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.     

基于PFC2D模拟的矿物粒径非均质效应研究

岩石作为矿物颗粒的集合体,矿物粒径非均质性对其宏观力学特性影响比较明显。基于颗粒流程序PFC2D,通过设置不同种类粒径组合及粒径比来体现粒径非均质性,研究了粒径非均质性对岩石材料宏观力学特性（弹性模量、峰值强度、泊松比）的影响。研究中设计了6种粒径组合方案,粒径种类数分别为:连续粒径、10种、8种、5种、3种、2种,每种方案下设置5种平均粒径及4种粒径比,进行单轴压缩试验。结果表明,岩石内部存在颗粒尺寸效应和粒径非均质效应,岩石弹性模量和峰值强度随粒径增大均呈减小的趋势,随粒径非均质性的提高整体上也呈减小的趋势,但局部变化阶段受模型中细颗粒含量及数量的影响会呈增大的趋势。粒径对弹性模量的作用机制主要是通过影响模型孔隙率实现的。研究结果揭示了岩石宏观特性的变化是模型内颗粒尺寸效应和粒径非均质性效应共同作用的结果,为掌握矿物粒径对岩石强度及变形特性的影响提供了一定依据。     

中低应变率加载条件下花岗岩尺寸效应的能量特征研究

能量相互转化过程的综合作用导致了岩石破坏,而其破坏的根本原因是岩石中储存的应变能的释放。对中低应变率加载条件下岩石尺寸效应能量特征的研究结果表明：花岗岩破坏时吸收的总能量U、弹性应变能Ue以及损伤应变能Ud均随试件尺寸的增长而降低;岩石强度与岩石中储存的能量有关,尤其与弹性储能有关,即弹性应变能愈高,岩石强度越大;试件长度由50 mm 变为125 mm时,弹性储能逐渐降低,岩石破坏形态从劈裂破坏变为剪切破坏,大尺寸时局部化变形明显。能量是不同应变率加载条件下岩石破坏细微观及宏观特征存在差异的内在动力;亦是导致岩石强度存在尺寸效应的本质动因。     

Failure and size effect for notched and unnotched concrete beams

Modelling failure in geomaterials, concrete or other quasi‐brittle materials and proper accounting for size effect, geometry and boundary effects are still pending issues. Regularised failure models are capable of describing size effect on specimens with a specific geometry, but extrapolations to other geometries are rare, mostly because experimental data presenting size effect for different geometries and for the same material are lacking. Three‐point bending fracture tests of geometrically similar notched and unnotched specimens are presented. The experimental results are compared with numerical simulations performed with an integral‐type non‐local model. Comparisons illustrate the shortcomings of this classical formulation, which fails to describe size effect over the investigated range of geometries and sizes. Finally, experimental results are also compared with the universal size effect law. Copyright © 2013 John Wiley & Sons, Ltd.     

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。     

不同围压下岩石抗压强度与变形参数尺寸效应的数值模拟

岩石抗压强度和变形参数是岩石工程设计的重要指标。由于岩石是典型的非均质材料,其强度和变形特性随样品尺 寸的变化而不同。本文采用PFC2D程序模拟了不同围压下不同尺寸岩样的压缩试验。结果表明（1） 岩样具有明显的尺寸效 应。同一围压下,尺寸越大,岩石强度、峰值应变和压缩模量越小,尺寸的变化对岩样的破坏模式影响较小;（2） 岩样具 有明显的围压效应。同一尺寸的岩样,随着围压的增大,岩石强度、峰值应变和压缩模量均增加,其中强度和峰值应变随 围压的增加呈线性增加。同时,随着围压的增大,岩石破裂模式由轴向劈裂破坏向剪切破坏变化;（3） 围压的存在会影响 岩样的尺寸效应。不同尺寸岩样的强度和峰值应变在相同围压区间内的增量基本相同,同时随着围压的增大,其强度和峰 值应变增加,进而使岩石强度和峰值应变的尺寸效应弱化;而不同尺寸岩样的压缩模量在相同围压区间内的增长率大致相 同,因而造成围压对压缩模量尺寸效应的影响较小     

单轴压缩下绿砂岩长期强度的尺寸效应研究

岩石的蠕变特性是影响岩体工程稳定性的重要因素,而岩石的长期强度是确定岩体工程长期稳定的一个重要指标。由于岩石材料的非均质性,其长期强度具有明显的尺寸效应。为了研究岩石长期强度的尺寸效应,首先,在幂函数模型基础上,基于损伤力学理论,建立了能够描述岩石蠕变全过程的非线性蠕变损伤模型;然后,把运用该模型计算得到的单轴压缩蠕变数值模拟结果与室内单轴压缩蠕变试验结果进行对比,验证了模型的正确性;最后,采用所提出的模型对7个不同尺寸的岩样进行了单轴压缩蠕变数值模拟,并对岩石长期强度尺寸效应进行了分析。数值模拟结果表明：随着试样尺寸的逐渐增大,岩石长期强度值逐渐减小,当试样尺寸增大到一定程度时,岩石长期强度稳定在一个特定值附近。     

掘削卵砾石地层颗粒离散元模拟中的细观参数取值讨论

卵砾石地层被掘削时,其主要破坏模式并非一般的宏观整体剪切破坏,而是刀具切入卵砾石间的缝隙,将卵砾石颗粒剥离出原始地层,该过程较为契合颗粒离散元的物理力学假设。为确定掘削工况下的颗粒材料最优细观参数,对不同的颗粒接触法向刚度、接触刚度比、粒间摩擦系数、颗粒形状、颗粒尺寸等的颗粒材料开展了截割三维仿真试验,并分析研究了不同细观参数对掘削效果的影响。计算结果显示：颗粒接触法向刚度、接触刚度比的多种细观参数组合可以对应同一个宏观弹性模量值,接触刚度比大的细观参数组合的抗掘削能力更大。颗粒形状、粒间摩擦系数的多种细观参数组合可以对应同一个内摩擦角值,形状复杂的颗粒材料具有更大的抗掘削能力。在宏观参数相同的情况下,平均粒径更大的颗粒材料抗掘削能力更大。因此,利用颗粒离散元模拟掘削卵砾石地层问题时,除需保证虚拟颗粒材料的宏观整体剪切破坏响应与真实材料基本一致外,还需根据材料的抗掘削能力进一步标定细观参数,以获得更贴近实际情况的模拟效果。文章提出的方法可以为其他颗粒离散元掘削工况数值模拟中的参数标定提供参照依据。     

A Shear Model Accounting Scale Effect in Rock Joints Behavior

Understanding the scale effect on the mechanical behavior of a single rock joint is still very important in rock engineering. Rock joints can be classified into three different categories depending on their scale: the “micro scale” which is the scale of the asperities; the “meso scale” is the scale of the specimens tested in laboratory; and the “macro scale” which is the scale of the rock mass. The purpose of this paper is to propose an effective way to model rock joints at both the meso and macro scale. An original constitutive mechanical model, in which parameters are deduced from experimental results, has been developed. This model is then extended to simulate the discontinuities occurring at a larger size. At the macro scale, the constitutive modeling was carried out for both small and large relative displacements. Large displacements lead to substantial changes in dilation. For both cases, the peak shear stress vanishes for joints longer than 2 m.     

Modeling Strain Rate Effect of Heterogeneous Materials Using SPH Method

The strain rate effect on the dynamic compressive failure of heterogeneous material based on the smoothed particle hydrodynamics (SPH) method is studied. The SPH method employs a rate-insensitive elasto-plastic damage model incorporated with a Weibull distribution law to reflect the mechanical behavior of heterogeneous rock-like materials. A series of simulations are performed for heterogeneous specimens by applying axial velocity conditions, which induce different strain-rate loadings to the specimen. A detailed failure process of the specimens in terms of microscopic crack-activities and the macro-mechanical response are discussed. Failure mechanisms between the low and high strain rate cases are compared. The result shows that the strain-rate effects on the rock strength are mainly caused by the changing internal pressure due to the inertial effects as well as the material heterogeneity. It also demonstrates that the inertial effect becomes significant only when the induced strain rate exceeds a threshold, below which, the dynamic strength enhancement can be explained due to the heterogeneities in the material. It also shows that the dynamic strength is affected more significantly for a relatively more heterogeneous specimen, which coincides with the experimental results showing that the poor quality specimen had a relatively larger increase in the dynamic strength.     

Effects of anisotropy in correlation structure on the stability of an undrained clay slope

Slopes are mainly naturally occurred deposits, so slope stability is highly affected by inherent uncertainty. In this paper, the influence of heterogeneity of undrained shear strength on the performance of a clay slope is investigated. A numerical procedure for a probabilistic slope stability analysis based on a Monte Carlo simulation that considers the spatial variability of the soil properties is presented to assess the influence of randomly distributed undrained shear strength and to compute reliability as a function of safety factor. In the proposed method, commercially available finite difference numerical code FLAC 5.0 is merged with random field theory. The results obtained in this study are useful to understand the effect of undrained shear strength variations in slope stability analysis under different slope conditions and material properties. Coefficient of variation and heterogeneity anisotropy of undrained shear strength were proven to have significant effect on the reliability of safety factor calculations. However, it is shown that anisotropy of the heterogeneity has a dual effect on reliability index depending on the level of safety factor adopted.     

脆性颗粒材料的动态多尺度模型研究

脆性颗粒材料的多尺度模型一般包含微观尺度的基本粒子、细观尺度的颗粒和宏观尺度的颗粒堆积体3个尺度。基于离散元方法（DEM）构建多尺度模型,并将该模型应用于动态加载。首先,对多尺度模型所涉及的两种接触模型和两种黏结模型的参数进行分析,详细讨论微细观模型参数与宏观材料常数之间的联系。然后,选用Hertz-Mindlin接触模型[1]和平行键黏结模型,建造石英砂的动态多尺度模型。通过选择合适的强度和局部阻尼参数发现,模型宏细观尺度上的动态压缩响应与对石英砂的相关试验结果吻合很好。利用多尺度模型和选定的参数,探讨与动态加载密切相关的局部阻尼机制对多尺度模型各个尺度上力学响应的影响。结果表明,阻尼越大则颗粒材料对波的衰减能力越强,但过高的阻尼会使团簇强度和模型的宏观压缩曲线都表现出异常的加载速度效应（后者实际是阻尼引起的微惯性效应）。另外,高阻尼会过度衰减颗粒破碎过程产生的应力波,从而阻碍颗粒破碎。最后,应用改进的动态多尺度模型,对脆性颗粒材料的动态破碎特性进行研究,发现该模型不但能给出与试验相吻合的颗粒级配曲线,还能揭示出颗粒破碎过程中微裂纹分布的空间不均匀性,即颗粒破碎过程中波的产生机制和衰减机制相互作用导致的微裂纹聚团分布的现象。     

裂隙岩体等效力学参数结构效应的计算机模拟试验研究

为研究裂隙岩体结构效应对其等效力学参数的影响,引入基于离散元的合成岩体技术,通过可控的改变三维岩体结构网络中的结构参数,制作相应的合成岩体试件,开展计算机模拟试验研究。结果表明：随岩体中裂隙体积密度增大,裂隙的变形参数和强度参数随裂隙密度增加而减少,其中等效弹性模量对结构面密度变化最为敏感;随岩体中裂隙倾角增加,岩体等效弹性模量随之单调增加,且等效弹性模量的离散程度（标准差）随倾角增加而减小,而各强度参数指标则先减少而后增加,形成一个U形变化规律;岩体等效力学参数均随结构面尺寸增加而减小,同时等效力学参数的离散程度（标准差）随结构面直径增加而增加,其中单轴抗压强度指标变化最为敏感;岩体等效力学参数对裂隙尺寸和产状的离散程度不敏感。该研究结论可为其他结构效应研究提供一种新思路。     

Mechanical behavior and microstructural variation of loess under dynamic compaction

The laboratory dynamic compaction test was used to study the effects of dynamic impact loads on the shear strength characteristics of loess. Loess specimens were compacted by different numbers of blows and their shear strengths measured. The experimental results revealed that the shear strength varies in stages with the number of blows. During the initial stage, the shear strength increases with the number of blows. It reaches a peak value and then decreases with the number of blows. To reveal the relationship between this alternation in shear strength and microstructural variation, quantitative microstructural analyses were performed on some tested specimens at different stages of strength evolution. This microstructural study demonstrated that the variation of shear strength is directly related to the alteration of microstructure. It is concluded that the shear strength of loess is basically controlled by its microstructural state. Growing particle size heterogeneity, varying particle orientations and increasing microstructural damage are the main causes of the alternation of shear strength.     

Practical determination of mechanical design parameters of intact rock considering scale effect

As a rule, the change in mechanical properties of rock by specimen size is regarded as scale effect. A rock mass basically consists of two components: intact rock and discontinuities, each of which has different scale effects. In order to numerically analyze the behavior of discontinuous rock masses, sufficient mechanical properties must be determined not only for discontinuities but also for intact rock taking into consideration the different scale effects. This paper reviews the scale effect on strength and deformation characteristics of intact rock, and also discusses the possibility of using standard specimens to estimate strength and deformation characteristics of actual-scale rock. Finally, we propose an adequate method for the practical determination of mechanical design parameters based on the above discussions.     

The effect of specimen diameter size on uniaxial compressive strength,P-wave velocity and the correlation between them

Estimation of uniaxial compressive strength (UCS) by P-wave velocity (V_P) is of great interest to geotechnical engineers in various design projects. The specimen diameter size is one of the main factors that influence rock parameters such as UCS and V_P. In this study, the diameter size of specimens that effect UCS and V_P is investigated. Moreover, the correlation between UCS and V_P are examined via empirical analysis. For this purpose, 15 travertine samples were collected and core specimens with a diameters size of 38, 44, 54, 64 and 74 mm were prepared. Then, uniaxial compressive strength and P-wave velocity tests were conducted according to the procedure suggested by ISRM (1981). It is concluded that the diameter size of the specimen has a significant effect on UCS and V_P. Moreover, it was found that the best correlation between relevant parameters obtained for the specimen diameter of 38 mm.     

Gas-phase molecular structure and energetics of anionic silicates

The gas-phase stabilities of linear, branched and cyclic silicates made of up to five silicon atoms were studied with density functional theory (DFT). The starting geometries for the DFT calculations at the B3LYP/6-311+G(2d,2p) level of theory were obtained from classical molecular dynamics simulations. We have observed that geometric parameters and charges are mainly affected by the degree of deprotonation. Charges on Si atoms are also influenced by their degree of substitution. The enthalpy of deprotonation of the neutral species was found to decrease with the size of the molecule, while the average deprotonation enthalpy of highly charged compounds increased with molecular size. Furthermore, the formation of rings in highly charged silicates is enthalpically preferred to chain growth. These observations result from two competing effects: the easier distribution of negative charge in silicates with low charge density and the strong intramolecular repulsions present in silicates with high charge density. As a consequence, highly charged silicates in the gas phase tend to be as small and as highly condensed as possible, which is in line with experimental observations from solution NMR.     

Simulating damage evolution and fracture propagation in sandstone containing a preexisting 3-D surface flaw under uniaxial compression

Preexisting flaws and rock heterogeneity have important ramifications on the process of rock fracturing and on rock stability in many applications. Therefore, there is great interest in numerical modelling of rock fracture and the underlying mechanisms. We simulated damage evolution and fracture propagation in sandstone specimens containing a preexisting 3-D surface flaw under uniaxial compression. We applied the linear elastic damage model based on the unified strength theory following the rock failure process analysis code. However, in contrast to the rock failure process analysis code, we used the finite element method with tetrahedron elements on unstructured meshes. It provided higher geometrical flexibility and allowed for a more accurate representation of the disk-shaped flaw with various flaw depths, angles, and lengths through locally adapted meshes. The rock heterogeneity was modelled by sampling the initial local Young's modulus from a Weibull distribution over a cubic grid. The values were then interpolated to the computational finite element method mesh. This method introduced an additional length scale for the rock heterogeneity represented by the cell size in the sampling grid. The generation of three typical surface cracking patterns, called wing cracks, anti-wing cracks, and far-field cracks, were identified in the simulation results. These depend on the geometry of the preexisting surface flaw. The simulated fracture propagation, coalescence types, and failure modes for the specimens with preexisting surface flaw show good agreement with recent experimental studies.     

Three-dimensional finite element simulation of fracture propagation in rock specimens with pre-existing fissure(s) under compression and their strength analysis

A FORTRAN program, consistent with the commercially available finite element (FE) code ABAQUS, is developed based on a three-dimensional (3D) linear elastic brittle damage constitutive model with two damage criteria. To consider the heterogeneity of rock, the developed FORTRAN program is used to set the stiffness and strength properties of each element of the FE model following a Weibull distribution function. The reliability of the program is assessed against available experimental results for granite cylindrical specimens with a throughgoing, flat and inclined fissure. The calibration procedure of the material parameters is explained in detail, and it is shown that the compressive to tensile strength ratio can have a substantial influence on the failure response of the specimens. Numerical simulations are conducted for models with different levels of heterogeneity. The results show a smaller load bearing capacity for models with less homogeneity, representing gradual coalescence of fully damaged elements forming throughout the models during loading. The maximum load bearing capacity is studied for various combinations of inclination angles of two centrally aligned, throughgoing and flat fissures of equal length embedded in cylindrical models under uniaxial and multiaxial loading conditions. The key role of the compressive to tensile strength ratio is highlighted by repeating certain simulations with a lower compressive to tensile strength ratio. It is proven that the peak loads of the rock models with sufficiently small compressive to tensile strength ratios containing two throughgoing fissures of equal length are similar, provided that the minimum inclination angles of the models are the same. The results are presented and discussed with respect to the existing experimental findings in the literature, suggesting that the numerical model applied in this study can provide useful insight into the failure behaviour of rock-like materials.     

Variational safety factors and slip surfaces of slope using three-dimensional strength reduction analysis

This paper describes the effect of boundary conditions combined with geometric and strength parameters on slope stability, including safety factor and slip surface, using numerical strength reduction analysis. The different boundary conditions are discussed, which include the fully restrained boundary, half-restrained boundary, and free boundary on the safety factor of slope. The effects of geometric and strength parameters on the safety factor of slope are then examined. Discrepancies between the slip surface shape and the escaping points are also presented to assess slope stability.