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.     

The origin of accretionary lapilli

Experimental investigations in a recirculating wind tunnel of the mechanisms of formation of accretionary lapilli have demonstrated that growth is controlled by collision of liquid-coated particles, due to differences in fall velocities, and binding as a result of surface tension forces and secondary mineral growth. The liquids present on particle surfaces in eruption plumes are acid solutions stable at 100% relative humidity, from which secondary minerals, e.g. calcium sulphate and sodium chloride, precipitate prior to impact of accretionary lapilli with the ground. Concentric grain-size zones within accretionary lapilli build up due to differences in the supply of particular particle sizes during aggregate growth. Accretionary lapilli do not evolve by scavenging of particles by liquid drops followed by evaporation — a process which, in wind tunnel experiments, generates horizontally layered hemispherical aggregates. Size analysis of particles in the wind tunnel air stream and particles adhering to growing aggregates demonstrate that the aggregation coefficient is highly grain-size dependent. Theoretical simulation of accretionary lapilli growth in eruption plumes predicts maximum sizes in the range 0.7–20 mm for ash cloud thicknesses of 0.5–10 km respectively.     

矢量曲线的视觉清晰度及在网络地图综合中的应用

互联网用户参与的地图制图容易出现视觉冲突、压盖、拥挤等地图表达问题,需要引入地图自动综合协助解决。网络地图中由于原图比例尺和综合后比例尺均难以准确量化,常规地图自动综合基于“原图比例尺-综合后比例尺”判断是否需要综合的方法已不再适用。矢量数据在可视化后会产生视觉粘连,视觉粘连越明显,地图表达效果越差,综合的需求也越强烈。基于此规律,本文提出对视觉粘连进行定量描述并据此判断是否需要综合。首先,从人类视觉感受出发,结合栅格化思想设计了矢量曲线视觉粘连的量化指标——视觉清晰度。然后,基于“金字塔式”的尺度空间计算曲线在多个比例尺表达的清晰度,并拟合了清晰度的变化函数。最后,将该函数应用于众源地理数据的网络地图综合决策。试验结果表明,本文方法可准确判断每条矢量曲线是否需要综合,能有效解决地理数据尺度异质性带来的可视化难题。同时,清晰度变化函数将曲线的尺度描述由静态数值扩展到连续函数,有望更好地支持多尺度空间数据处理及网络地图综合等问题。     

驱动重联过程中等离子体团的聚合

本文对驱动重联过程作了二维可压缩磁流体动力学模拟．对于长的计算域（１：４），在持续入流的作用下形成了双重磁岛结构，这些磁岛在向外运动的过程中不断靠近，逐渐聚合成为一个大的等离子体团，并继续向外运动．这说明在地球磁层顶和磁尾所观测到的大尺度磁结构，很可能是在驱动重联过程中，由较小的等离子体团聚合后形成的．并初步揭示了在空间等离子体中，磁岛的聚合过程难以直接观测的动力学原因．     

The coalescence of water drops II. The coalescence problem and coalescence efficiency

By the use of the model of approaching drops (Arbel and Levin, 1977) the coalescence efficiencies of drops are computed. It is found that for interactions of drops at their terminal velocities the coalescence depends both on the size of the large drop and on the size ratio of the interacting drops in agreement with the experimental results of Whelpdale and List (1971) and Levin and Machnes (1977).The results were found to be sensitive to the assumption of the drops deformation and to the critical separation distance. This distance is defined as the distance at which the drops begin to merge. The variations of the coalescence efficiency with these parameters is discussed.Appendix: List of symbols D distance between the deformed surfaces of the drops - D _o initial value ofD - D _s stop distance, the distance at which the impact velocity vanishes - D _c critical coalescence distance - E collection efficiency - E ₁ collision efficiency - E ₂ coalescence efficiency - E _2R coalescence efficiency for collisions with stationary targets - F _c centrifugal force - p ratio of the radii of the interacting drops - r _o initial distance between drops' centers - R _L radius of larger drop - R _s radius of smaller drop - R _D radius of deformation - v approach velocity of two deformed surfaces - v _o initial value ofv - V _i impact velocity (given negative sign when drops approach each other) - V _c critical impact velocity - W _i velocity of the smaller drop at infinity for it to reachD _o with velocityv _o - x _i impact distance, the distance between the trajectories of the two drops - x _c critical impact distance for coalescence -  average critical impact distance for coalescence - X _c critical impact distance for collisions - coefficient of deformation given in equation 1 - _i impact angle defined byWhelpdale andList (1971) given also inArbel andLevin (1977) - coefficient of deformation given in equation 2 - viscosity of air - _i impact angle used inArbel andLevin (1977) and here - _c critical angle for coalescence - average critical angle for coalescence On sabbatical leave (1976–77) from the Department of Geophysics and Planetary Sciences, Tel Aviv University, Ramat Aviv, Israel.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

舰船气泡尾流分布的BPBE表征方法研究

基于气泡群平衡方程(BPBE),提出一种用于更系统表征舰船气泡尾流变化特征的数值模型。模型的创新处在于既能反映气体传质因素的影响,又考虑了尾流中实际存在的气泡聚并现象,且具有简单易行,运算效率高的特点。分析结果表明:聚并在近尾流区作用强烈,传质在远程尾流区作用明显;聚并对BND的分布变化影响不大,对气含量的发展变化则发挥着主要作用;尺寸为70~80 um的气泡BND最大,尺寸为200 um的气泡气含量最大。     

交叉裂隙岩体裂纹扩展试验及混合有限-离散元数值模拟研究

对预制交叉裂隙岩石试样进行裂纹扩展试验,研究了裂纹萌生、扩展、聚合过程,分析了主裂隙和轴向载荷夹角及主次裂隙夹角对裂纹起裂应力和聚合应力的影响,并用混合有限元-离散元程序,即图形处理器并行化的3D Y-HFDEM代码对试验进行了仿真计算,实现了岩石破坏从连续介质向非连续介质的过渡,对裂纹类及损伤破坏模式进行了识别,捕捉到了试验中难以发现的现象。研究表明：随主裂隙与轴向载荷夹角增加,裂纹聚合区的拉伸裂纹数量增加;裂纹起裂和聚合应力与主裂隙与轴向载荷夹角成正比;主次裂隙夹角增加,岩石的破坏模式由拉伸破坏转为剪切破坏,交叉裂隙加剧岩石破碎程度;主裂隙尖端萌生扩展的拉伸-剪切混合裂缝引起的破坏在岩石破坏中占主导地位,是导致岩体失去承载能力的主控裂纹;混合有限元-离散元仿真软件GPGPU并行化的3D Y-HFDEM IDE在岩石裂纹扩展研究中具有优势,可以捕捉实验室难以发现的损伤断裂类型,可以作为岩石裂纹扩展研究的有力工具。     

动载下3条断续裂隙岩样的裂缝贯通机制

采用含3条断续预制裂隙的类砂岩模型试样进行单轴动力加载试验,对不同裂隙空间位置条件下断续裂隙岩体中裂隙的贯通机制进行了研究。静、动荷载下的对比研究成果显示：不同空间位置的裂隙贯通方式存在较大差异,且对动载的响应不同;动载下分支裂纹扩展及贯通具有惯性效应,即动载下裂尖次生共面、次生倾斜裂纹起裂后易朝原起裂方向快速发展,动载下易在两预制裂隙内端部产生直接贯通。这与静载下岩桥处的贯通常通过分支裂纹拐折扩展、相连不同,这也是导致裂隙试样中低应变速率下强度增大（即速率效应）的主要原因。同时,试验结果也表明：含裂隙试样静、动荷载下裂隙间的多次贯通是导致其呈现出渐进破坏特征的主要原因。     

Development of garnet porphyroblasts by multiple nucleation,coalescence and boundary misorientation‐driven rotations

Two types of garnet porphyroblast occur in the Schneeberg Complex of the Italian Alps. Type 1 porphyroblasts form ellipsoidal pods with a centre consisting of unstrained quartz, decussate mica and small garnet grains, and a margin containing large garnet grains. Orientation contrast imaging using the scanning electron microscope shows that the larger marginal garnet grains comprise a number of orientation subdomains. Individual garnet grains without subdomains are small (< 50 µm), faceted and idioblastic, and have simple zoning profiles with Ca‐rich cores and Ca‐poor rims. Subdomains of larger garnet grains are similar in size to the individual, small garnet grains. Type 2 porphyroblasts comprise only ellipsoidal garnet, with small subdomains in the centre and larger subdomains at the margin. Each subdomain has its own Ca high, Ca dropping towards subdomain boundaries. Garnet grains, with or without subdomains, all have the same Ca‐poor composition at rims in contact with other minerals. The compositional zonation patterns are best explained by simultaneous, multiple nucleation, followed by growth and amalgamation of individual garnet grains. The range of individual garnet and garnet subdomain sizes can be explained by a faster growth rate at the porphyroblast margin than in the centre. The difference between Type 1 and Type 2 porphyroblasts is probably related to the growth rate differential across the porphyroblast. Electron backscatter diffraction shows that small, individual garnet grains are randomly oriented. Large marginal garnet grains and subdomain‐bearing garnet grains have a strong preferred orientation, clustering around a single garnet orientation. Misorientations across subdomain boundaries are small and misorientation axes are randomly oriented with respect to crystallographic orientations. The only explanation that fits the observational data is that individual garnet grains rotated towards coincident orientations once they came into contact with each other. This process was driven by the reduction of subdomain boundary energy associated with misorientation loss. Rotation of garnet grains was accommodated by diffusion in the subdomain boundary and diffusional creep and rigid body rotation of other minerals (quartz and mica) around the garnet. An analytical model, in which the kinetics of garnet rotation are controlled by the rheology of surrounding quartz, suggests that, at the conditions of metamorphism, the rotation required to give a strong preferred orientation can occur on a similar time‐scale to that of porphyroblast growth.     

安徽省姑山铁矿床中赤铁矿微晶的聚合

安徽省姑山铁矿床的矿石产在中生代辉长闪长岩与以三叠纪页岩，粉砂岩和砂岩为主的围岩的接触带上，矿石成分主要是微晶赤铁矿，其粒径为０．０１－０．０５ｍｍ，并与玉髓和细粒石英相交生，粒径达１－２ｍｍ的赤铁矿斑晶呈板状自形晶浸染于块状矿石中，显微镜观察表明，赤铁矿自形斑晶是在成矿期后由赤铁矿微晶聚合而成的。整个聚合过程包括微晶颗粒的相互靠近，颗粒旋转，结晶方位的定向以及最终的焊结，从而形成光性均一的变斑晶