress for wet granular soils with micromechanics

A possible effective stress variable for wet granular materials is numerically investigated based on an adapted discrete element method (DEM) model for an ideal three‐phase system. The DEM simulations consider granular materials made of nearly monodisperse spherical particles, in the pendular regime with the pore fluid mixture consisting of distinct water menisci bridging particle pairs. The contact force‐related stress contribution to the total stresses is isolated and tested as the effective stress candidate for dense or loose systems. It is first recalled that this contact stress tensor is indeed an adequate effective stress that describes stress limit states of wet samples with the same Mohr‐Coulomb criterion associated with their dry counterparts. As for constitutive relationships, it is demonstrated that the contact stress tensor used in conjunction with dry constitutive relations does describe the strains of wet samples during an initial strain regime but not beyond. Outside this so‐called quasi‐static strain regime, whose extent is much greater for dense than loose materials, dramatic changes in the contact network prevent macroscale contact stress‐strain relationships to apply in the same manner to dry and unsaturated conditions. The presented numerical results also reveal unexpected constitutive bifurcations for the loose material, related to stick‐slip macrobehavior.     

Numerical estimation of REV and permeability tensor for fractured rock masses by composite element method

The Monte Carlo method is used to generate parent stochastic discrete fracture network, from which a series of fractured rock samples of different sizes and orientations are extracted. The fracture network combined with a regular grid forms composite element mesh of the fractured rock sample, in which each composite element is composed of sub‐elements incised by fracture segments. The composite element method (CEM) for the seepage is implemented to obtain the nodal hydraulic potential as well as the seepage flow rates through the fractured rock samples. The application of CEM enables a large quantity of stochastic tests for the fractured rock samples because the pre‐process is facilitated greatly. By changing the sizes and orientations of the samples, the analysis of the seepage characteristics is realized to evaluate the variation of the permeability components, the existence of the permeability tensor and the representative element volume. The feasibility and effectiveness are illustrated in a numerical example. Copyright © 2008 John Wiley & Sons, Ltd.     

Discrete element modeling of direct shear tests for a granular material

A succinct 3D discrete element model, with clumps to resemble the real shapes of granular materials, is developed. The quaternion method is introduced to transform the motion and force of a clump between local and global coordinates. The Hertz–Mindlin elastic contact force model, incorporated with the nonlinear normal viscous force and the Mohr–Coulomb friction law, is used to describe the interactions between particles. The proposed discrete element model is used to simulate direct shear tests of the irregular limestone rubbles. The simulation results of vertical displacements and shear stresses with a mixture of clumps are compared well with that of laboratory tests. The bulk friction coefficients are calculated and discussed under different contact friction coefficients and normal stresses. Copyright © 2009 John Wiley & Sons, Ltd.     

Statistical analysis of stress transmission in wet granular materials

The micromechanics of wet granular materials encompasses complex microstructural and capillary interconnects that can be readily described through a formal derivation of stress transmission in such a 3‐phase medium. In the quest for defining an appropriate stress measure, the stress tensor expression that results from homogenization [Duriez et al. J Mech Phys Solids 99 (2017): 495‐511] of such a medium provides theoretical insights necessary to extract useful information on the relationship between capillary effects and microforce interactions via several small‐scale parameters whose evaluation can be challenging. Using instead a statistical approach where microvariable distributions are described by probability density functions, the current study provides simple estimates of stress components in terms of only a few tractable microvariables such as coordination number and fabric anisotropy. In particular, the latter recognizes details of contacts such as force interactions being either mechanical or capillary, including interactions with and without mechanical contact. The developed expressions are in a good agreement with discrete element method simulation results of the triaxial loading of a wet granular assembly, notably for hydrostatic (mean) pressure. A new set of dimensionless groups is also identified to characterize the significance of mechanical and capillary physics, which facilitates a better understanding of the contribution of dominating elements to stress, while also providing the opportunity to incorporate important capillary effects in micromechanically based constitutive formulations.     

考虑转动阻抗的粗粒土离散元模拟

转动阻抗被定义为作用颗粒接触上的一对对称力偶,用来抵抗颗粒之间的相互转动。将转动阻抗引入到离散元模拟中是对传统离散单元法的重要改进。开发出考虑颗粒转动阻抗的接触模型,并将其嵌入到PFC2D中,利用该模型进行粗粒土的双轴剪切数值模型试验,研究剪切过程中转动阻抗对粗粒土的宏细观力学性质的影响。结果显示,在宏观方面,颗粒转动阻抗对粗粒土的宏观力学行为（应力-应变及体应变-轴应变行为）有重要的影响,随着转动阻抗的增加,粗粒土的剪切强度和最大摩擦角随之增加,这与已有的研究结果一致,证明所建模型是可靠的;在微观方面,考察转动阻抗对粗粒土内部微观结构的影响发现,随着转动阻抗的增加,粗粒土的内部的接触数目减少,而粗粒土的剪切强度增加,表明转动阻抗能够提高粗粒土力链网络的稳定性,同时发现随着转动阻抗的增加,粗粒土的各向异性增加主要是强力链各向异性的增加,说明转动阻抗增强了强力链的传递力的能力以及抵抗力链屈曲破坏能力。数值模拟结果表明,增加颗粒转动阻抗,粗粒土出现组构与轴应变非共轴的现象。     

基于互补理论的扩展有限元接触问题实现

在处理含有裂隙这类不连续问题时,常规有限元方法需要对裂隙尖端部位进行局部网格加密,当裂隙扩展时还需要进行网络重构。基于单位分解思想的扩展有限元成功解决了常规有限元难以处理的裂隙类不连续问题。在研究复合裂隙时,通常需要考虑裂隙的接触问题。基于互补理论,建立了裂隙面上相对位移和接触力的互补方程,并采用牛顿法求解,无需开闭迭代,且能够快速收敛。最后,对含裂隙平板进行受压数值试验,计算结果表明,基于互补理论的扩展有限元接触算法能够有效地阻止裂隙两端网格的相互嵌入,且获得裂隙面上的应力分布与实际一致。     

基于SEM的可变形块体离散元法研究

针对边坡工程中岩土体连续-非连续渐进破坏的特点,提出一种新的变形体离散元方法（DEM）。与传统有限单元法（FEM）不同,弹簧元法（SEM）通过构建一组广义弹簧系统描述单元的力学行为。弹簧元法中的一个广义弹簧可以具有多个方向的刚度系数,确定广义弹簧系统的构造形式及其各刚度系数表达式是弹簧元法的核心。以三角形单元为例,介绍平面弹簧元的基本理论。对任何二维正交广义弹簧系统,通过定义广义弹簧变形与单元应变之间的关系,直接对比单元的应变能与弹簧系统的弹性势能即可得到广义弹簧刚度系数的表达形式。定义泊松刚度系数和纯剪刚度系数两个系统参数,描述正交广义弹簧之间的联系。对任意泊松比的材料,该方法都可准确地描述泊松效应的影响,计算结果与传统有限元法一致。该方法不需要求得有限元单元刚度矩阵的具体形式,具有直接方便、物理意义明确的优点,应用该方法给出任意4节点单元弹簧系统的构造形式及其各刚度系数的表达式。基于SEM的可变形块体离散元法,用弹簧元中的广义弹簧求解块体变形,用离散元中的接触弹簧计算块体间作用力,在单元节点的控制方程中实现弹簧元-离散元耦合计算,通过接触弹簧的状态实现材料由连续到非连续的破坏过程。在基于连续介质离散元法（CDEM）程序的基础上实现弹簧元-离散元耦合程序,应用耦合程序计算均质土坡在重力作用下的弹塑性变形和基覆边坡在重力作用下的破坏,初步证明该方法用于边坡变形渐进破坏分析的可行性。     

Bond rolling resistance and its effect on yielding of bonded granulates by DEM analyses

A discrete element modelling of bonded granulates and investigation on the bond effect on their behaviour are very important to geomechanics. This paper presents a two‐dimensional (2‐D) discrete element theory for bonded granulates with bond rolling resistance and provides a numerical investigation into the effect of bond rolling resistance on the yielding of bonded granulates. The model consists of mechanical contact models and equations governing the motion of bonded particles. The key point of the theory is that the assumption in the original bond contact model previously proposed by the authors (55th CSCE‐ASCE Conference, Hamilton, Ont., Canada, 2002; 313–320; J. Eng. Mech. (ASCE) 2005; 131 (11):1209–1213) that bonded particles are in contact at discrete points, is here replaced by a more reliable assumption that bonded particles are in contact over a width. By making the idealization that the bond contact width is continuously distributed with the normal/tangential basic elements (BE) (each BE is composed of spring, dashpot, bond, slider or divider), we establish a bond rolling contact model together with bond normal/tangential contact models, and also relate the governing equations to local equilibrium. Only one physical parameter β needs to be introduced in the theory in comparison to the original bond discrete element model. The model has been implemented into a 2‐D distinct element method code, NS2D. Using the NS2D, a total of 86 1‐D, constant stress ratio, and biaxial compressions tests have been carried out on the bonded granular samples of different densities, bonding strengths and rolling resistances. The numerical results show that: (i) the new theory predicts a larger internal friction angle, a larger yielding stress, more brittle behaviour and larger final broken contact ratio than the original bond model; (ii) the yielding stress increases nonlinearly with the increasing value of β, and (iii) the first‐yield curve (initiation of bond breakage), which define a zone of none bond breakage and which shape and size are affected by the material density, is amplified by the bond rolling resistance in analogous to that predicted by the original bond model. Copyright © 2006 John Wiley & Sons, Ltd.     

CFD-DEM耦合模拟中拖曳力模型精度

CFD-DEM耦合方法已广泛应用于岩土流固耦合问题分析,其模拟准确性与其中用于处理颗粒-流体相互作用的拖曳力模型密切相关。为了探究拖曳力模型精度的影响因素,采用CFD-DEM耦合方法建立了水中单颗粒沉降数值模型,模拟中考虑了3种典型拖曳力模型以及多种颗粒尺寸,将模拟得到的最终沉降速度与经验公式预测结果进行对比,分析了不同颗粒雷诺数（Re_p）时3种拖曳力模型（Ergun、Wen和Yu模型,Di Felice模型,Hill和Koch模型）的模拟精度。结果表明,Ergun、Wen和Yu模型以及Di Felice模型的精度均随着Re_p的增大而降低,而Hill和Koch模型的精度随着Re_p的增大出现先升高后降低的趋势：一般情况下,当Re_p≤14以及Re_p>72时,3种拖曳力模型的精度从高到低顺序为Ergun、Wen和Yu模型> Di Felice模型> Hill和Koch模型;而当14< Re_p≤40时,Hill和Koch模型的精度最高,Di Felice模型的精度最低;当40<Re_p≤72时,3种拖曳力模型的精度从高到低顺序为Ergun、Wen和Yu模型>Hill和Koch模型>Di Felice模型。     

Nodal-based three-dimensional discontinuous deformation analysis (3-D DDA)

This paper presents a new numerical model that can add a finite element mesh into each block of the three-dimensional discontinuous deformation analysis (3-D DDA), originally developed by Gen-hua Shi. The main objectives of this research are to enhance DDA block’s deformability. Formulations of stiffness and force matrices in 3-D DDA with conventional Trilinear (8-node) and Serendipity (20-node) hexahedral isoparametric finite elements meshed block system due to elastic stress, initial stress, point load, body force, displacement constraints, inertia force, normal and shear contact forces are derived in detail for program coding. The program code for the Trilinear and Serendipity hexahedron elements have been developed, and it has been applied to some examples to show the advantages achieved when finite element is associated with 3-D DDA to handle problems under large displacements and deformations. Results calculated for the same models by use of the original 3-D DDA are far from the theoretical solutions while the results of new numerical model are quite good in agreement with theoretical solutions; however, for the Trilinear elements, more number of elements are needed.     

注浆成型螺纹桩桩土接触面机制的离散元模拟

为了揭示新型注浆成型螺纹桩的承载力特性及桩土接触特性,利用二维离散元（DEM）数值分析不同螺纹间距的桩-土接触特性。在既有螺纹桩-土界面的大型直剪试验方案的基础上,建立模拟试验的离散元模型。通过模拟试验的伺服加载机制,实现在接触面法向上施加恒定的压力,然后水平移动接触面底板进行剪切,得到不同螺纹数下剪切位移与剪切应力的关系曲线、孔隙比分布图和力链传力机制。离散元分析表明,存在一个最优的螺纹间距,使接触面的极限抗剪强度最大;螺纹桩桩土接触面周围土体会出现一个拱形的破坏面,该微观机制与室内试验观察一致。     

基于数值流形法的三维裂纹扩展研究

基于数值流形法（NMM）进行三维裂纹扩展分析研究,编写了相应的C++程序。充分发挥数值流形法在非连续变形分析领域的优势,不需要扩展有限元中的水平集和阶跃函数概念,应用数值流形法计算结果分析裂纹尖端线的破坏状况,对已有的非局部求迹法和三角形推进法进行简化和扩展,提出一种简化算法确定最终的新裂纹扩展面。应用简化算法对水平钱币型裂纹扩展问题进行数值模拟和对比分析研究。计算结果表明,基于数值流形法的三维裂纹扩展算法是可行的,采用简化处理之后,克服原有算法的不足,大大减少了新裂纹尖端线和新裂纹面的数目,降低了计算网格对新裂纹面的影响,提高了计算效率和扩大了应用范围。