The strength and fractal dimension characteristics of alum–kaolin flocs

Flocs generated by various shear forces exhibit different characteristics of size, strength and structure. These properties were investigated by employing a continuous optical monitoring and a microscope with CCD camera to directly monitor aggregation under six different shear intensities. The floc structure was characterized by the fractal dimension. The results showed that the flocculation index (FI) decreased from 1.16 at 20 rpm to 0.25 at 250 rpm and the floc size decreased from 550 μm to 150 μm, meantime, the FI value showed a good correlation with floc size. In order to determine the floc strength, two methods were used. One was the strength factor, ranging from 18.3% to 62.5%, calculated from FI curve, and the other was a theoretical value between 0.005 N/m² and 0.240 N/m², estimated by calculation. The floc strength increased with the G value in both cases. Furthermore, the fractal dimension increased with G and its value was between 1.30 and 1.63. The relation between fractal dimension and strength was also obtained.     

Relationships between fractal road and drainage networks in Wuling mountainous area: Another symmetric understanding of human-environment relations

Symmetrical relationships between humans and their environment have been referred to as an extension of symmetries in the human geographical system and have drawn great attention. This paper explored the symmetry between physical and human systems through fractal analysis of the road and drainage networks in Wuling mountainous area. We found that both the road and drainage networks reflect weak clustering distributions. The evolution of the road network shared a significant self-organizing composition, while the drainage network showed obvious double fraetal characteristics. The geometric fractal dimension of the road network was larger than that of the drainage network. In addition, when assigned a weight relating to hierarchy or length, neither the road network nor drainage network showed a fractal property. These findings indicated that the fractal evolution of the road network shared certain similarities with fractal distribution of the drainage network. The symmetry between the two systems resulted from an interactive process of destroying symmetry at the lower order and reconstructing symmetry at the higher order. The relationships between the fractal dimensions of the rural-urban road network, the drainage network andthe urban system indicated that the development of this area was to achieve the symmetrical isomorphism of physical-human geographical systems.     

岩石颗粒破碎的尺寸效应

固体颗粒破碎强度的尺寸效应是一种普遍存在的现象,冰块、岩石颗粒、陶瓷和混凝土块等的破碎强度都表现出随颗粒直径增加而减小的现象,分形模型为解释固体颗粒破碎强度的尺寸效应提供了可行的方法。本文采用Steacy和Sammis分形模型模拟了岩石颗粒压碎特征,分析岩石颗粒破碎后的颗粒分布规律,给出颗粒破碎分维的确定方法,建立颗粒压碎强度与粒径的理论关系,颗粒破碎强度与颗粒粒径的关系用分维D表示为fdD-3。已有的颗粒破碎分布的数据表明,岩石颗粒破碎的分维大约为2.50～2.60,颗粒破碎强度符合用分维表示的尺寸效应。     

Evolution of neotectonic activity of East Anatolian Fault System (EAFS) in Bingöl pull-apart basin,based on fractal dimension and morphometric indices

This study is an attempt of a semi-automatic geomorphological GIS analysis based on morphometric indices. In the study, 10-m-resolution Digital Elevation Models (DEMs) are used to assess the neotectonic signals regarding the recent topographic developments and to attach additional significance to active tectonics in the Bingöl basin area. The methodology incorporates the determination of the structural similarities of the faults in the basins using fractal concepts and the application of four morphometric indices (Stream Power Index (SP), Multi-resolution Index of Valley Bottom Flatness (MRVBF), Terrain Ruggedness Index (TRI) and Valley Width-to-Height Ratio (Vf)). In order to detect the deviation from spatial randomness of the applied indices, the weighted correlation coefficient Moran’s I is used and the results are interpreted at a confidence interval of 99%. The spatial distribution of integrated index values is evaluated with the tectonically active fault zones in order to determine the probable activity and the structural deformation in the basin.The applied methodology reveals that the fractal analysis of the fault lines and the spatial analysis of the morphometric indices proved to be effective tools in analyzing the tectonic influence of the fault system on the basin area. Within the basin area, a relatively lesser degree of tectonic activity is observed, in contrast with the high tectonic activity outside the basin.     

地形地表的不规则起伏对雷电电磁场传输的影响

为了研究地形地表的不规则起伏(简称粗糙地表)对雷电电磁场传播的影响,首先利用二维分形方法模拟了粗糙地表,然后利用Barrick表面阻抗理论和Wait近似算法研究了粗糙地表对雷电电磁场传播的影响。结果表明,粗糙地表对地闪首次回击垂直电场的影响较小,但对继后回击存在明显的影响。随着粗糙度的增加,继后回击垂直电场峰值的衰减程度明显增加,且时域脉冲波形上升沿时间增大。如继后回击电磁场传播100 km,均方高为30 m的粗糙地表(电导率σ=0.1 S/m)引起时域电磁场波形上升沿时间额外增约1.5μs,电场峰值额外减小约12%,且其影响随着地面电导率的减小而增大。因此,在实际工作中应考虑复杂地形地表对闪电定位系统探测精度和效率的可能影响。     

Surface roughness of alumina fragments caused by hypervelocity impact

Hypervelocity impact experiments are carried out with alumina ceramic targets at impact velocities of 2-4 km/s. The fractal dimension (or roughness exponent) of fragment surfaces is estimated by two different methods (different length scales). One is a divider method (large scale) and the other is a gas-absorption one (small scale). The obtained fractal dimensions are different: ∼2.2-2.4 for larger scale and ∼2.5-2.7 for smaller scale. These values are regardless of the degree of fragmentation.     

Investigation of fractal distribution law for the trace number of random and grouped fractures in a geological mass

A fractal study method of the number of geological mass fractures is introduced in detail in this paper. Three main aspects of the problem were studied: (1) The random distribution of fractures in a geological mass was in good agreement with the fractal law. The size scale of the studied geological mass ranged from 2400 m to 1 mm for the length of each side, and the geological mass samples were taken from 13 coal areas in China. (2) The geological mass fractures were evidently directional and anisotropic, having originated from tectonic movement. Observation and statistics for the data from the Xuangang, Fenxi and Dongshan coal areas in Shanxi, China, demonstrated that the fracture distribution of each group, classified by the strike of the strata, still follow the fractal law, even though the fractal dimension varies to a certain extent with different strikes. (3) The sedimentary strata containing the coal seams, as a geological mass, underwent almost similar tectonic movements in their geological history. The mechanical experiments on geological mass samples from Fenxi and Jiexiu in Shanxi demonstrated that the fractal dimension of the number of fractures in the same strata is in good power function with the product of strength and elastic modulus. The larger the product of the strength of the elastic modulus is, the larger is the fractal dimension, and vice versa.     

Fractal analysis of quartz grain boundary sutures in a granite (Malanjkhand,Central India) — Implications to infer regional tectonics

In the present paper the intensity of serration of quartz grain boundary sutures in the Palaeoproterozoic age Malanjkhand granite (Central India) is quantified using the ruler method of fractal analyses. The northern margin of the granite has proximity to the Central Indian Suture (CIS) that forms the southernmost part of Central Indian Tectonic Zone (CITZ) along which amalgamation of the northern and southern Indian shields took place. The fractal dimension (D) of the quartz sutures is calculated in 13 samples collected at varying distance from the CIS. D values are noted to increase in samples towards the CIS. This demonstrates the influence of the tectonic events along the CIS on fabric development in the Malanjkhand granite. Magmatic fabric defined by preferentially oriented feldspar laths and high-T solid-state deformation fabrics are observed in areas distant from the CIS. In contrast, mylonites and low-T fabrics such as bulging quartz grain boundaries occur in proximity to the CIS. It is inferred that the emplacement and high-T fabric development in the Malanjkhand granite was synchronous with regional accretionary processes that occurred in the region during the Palaeoproterozoic. Two different possibilities, one involving a single tectonic event and the other involving multiple tectonic events are discussed to explain the superimposition of low-T over high-T fabric due to which intensity of quartz grain boundary serration increases towards the CIS.     

小尺度断层定量预测及对注水开发的影响——以渤中34油田为例

大尺度断层往往控制了沉积盆地的形成和油气成藏,而小尺度断层则影响着注水开发效果和剩余油分布.大尺度断层可以通过二维或三维地震资料识别,而小尺度断层的识别则特别困难.本文提出了一种基于断层分形生长模式和三维地质力学模拟相结合来确定小尺度断层的数量、发育位置和方位的方法,并根据油田开发动态资料来确定小尺度断层对注水开发和剩余油分布的影响.将地震上识别的大尺度断层引入到三维数值力学模型中,模拟大尺度断层形成时期断裂带附近的应力扰动作用,然后结合破裂准则来建立最易发生破裂的方位和最大库伦剪切应力网格,以这两套网格和断层尺度的幂律分布确定的小尺度断层数量为约束条件来确定随机模型,对小尺度断层的密度、产状和发育位置进行定量预测.研究表明:利用分形理论和三维地质力学模拟可以对大尺度断层伴生小尺度断层进行有效预测;小尺度断层对注水开发效果和剩余油分布的影响取决于小尺度断层的规模(断距)以及小尺度断层方位和注采方向的关系.     

桂中坳陷环江凹陷上古生界海相页岩储层孔隙结构和分形特征研究

通过有机地化分析、全岩X衍射矿物分析、甲烷等温吸附及低压氮气吸附实验,本文对桂中坳陷环江凹陷上古生界页岩样品的孔隙结构及分形特征进行了研究.结果表明:研究区页岩总有机碳含量(TOC)平均为2.40%,热成熟度(Ro)平均为2.65%,处于过成熟演化阶段.页岩主要的矿物组成为石英和黏土.页岩的比表面积平均为5.86 m2/g,孔容平均为0.014 9 mL/g,平均孔径为11.2 nm.页岩中发育大量的中孔,主要呈两端开口的圆筒形孔或四边开放的平行板状孔.页岩中TOC含量和石英含量越多,微-中孔越发育、比表面积和孔容越大,而平均孔径则变小.通过Frenkel-Halsey-Hill (FHH)模型和氮气吸附实验数据计算得到孔隙表面分形维数D1(平均为2.428 4)和孔隙结构分形维数D2(平均为2.622 2),对应的相对压力(P/P0)分别是0~ 0.45和0.45 ~ 0.99.分形维数D1、D2随着比表面积、孔容的增加而增加,而平均孔径随着前者的增加而减小.分形维数D1、D2、TOC含量、石英含量和甲烷吸附量之间呈现较好的正相关性,但随着黏土矿物含量的增多而减小.分形维数D1与Langmuir压力存在弱负相关性,分形维数D2随Langmuir压力增大有变大的趋势.桂中坳陷西北部页岩分形维数越大,孔隙结构越复杂,其对天然气的吸附和存储能力越强.