Discrete element modeling of crushable sands considering realistic particle shape effect

This study proposed a novel approach for generating crushable agglomerates with realistic particle shapes in discrete element modeling (DEM). The morphologies of sand particles were obtained by X-ray micro-computed tomography scanning and image processing. Based on the particle surface reconstructed by spherical harmonic analysis, the crushable agglomerates with realistic particle shapes can be generated in DEM simulations. The results of single particle crushing tests showed that particle shapes significantly influence the fracture patterns and crushing strengths of sand particles. Furthermore, two one-dimensional compression tests were conducted to investigate the particle shape effect on micro- and macro-mechanical behaviors of crushable sands.     

多块体形状堆石体碾压颗粒破碎数值模拟

通过6种典型堆石块体的形状近似,分别采用两种接触本构模型建立了多块体形状堆石体离散元数值模型,研究堆石体在碾压荷载作用下的颗粒破碎过程,建立颗粒破碎的量化计算方法,分析碾压前、后堆石级配曲线的变化,讨论接触本构模型和颗粒形状对块体破碎的影响。模拟结果显示,碾压荷载下堆石颗粒以张拉破碎为主,随着碾压遍数的增加,局部开始出现剪切破碎;提出的颗粒破碎量化计算方法,在大粒径范围对粒径变化幅度预测偏大,但级配曲线整体趋势与实测结果比较吻合;相比较于接触连接模型,平行连接模型与现场碾压试验结果更接近。6种块体形状的数值结果显示,随着形状系数的增加,在其他条件不变的情况下颗粒破碎率逐渐降低,其中类长方形块体在碾压荷载作用下颗粒破碎最明显。相比较于纯圆颗粒或者单一非圆颗粒,采用的6种颗粒形状建立的堆石体振动碾压离散元模型,更接近现场实际情况。     

Grain crushing in geoscience materials-Key issues on crushing response,measurement and modeling:Review and preface

Grain crushing is commonly encountered in deep foundation engineering,high rockfill dam engineering,railway engineering,mining engineering,coastal engineering,petroleum engineering,and other geoscience application.Grain crushing is affected by fundamental soil characteristics,such as their mineral strength,grain size and distribution,grain shape,density and specimen size,and also by external factors including stress magnitude and path,loading rate and duration,degree of saturation,temperature and geochemical environment.Crushable material becomes a series of different materials with the change in its grading during grain crushing,resulting in a decrease in strength and dilatancy and an increase in compressibility.Effects of grain crushing on strength,dilatancy,deformation and failure mechanisms have been extensively investigated through laboratory testing,discrete element method(DEM)modelling,Weibull statistics,and constitutive modelling within the framework of the extended crushing-dependent critical state theory or the energy-based theory.Eleven papers summarized in this review article for this special issue addressed the above issues in grain crushing through the advanced testing and modelling.     

沉桩过程中钙质砂颗粒破碎特性模拟研究

基于二维离散单元法,对沉桩过程中钙质砂颗粒破碎情况进行了模拟。采用簇粒来模拟易破碎的钙质砂颗粒,并用形状与变形特性相同的聚粒单元来模拟不可破碎颗粒,对这两种单元特性进行对比,分析不同桩型的沉桩过程、桩周土体的力学响应、沉桩过程中钙质砂的颗粒破碎现象。结果表明：破碎颗粒将引起桩侧土体级配的重新调整,与桩体接触好于不可破碎土体;桩处于颗粒破碎的钙质砂中,其沉桩速度较快,对地基土扰动小于未发生颗粒破碎的情况;对于不同桩型、不同土层,桩体压入过程中,桩周土体应力场分布具有相似性;靠近桩端附近,土中水平应力和竖向应力急剧增大,形成应力核;同等条件下发生颗粒破碎的钙质砂地基土中,桩端应力峰值高于不可破碎土体。     

Numerical modelling of railway ballast at the particle scale

The paper describes the development of a technique to simulate triaxial tests on specimens of railway ballast numerically at the particle scale and its validation with reference to physical test data. The ballast particles were modelled using potential particles and the well‐known discrete element method. The shapes of these elemental particles, the particle size distribution and the number of particles (N = 2800) in each numerical triaxial specimen all matched closely to the real ballast material being modelled. Confining pressures were applied to the specimen via a dynamic triangulation of the outer particle centroids. A parametric study was carried out to investigate the effects on the simulation of timestep, strain rate, damping, contact stiffness and inter‐particle friction. Finally, a set of parameters was selected that provided the best fit to experimental triaxial data, with very close agreement of mobilized friction and volumetric strain behaviour. Copyright © 2015 John Wiley & Sons, Ltd.     

基于尺寸效应的粗粒土单颗粒破碎试验及数值模拟

在外荷载等因素作用下,粗粒土易发生颗粒破碎。对泥岩和砂岩颗粒进行了一系列的单颗粒破碎试验,基于尺寸效应和颗粒破碎分形模型,研究了单颗粒破碎强度、破碎能量及Weibull模量等与分形维数间的关系。利用PFC^3D对单颗粒破碎过程进行分析,并与试验数据对比,验证了数值程序的可靠性;随后扩展到大颗粒粒径,分析了其单破碎强度及破碎能量。结果表明:在同类试验条件下,不同材料所得的分形维数是不同的;不同粒径砂岩的破碎程度均大于泥岩;单颗粒破碎强度具有明显的尺寸效应;单颗粒破碎强度与破碎能量均可通过分形维数与颗粒粒径预测得出;修正后的Weibull模量也可通过分形维数得出;数值模拟结果与试验结果及预测结果基本一致;大颗粒粒径单颗粒破碎强度模拟结果与预测结果基本一致,破碎能量稍有差异,需进一步试验验证。研究成果可为获取大粒径粗粒土的单颗粒强度与变形特性提供参考。     

考虑土石料颗粒破碎和密度变化的次塑性本构模型建模方法

试验和现场观测都发现高土石坝的坝料在高压及湿化作用下会发生显著的颗粒破碎,颗粒破碎会改变土石料的级配曲线和密度,因而影响其后继力学行为,因此,土石料的颗粒破碎是当前岩土工程领域的研究热点。为了模拟土石料在高压及湿化作用下发生显著的颗粒破碎现象,以及循环加载中的颗粒破碎与应力诱导各向异性随动硬化共同影响下土石料的变形,本文提出了一个建模方法,考虑土石料颗粒破碎和密度变化的影响。所建议的次塑性本构模型在经过试验资料的验证后可用于动力有限元数值计算。     

各向异性结构性砂土离散元分析

天然沉积砂土力学特性受各向异性及结构性影响明显,实际工程中不能忽视。为探究二者的影响,首先在二维离散元程序NS2D中采用椭圆颗粒模拟了重力场中颗粒长轴主方向为水平的各向异性净砂样,随后基于结构性砂土胶结厚度分布规律及室内试验提出了一个新的微观胶结接触模型并将其引入各向异性净砂样以模拟天然各向异性结构性砂土,最后对该离散元试样进行了双轴试验模拟,将模拟结果与室内试验结果对比以验证该模型的适用性,并对其微观力学特性变化进行研 究。分析结果表明,随着剪切进行,各向异性结构性砂土呈明显应变软化及剪胀现象;胶结接触逐渐减少,且主方向始终为竖向方向;胶结破坏速率及胶结破坏率变化情况与宏观力学响应较一致,且胶结物多为拉剪破坏;土颗粒排列主方向始终为水平向,且水平向排列颗粒所占比例略微增大。     

Discrete element modeling of dynamic behaviors of railway ballast under cyclic loading with dilated polyhedra

The dynamic behaviors of railway ballast under cyclic loading are simulated with discrete element method (DEM). Dilated polyhedra are constructed based on the Minkowski sum operator in order to resemble the irregular shapes of ballast particles. The polyhedral particle generation, contact detection between particles and contact laws are presented. Ballast box tests with periodic lateral boundaries are conducted to simulate the dynamics of the sleeper and ballast particles. The settlement and effective stiffness of ballast bed are investigated under cyclic loadings with five distinct frequencies. The settlement of ballast bed is significant in the first several cycles and increases with the number of cycles gradually. The higher frequency loading generates larger displacement in the same simulation time. The effective stiffness of ballast bed increases gradually. To study the effect of particles' sharpness, dilated polyhedra with different dilating radii and spherical particles are also developed. Simulation results show the sharper the ballast particles are, the smaller the produced settlement. Copyright © 2016 John Wiley & Sons, Ltd.     

剪切作用下钙质砂颗粒破碎试验研究

钙质砂是一种海洋沉积物,与陆源砂比起来,钙质砂受力后易产生颗粒破碎,从而使其力学性质发生变化。对取自南沙群岛永暑礁附近海域的钙质砂进行了不同围压、不同应变下的三轴剪切试验,对试验前后的试样进行了颗粒大小分析试验。试验结果表明,钙质砂在三轴剪切作用下颗粒破碎十分严重,同时用Hardin模型对其破碎进行了度量,并就围压、剪切应变与破碎之间的关系进行了分析。     

基于线性拟合的颗粒材料破碎状态表征

在荷载等因素作用下发生颗粒破碎是岩土材料的固有属性,选择合适的颗粒破碎状态表征指标是颗粒破碎问题研究中首先要解决的问题。基于颗粒破碎导致细颗粒含量增加,级配曲线抬升并趋向于分形的客观事实,提出了利用级配曲线的拟合直线的斜率和相关系数的变化规律描述颗粒破碎状态及其演化的新方法。在该基础上,提出了表征颗粒破碎状态的破碎分形指数及破碎分形相关性指数的概念,阐述了二者随颗粒破碎的发展规律。与试验结果对比表明,提出的状态指标与试验结果能够很好的吻合,颗粒破碎状态存在明确的对应关系,能够表征颗粒破碎难易程度及其发展趋势,为研究颗粒破碎问题提供了新思路。     

Discrete element analysis of breakage of irregularly shaped railway ballast

In order to reduce the maintenance costs of ballasted railway track and improve passenger comfort, the railway ballast particle breakage and its effect on track settlement need to be better understood. The failure process of individual railway ballast loaded between flat platens is simulated using the discrete element method, considering its irregular shape with the incorporation of parallel bonds. The tensile strength, the stress of a survival probability of 37% of samples, is obtained and compared with laboratory results from published literature for the verification of DEM simulations. The evolution to failure of the particle is understood from the stress-strain curve and progressive failure modes. The internal breakage mechanisms are analysed by tracking the accumulation of bond breakage number and the contact force distributions.     

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。     

DEM simulation of the behaviour of geogrid stabilised ballast fouled with coal

Geogrids are commonly used in railway construction for reinforcement and stabilisation. When railway ballast becomes fouled due to ballast breakage, infiltration of coal fines, dust and subgrade soil pumping, the reinforcement effect of geogrids decreases significantly. This paper presents results obtained from Discrete Element Method (DEM) to study the interface behaviour of coal-fouled ballast reinforced by geogrid subjected to direct shear testing. In this study, irregularly-shaped aggregates (ballast) were modelled by clumping together 10–20 spheres in appropriate sizes and positions. The geogrid was modelled by bonding a large number of small spheres together to form the desired grid geometry and apertures. Fouled ballast with 40% Void Contaminant Index (VCI) was modelled by injecting a predetermined number of miniature spheres into the voids of fresh ballast. A series of direct shear tests for fresh and fouled ballast reinforced by the geogrid subjected to normal shear stresses varying from 15 kPa to 75 kPa were then simulated in the DEM. The numerical results showed a good agreement the laboratory data, indicating that the DEM model is able to capture the behaviour of both fresh and coal-fouled ballast reinforced by the geogrid. The advantages of the proposed DEM model in terms of capturing the correct stress–displacement and volumetric behaviour of ballast, as well as the contact forces and strains developed in the geogrids are discussed.     

循环荷载作用下考虑颗粒破碎的堆石体本构模型

中国西部兴建的很多200～300 m高的堆石坝处于高烈度地震区。应力水平高时堆石体的颗粒破碎对其在循环荷载作用下的应力、应变特性有重要的影响。基于广义塑性理论,通过引入状态参数,建立了循环荷载作用下考虑颗粒破碎的堆石体的本构模型,并给出了模型参数的确定方法。与堆石体在400、800、1 500、2 200 kPa围压作用时的试验结果对比,表明所提出的本构模型可以较好地模拟循环荷载作用下颗粒破碎时堆石体的动应力和动应变响应。     

Discrete element modeling of transversely isotropic rocks with non-continuous planar fabrics under Brazilian test

Acta Geotechnica - A new numerical approach based on the particle discrete element method (PDEM) is developed to investigate the mechanical behavior of transversely isotropic rocks with...     

粗粒土尺寸效应的离散元分析

在土工试验中,粗粒土的力学性质需要考虑颗粒粒径R和试样尺寸L的影响,而利用离散元软件进行数值模拟时,模拟结果的准确性受到计算规模的影响,而计算规模由特征长度比值L/R控制。利用量纲分析理论,可以得到粗粒土数值模型的微观参数和宏观力学参数之间的相似关系,而影响粗粒土抗剪强度的无量纲参数组中,包含特征长度比值L/R。一系列数值三轴压缩试验表明：当L/R足够大（L/R >40）时,L/R对粗粒土抗剪强度没有影响;当L/R较小（L/R<30）时,由于边界摩擦作用,试样的抗剪强度会随着L/R的变化而有较大改变。文中也对离散元软件PFC2D/3D提供的伺服机制进行了讨论。     

不同因素影响下层间错动带颗粒破碎和剪切强度特性试验研究

为了获得不同初始颗粒粒径分布和含水率对层间错动带颗粒破碎和剪切强度特性的影响,通过对比泥夹碎屑、泥夹粉砂、全泥型3种不同层间错动带类型与现场3种不同含水率（10%、7%和3%）试样在法向压力2～10 MPa作用下的反复直剪试验和剪切面颗粒粒径分析试验结果,可得出以下结论：①粗颗粒越多（d60越大）,采用相对颗粒破碎势Br量化的颗粒破碎程度越大;②较干颗粒（低含水率）由于磨损产生了更多的细小颗粒,而较湿颗粒（高含水率）由于破裂和摩擦产生了较大颗粒;③粗颗粒仅对峰值抗剪强度产生一定的影响,且粗颗粒越多,残余强度包线非线性越强;④黏聚力和内摩擦角随含水率线性减小,且低含水率试样残余强度包线非线性最强;⑤残余内摩擦角随颗粒破碎后的黏粒含量（<2 μm）线性减小。提出的残余内摩擦角初步预测公式可供实际工程参考。     

Discrete element modeling of the faulting in the sedimentary cover above an active salt diapir

Geological mapping, seismic analyses, and analogue experiments show that active salt diapirism results in significant faulting in the overburden strata. Faults associated with active diapirism generally develop over the crest of the dome and form a radial pattern. In this study, we have created a 3-D discrete element model and used this model to investigate the fault system over active diapirs. The model reproduces some common features observed in physical experiments and natural examples. The discrete element results show that most faults initiate near the model surface and have displacement decreasing downward. In addition, model results indicate that the earliest fault, working as the master fault, has a strong influence on the subsequent fault pattern. The footwall of the master fault is mainly deformed by arc-parallel stretching and develops a subradial fault pattern, whereas the hanging wall is deformed by both arc-parallel stretching and gliding along the master fault and top of salt, and hence develops both parallel and oblique faults. Model results replicate the fault pattern and deformation mechanism of the Reitbrook dome, Germany.     

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.