Meso‐scale particle modeling of concrete deterioration caused by alkali‐aggregate reaction

A meso‐scale particle model is presented to simulate the expansion of concrete subjected to alkali‐aggregate reaction (AAR) and to analyze the AAR‐induced degradation of the mechanical properties. It is the first attempt to evaluate the deterioration mechanism due to AAR using the discrete‐element method. A three‐phase meso‐scale model for concrete composed of aggregates, mortar and the interface is established with the combination of a pre‐processing approach and the particle flow code, PFC2D. A homogeneous aggregate expansion approach is applied to model the AAR expansion. Uniaxial compression tests are conducted for the AAR‐affected concrete to examine the effects on the mechanical properties. Two specimens with different aggregate sizes are analyzed to consider the effects of aggregate size on AAR. The results show that the meso‐scale particle model is valid to predict the expansion and the internal micro‐cracking patterns caused by AAR. The two different specimens exhibit similar behavior. The Young's modulus and compressive strength are significantly reduced with the increase of AAR expansion. The shape of the stress–strain curves obtained from the compression tests clearly reflects the influence of internal micro‐cracks: an increased nonlinearity before the peak loading and a more gradual softening for more severely affected specimens. Similar macroscopic failure patterns of the specimens under compression are observed in terms of diagonal macroscopic cracks splitting the specimen into several triangular pieces, whereas localized micro‐cracks forming in slightly affected specimens are different from branching and diffusing cracks in severely affected ones, demonstrating different failure mechanisms. Copyright © 2012 John Wiley & Sons, Ltd.     

How water use of <Emphasis Type="Italic">Salix</Emphasis><Emphasis Type="Italic">psammophila</Emphasis> bush depends on groundwater depth in a semi-desert area

To investigate the groundwater levels changes effects on the transpiration of Salix psammophila (S. psammophila) bush, systemic measurements of meteorological conditions, sap flow of S. psammophila, soil water contents and groundwater levels were conducted in the Hailiutu River catchment, NW of China. Based on the collected field data, Hydrus-1D software package was used to calibrate water movement for root uptake in the saturated–unsaturated zone. The soil hydraulic parameters and root uptake function parameters were calibrated. The simulated results of soil water contents and sap flow fitted well with the observed ones. Based on the calibrated hydraulic parameters, different groundwater levels were imposed at the low boundary to simulate the groundwater levels changes effects on the transpiration. The relationship between ratio of actual transpiration and potential (T/T _p) and groundwater water table depth was established. The results shows that the ratio of actual transpiration and potential transpiration decreases with groundwater table depth increase as inverse ‘S’ shape. And the turn point is corresponding to the extinct depth, i.e., no groundwater contribution to S. psammophila transpiration. To further verify this phenomenon is universal, the soil hydraulic parameters were replaced with the other five groups in the calibrated forward model. The results confirmed the similar changes of T _a/T _p with the groundwater levels changed, i.e. inverse ‘S’ shape. However, the extinction depth is different corresponding to different soil hydraulic parameters. So, the research results indicated the relationship between transpiration and groundwater levels is non-linear function.     

Modelling the flow of self‐compacting concrete

A Lagrangian particle‐based method, smooth particle hydrodynamics (SPH), is used in this paper to model the flow of self‐compacting concretes (SCC) with or without short steel fibres. An incompressible SPH method is presented to simulate the flow of such non‐Newtonian fluids whose behaviour is described by a Bingham‐type model, in which the kink in the shear stress vs shear strain rate diagram is first appropriately smoothed out. The viscosity of the SCC is predicted from the measured viscosity of the paste using micromechanical models in which the second phase aggregates are treated as rigid spheres and the short steel fibres as slender rigid bodies. The basic equations solved in the SPH are the incompressible mass conservation and Navier–Stokes equations. The solution procedure uses prediction–correction fractional steps with the temporal velocity field integrated forward in time without enforcing incompressibility in the prediction step. The resulting temporal velocity field is then implicitly projected on to a divergence‐free space to satisfy incompressibility through a pressure Poisson equation derived from an approximate pressure projection. The results of the numerical simulation are benchmarked against actual slump tests carried out in the laboratory. The numerical results are in excellent agreement with test results, thus demonstrating the capability of SPH and a proper rheological model to predict SCC flow and mould‐filling behaviour. Copyright © 2010 John Wiley & Sons, Ltd.     

抗转动对颗粒材料组构特性的影响研究

颗粒材料大多由不规则形状的颗粒组成,如砂土、谷物等,抵抗转动是不规则形状颗粒的固有特性。已有研究表明,颗粒抗转动特性对其宏观力学特性有显著影响。因此,在颗粒材料的细观数值模拟中或采用非圆颗粒,或在圆颗粒离散元模拟中采用考虑抗转动的接触模型。采用有限元-离散元耦合方法（FDEM）和离散元方法（DEM）分别对椭球形状颗粒和具有抗转动能力的圆球颗粒进行三轴剪切数值模拟,指出了采用抗转动接触模型考虑颗粒形状影响的局限性,并基于颗粒的局部排布结构揭示了形状影响的细观来源。峰值内摩擦角和剪胀均随着转动摩擦系数和形状偏离圆球程度而单调增加,但颗粒形状对它们的影响呈现出明显的收敛趋势。细观组构分析也表明,虽然颗粒形状和转动摩擦都能显著增强组构各向异性,但是组构各向异性的演化模式有明显的区别。造成以上结果的差异在于其抵抗转动的影响机制不同。转动摩擦是通过限制颗粒转动,增强了颗粒间的稳定承载能力,而非圆颗粒是通过咬合作用形成稳定的局部排列结构。由于椭球颗粒腹部比端部能够传递更大的接触力,颗粒受剪切后发生转动,颗粒长轴倾向于正交大主应力方向,呈现交错排列,颗粒间相互锁定。     

粗粒料强度及变形特性的细观模拟

粗粒料是一定级配的岩石颗粒集合体,具有独特的物理力学特性。以粗粒料室内三轴固结排水试验成果为基础,基于离散元颗粒流理论,从细观角度出发,以PFC3D为工具,通过自编程及二次开发,得到按级配生成的粗粒料三轴试验数值模型。引入clump颗粒考虑颗粒形状对粗粒料强度及变形的影响,分析剪胀、颗粒形状、颗粒重排的关系。结果表明：颗粒形状是影响粗粒料强度与变形的主要因素,在其他细观参数一定的情况下,改变颗粒形状,可以显著影响粗粒料的力学行为;BPM模型的应力-应变关系只在低围压下与试验值吻合,随着围压的增大,偏差越来越大;而引入clump颗粒的PFC3D数值模型能很好地模拟粗粒料室内三轴固结排水试验的应力-应变特性,但由于BPM及clump都是刚性颗粒,没有考虑颗粒变形及破碎,造成应变剪胀偏大。     

基于精确缩尺的颗粒材料流变研究

基于Feng Y T提出的精确缩尺方法,即根据几何相似、静力相似、动力相似3个相似原理建立一套缩尺准则,使得缩尺前后模型的力学响应保持一致。首次将该理论应用于颗粒材料的流变分析当中,采用Burgers黏塑性蠕变模型,引入流变参数,在原缩尺准则上进行理论推导,得到在二维和三维条件下的缩尺准则;其次在理论推导的基础上进行数值仿真验证。研究结果表明：严格按照拟定的缩尺准则选取参数后,缩尺后模型的力学响应能够保证和原尺寸模型完全一致,计算误差在3%以内,同时简要探讨了时间步长、黏性系数、颗粒数目、比尺数对数值试验的影响,为数值试验中相关参数的选取以及如何让数值模型反映材料真实的力学行为提供了有效参考。另外,由于缩尺模型采用与原模型相同的颗粒数目、颗粒形状、颗粒压实状态和比尺数,揭示了等比例缩尺对材料流变行为的影响。     

Bearing Capacity of the New Composite Foundation with Discrete Material-Concrete Compound Piles

In order to solve the bulging deformation and fracture at the top of widely used gravel piles in treating ground consolidation, a new, optimized composite foundation form was proposed. The composite foundation was constructed using discrete materials and concrete piles. Additionally, various parameters of this new composite foundation were analyzed, including foundation forms, construction technologies, bearing mechanism and failure mode. By applying cavity expansion theory, the Vesic cavity spreading pressure of the discrete material-concrete pile is solved as a polar axis symmetric problem on the basis of Mohr–Coulomb yield criterion. Then the computing formula for the ultimate bearing capacity of the discrete materials-concrete pile is elicited when the internal friction angle of soil in the piles is φ = 0 and φ ≠ 0. Finally, the ultimate bearing capacity value of the composite foundation is acquired through analytic calculation and numerical simulation. Finally, it is found that the calculation result is 14.4% lower than that of the simulated result, which is within the acceptable accuracy range and therefore proves the accuracy of the analytic calculation method for bearing capacity of the new composite foundation.     

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。     

颗粒形态对离散介质剪切强度的影响

自然条件下,颗粒介质大多以非规则单元形态存在。非规则几何形态对颗粒介质的宏观力学性能有很大影响。针对颗粒单元的不同几何形态,采用团颗粒单元对离散介质的直剪试验过程进行了离散元数值计算,详细地讨论了颗粒形态对离散介质剪切强度的影响。该非规则颗粒由不同形态、不同数目、镶嵌尺寸、组合方位和颗粒大小的球形颗粒进行随机构造,其在局部与整体坐标之间的转动、力矩和方位关系通过4元素方法进行确定,基本球体颗粒之间的作用力采用具有Mohr-Coulomb摩擦定侓的Hertz-Mindlin非线性接触模型,并考虑了非线性法向粘滞力的影响。通过构造7种具有相同的质量概率分布的不同形态的团颗粒,在不同法向应力下,对团颗粒的直剪试验进行了离散元模拟,分析了不同形态颗粒的剪切强度。通过对不同形态颗粒介质剪切强度的数值分析,进一步揭示了非规则颗粒间的咬合互锁效应,为分析非规则颗粒的宏观动力特性提供了依据。     

Timescales for mechanisms for the dynamical evolution of open star clusters

We have obtained the stellar velocity dispersion in three mutually perpendicular directions in the halos and cores of clusters as a function of time for several non-stationary open-cluster models. During the dynamical evolution of the open-cluster models, the velocity dispersions undergo oscillations that do not decay during 5–10 violent-relaxation timescales, τ _vr . We estimated the time for synchronization of the rotation of the open-cluster models and their motion around the center of the Galaxy, t _s , which, depending on the model parameters, is t _s ? (5–27)τ _vr . Synchronization mechanisms for the models are discussed. The disruption of the systems in the force field of the Galaxy is strongly affected by tidal friction. We have also estimated the time for the formation of a spherical stellar-velocity distribution in the cluster models, t _σ ? (6 ? 25)τ _vr . The impact of instability in the stellar motions in a cluster on the formation of a spherical velocity distribution in the open-cluster models is discussed. We have noted a tendency for a weakening of the dependence of the coarse phase density of the cluster on small initial perturbations of the stellar phase coordinates in the model cluster cores for times about five times longer than the violent-relaxation time.     

Effects of particle size of mono-disperse granular flows impacting a rigid barrier

Understanding the interaction between complex geophysical flows and barriers remains a critical challenge for protecting infrastructure in mountainous regions. The scientific challenge lies in understanding how grain stresses in complex geophysical flows become manifested in the dynamic response of a rigid barrier. A series of physical flume tests were conducted to investigate the influence of varying the particle diameter of mono-dispersed flows on the impact kinematics of a model rigid barrier. Particle sizes of 3, 10, 23 and 38 mm were investigated. Physical tests results were then used to calibrate a discrete element model for carrying out numerical back-analyses. Results reveal that aside from considering bulk characteristics of the flow, such as the average velocity and bulk density, the impact load strongly depends on the particle size. The particle size influences the degree of grain inertial stresses which become manifested as sharp impulses in the dynamic response of a rigid barrier. Impact models that only consider a single impulse using the equation of elastic collision warrant caution as a cluster of coarse grains induce numerous impulses that can exceed current design recommendations by several orders of magnitude. Although these impulses are transient, they may induce local strucutral damage. Furthermore, the equation of elastic collision should be adopted when the normalized particle size with the flow depth, δ/h, is larger than 0.9 for Froude numbers less than 3.5.     

Modelling hydraulic and capillary-driven two-phase fluid flow in unsaturated concretes at the meso-scale with a unique coupled DEM-CFD technique

The goal of the research was to demonstrate the impact of thin porous interfacial transition zones (ITZs) between aggregates and cement matrix on fluid flow in unsaturated concrete caused by hydraulic/capillary pressure. To demonstrate this impact, a novel coupled approach to simulate the two-phase (water and moist air) flow of hydraulically and capillary-driven fluid in unsaturated concrete was developed. By merging the discrete element method (DEM) with computational fluid dynamics (CFD) under isothermal settings, the process was numerically studied at the meso-scale in two-dimensional conditions. A flow network was used to describe fluid behaviour in a continuous domain between particles. Small concrete specimens of a simplified particle mesostructure were subjected to fully coupled hydro-mechanical simulation tests. A simple uniaxial compression test was used to calibrate the pure DEM represented by bonded spheres, while a permeability and sorptivity test for an assembly of spheres was used to calibrate the pure CFD. For simplified specimens of the pure cement matrix, cement matrix with aggregate, and cement matrix with aggregate and ITZ of a given thickness, DEM/CFD simulations were performed sequentially. The numerical results of permeability and sorptivity were directly compared to the data found in the literature. A satisfactory agreement was achieved. Porous ITZs in concrete were found to reduce sorption by slowing the capillary-driven fluid flow, and to speed the full saturation of pores when sufficiently high hydraulic water pressures were dominant.     

堆石料单粒强度尺寸效应的颗粒流模拟方法研究

围绕堆石料单粒强度尺寸效应的颗粒流模拟方法展开研究。首先,基于FISH二次开发建立了堆石料的随机不规则单粒模型,充分考虑堆石料的形状特征和破碎现象;然后,建立了堆石料单粒强度尺寸效应的等效模拟方法,以单粒强度随其粒径的变化规律为基础,推导了堆石料模型中细观黏结强度与堆石料等效粒径的负指数经验公式;其次,基于建立的数值模型对堆石料的室内单粒压缩试验进行仿真模拟,验证数值模型的正确性和合理性,并对较大粒径堆石料的单粒强度进行模拟预测,突出数值试验的优势;最后,基于建立的数值模型对相同粒径不同形状特征堆石料的单粒强度分布特征进行模拟研究。研究结果表明：（1）堆石料内部缺陷含量和尺寸随粒径增加对其单粒强度所产生的尺寸效应,可通过堆石料模型中细观强度参数随粒径折减进行等效模拟;（2）形状特征对堆石料的破裂机制具有重要影响,方形颗粒为压剪破裂,单粒强度较高,而随机不规则颗粒和圆形颗粒为拉剪或劈裂,单粒强度相对较低;（3）拉剪或劈裂条件下,堆石料形状越不规则,其单粒强度的离散程度越高,反之则离散程度越低。相关研究成果可为进一步研究荷载作用下堆石体内各粒径段堆石料的破碎量奠定基础,从而更加真实地反映堆石体的级配演化规律。     

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.     

DEM simulations of sandstone under true triaxial compressive tests

Numerically simulated true triaxial compression tests (σ ₁ ≥ σ ₂ ≥ σ ₃) are conducted in this study to elucidate the failure mechanism of sandstone using 3D discrete element method (DEM), in particular the effect of the intermediate principal stress (σ ₂). Eight series of tests (σ ₃ = 0, 10, 20, 30, 40, 50, 70, and 100 MPa) are conducted. Within each series, σ ₂ is varied from σ ₂ = σ ₃ to σ ₂ = σ ₁ from test to test. For each test, σ ₁ is raised monotonically to failure while keeping σ ₂ and σ ₃ constant. The DEM simulations reveal the effect of σ ₂ on the variations of peak stress, Young’s modulus, failure plane angles, the brittle–ductile transition, and the evolution of failure modes, the effect beyond the well-understood effect of σ ₃. The simulation is in qualitative agreement with the results obtained experimentally. Detailed analyses performed on the particle-scale responses further the understanding of the microscopic mechanisms. The distribution of contact force becomes more homogeneous with the increase of σ ₃, which leads to the resulting damage being more localized rather than diffused. The interaction between contact force distribution and coalescence of cracks determines the processes and patterns of fracturing in the sample scale. σ ₂ is found to affect the microscopic stress distribution as well as structure evolution, and this effect weakens with the increase of σ ₃.     

Micromechanical investigation of the particle size effect on the shear strength of uncrushable granular materials

Particle size strongly influences the shear strength of granular materials. However, previous studies of the particle size effect have focused mainly on the macroscopic behavior of granular materials, neglecting the associated micro-mechanism. In this study, the effect of particle size on the shear strength of uncrushable granular materials in biaxial testing is investigated using the discrete element method (DEM). First, a comprehensive calibration against experimental results is conducted to obtain the DEM parameters for two types of quartz sand. Then, a series of biaxial tests are simulated on sands with parallel particle size distributions to investigate the effect of particle size on macro- and microscopic behaviors. Finally, by adopting the rolling resistance method and the clump method, irregular-shaped particles are simulated to investigate how the particle size effect will be influenced by the particle shape. Simulation results demonstrate that (1) the peak shear strength increases with particle size, whereas the residual shear strength is independent of particle size; (2) the thickness of the shear band increases with the particle size, but its ratio decreases with particle size; (3) the particle size effect can be explained by the increase of friction utilization ratio with particle size; and (4) the particle size effect is more significant in granular materials that consist of particles with higher angularity.

     

基于细观力学的混凝土劈拉破坏率相关特性研究

提出了一种高效的混凝土细观力学预处理方法,其中包括基于背景网格的骨料投放与细观三组分的识别;建立了颗粒离散元的混凝土细观力学模型。利用该模型对不同应变率下混凝土的劈拉试验进行了数值仿真,仿真结果显示出的混凝土动力强度提高的规律以及不同应变率下混凝土的破坏模式与试验结果吻合较好。研究表明,随着应变率的提高,混凝土破坏时产生更多弥散状分布的裂纹,同时有些裂纹穿过强度较高的骨料,导致混凝土在高应变率破坏过程中消耗更多的能量,是混凝土的动力强度提高的重要原因。此外,在高应变率下,力链产生更多的分叉,空间分布的不均匀性和随机性增加,因此,在高应变率下混凝土动力强度表现出更大的离散性。     

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.     

Compressibility of Sands of Various Geologic Origins at Pre-crushing Stress Levels

This study quantifies the influence of various intrinsic soil properties including particle roundness, R, sphericity, S, 50% size by weight, D ₅₀, coefficient of uniformity, C _u, and the state property of relative density, D _r, on the compression and recompression indices, C _c and C _r, of sands of various geologic origins at pre-crushing stress levels. Twenty-four sands exhibiting a wide range of particle shapes, gradations, and geologic origins were collected for the study. The particle shapes were determined using a computational geometry algorithm which allows characterization of a statistically large number of particles in specimens. One dimensional oedometer tests were performed on the soils. The new data was augmented with many previously published results. Through statistical analyses, simple functional relationships are developed for C _c and C _r. In both cases, the models utilized only R and D _r since other intrinsic properties proved to have lesser direct influence on the compression indices. However, previous studies showed that the contributions of S and C _u are felt through their effects on index packing void ratios and thus on D _r. The accuracy of the models was confirmed by comparison of predicted and observed C _c and C _r values.     

非饱和土粒间毛细作用的微观不连续变形分析

非饱和土粒间毛细水作用是其基质吸力的主要来源。本文基于二维非连续变形分析算法(DDA),建立了一种能够模拟不同饱和度下毛细水分布状态及计算土水特征曲线的扩展DDA算法。该算法首先通过反复迭代的方式来计算出不同饱和度下毛细水弯液面的半径,并利用圆心轨迹交汇法确定粒间毛细水弯液面与颗粒的搭接位置,从而确定各个颗粒表面被毛细水浸湿的区域。而后利用Young-Laplace方程计算出各个浸湿区域毛细负压的大小,并将其与表面张力添加到传统DDA算法控制方程中。为验证该算法,参照真实黄土中含量最多的粗颗粒建立一理想黄土微观土骨架模型,模拟了不同饱和度下土体中的毛细水分布状态,并获得了土水特征曲线。将模拟结果与实测的土水特征曲线进行对比分析,结果显示预测值和实测值基本一致,该方法能够从微观上揭示非饱和土粒间吸力作用的本质。