FRACTAL DIMENSION AS MORPHOLOGY AND SIZE PARAMETERS OF FRACTURED PARTICLES OF ROCK

Semi-automatic image analysis system was used for the surface fractal dimension measurement of 15 kinds of rock-fractured particles. The results indicate that the surfaces of the particles that have a size of about 200 mesh are fractal, and that the fractal dimension is in the range of 2.07～2.11. Therefore, some definitions of particle size such as surface diameter, equivalent volumetricly surface diameter are equivocal without giving the step length and the drag diameter, free-fall diameter, and stokes’diameter may be modified by the fractal dimension.

Fractal features of size distribution of Chinese intercity bus hubs

Size distribution characteristics of intercity bus hubs in China from 1997 to 2（104 were analyzed regarding highway passenger volume as a size index of intercity bus hubs. Yearly fractal dimensions of intercity bus hub sizes were exactly calculated by a novel model. Fractal dimensions of the 200 biggest intercity bus hubs from 2000 to 2004 were 1. 486 2 to 1. 511 8, and that is consistent with fractal dimensions of Chinese urban system sizes. It showed that the size distribution of intercity bus hubs had fractal structure. Fractal dimensions from 1997 to 2004 indicated that intercity bus hub size distribution grew from bi-fractal to single fractal. It is concluded that the intercity bus hub system is in evolutionary progress, and the Central Government should support large intercity bus hubs more to optimize system structure.

Influence of Acid Treatment on Pore Structure and Fractal Characterization of a Tight Sandstone:A Case Study from Wudun Sag,Dunhuang Basin

In this study,X-ray diffraction,N_(2)adsorption(N_(2)A),and mercury intrusion(MI)experiments were used to investigate the influence of acid treatment on pore structure and fractal characterization of tight sandstones.The results showed that acid treatment generated a certain number of ink-bottle pores in fine sandstone,aggravated the ink-bottle effect in the sandy mudstone,and transformed some smaller pores into larger ones.After the acid treatment,both the pore volume in the range of 2–11 nm and 0.271–8μm for the fine sandstone and the entire pore size range for the sandy mudstone significantly increased.The dissolution of sandstone cement causes the fine sandstone particles to fall off and fill the pores;the porosity increased at first but then decreased with acid treatment time.The fractal dimension obtained using the Frenkel-Halsey-Hill model was positively correlated with acid treatment time.However,the total fractal dimensions obtained by MI tests showed different changes with acid treatment time in fine sandstone and sandy mudstone.These results provide good guiding significance for reservoir acidification stimulation.

Interactions between wind and water erosion change sediment yield and particle distribution under simulated conditions

Wind and water erosion are among the most important causes of soil loss, and understanding their interactions is important for estimating soil quality and environmental impacts in regions where both types of erosion occur. We used a wind tunnel and simulated rainfall to study sediment yield, particle-size distribution and the fractal dimension of the sediment particles under wind and water erosion. The experiment was conducted with wind ero- sion firstly and water erosion thereafter, under three wind speeds （0, 11 and 14 m/s） and three rainfall intensities （60, 80 and 100 ram/h）. The results showed that the sediment yield was positively correlated with wind speed and rain- fall intensity （P〈0.01）. Wind erosion exacerbated water erosion and increased sediment yield by 7.25%-38.97% relative to the absence of wind erosion. Wind erosion changed the sediment particle distribution by influencing the micro-topography of the sloping land surface. The clay, silt and sand contents of eroded sediment were also posi- tively correlated with wind speed and rainfall intensity （P〈0.01）. Wind erosion increased clay and silt contents by 0.35%-19.60% and 5.80%-21.10%, respectively, and decreased sand content by 2.40%-8.33%, relative to the absence of wind erosion. The effect of wind erosion on sediment particles became weaker with increasing rainfall intensities, which was consistent with the variation in sediment yield. However, particle-size distribution was not closely correlated with sediment yield （P〉0.05）. The fractal dimension of the sediment particles was significantly different under different intensities of water erosion （P〈0.05）, but no significant difference was found under wind and water erosion. The findings reported in this study implicated that both water and wind erosion should be controlled to reduce their intensifying effects, and the controlling of wind erosion could significantly reduce water erosion in this wind-water erosion crisscross region.

Application of the fractal theory for evaluating effects of coal comminution by waterjet

Comminution of coal to ultrafine sizes by high-pressure waterjet provides a novel method for preparation of coal-water fuels for next generation,near-zero emission electric power generation.The particle size distribution(PSD)of ground coal is a key parameter in the preparation of slurries as it determines the settling behavior of the particles and viscosity of the coal-water mixture.There are several methods available for representation and evaluation of particle size analysis data.However,fractal theory provides a means by which the entire PSD of comminuted materials can be quantified by using of a specific and exact value.In this paper,a volume-based fractal model was deduced to characterize the PSD of the coal which is ground in a specially designed comminution cell.During the size reduction process,the inlet pressures up to 276 MPa were used.

Effect of Fiber Properties on Nonwovens' Pore Structures with Fractal Geometry Analysis

Nonwovens＇ pore structures are very important to their mechanical and physical properties. And the pore structures are influenced by the fiber properties and fibers arrangement in web. In this paper, the fractal geometry, in combination with computer image anaysis, is used to express the irregularity of pore size distribution in nonwovens, and the effect of fiber properties on fractal dimension of pore size distribution is discussed by using simulated images which are composed of nonlinear staple fibers. The results show that the fiber properties, such as crimp, diameter, angular distribution, and especially the number of fibers prominently influence the pore structure.

煤张开型裂隙三维宏细观演化特征及扰动因素探究

裂隙演化方式受控于诸如矿物特征及围压条件等内外环境,为探究含裂隙煤体裂隙宏细观演化特征及影响因素的围压效应,基于工业CT扫描系统及其搭载的三轴加载系统对含裂隙煤体开展三轴静载试验,以多角度联合表征,对原生裂隙、矿物及围压的内外条件相互作用机制做出合理解释。结果表明:①围压会改变煤体初始损伤显著区位置,使其随围压升高由裂隙尖端过渡至煤体上、下端,且微孔隙和大尺寸裂隙之间比微孔隙和微孔隙之间更易相互贯通,并产生新的宏观裂纹。②围压升高使得三维动态分形维数由缓慢增加、快速增加和平稳增加转变为平稳增加、快速增加和缓慢增加的发展阶段,可表征裂隙的时间演化规律。③含裂隙煤体在单轴或低围压下呈纵向拉伸破坏,高围压会使其破坏方式趋于剪切,并通过2种途径提升煤体强度。④起裂角理论值偏离试验值程度随围压增加而增加,与煤体由矿物分布引起的离散度数值关系一致。⑤根据裂隙的受力成分及矿物分布特征将裂隙扩展行为分为直驱、绕核和错核3种类型,该扩展行为受围压对裂隙的作用力成分影响,由相对纯粹拉应力、拉伸–剪切复合应力和相对纯粹剪应力作用的裂纹分别对应以上3种扩展行为,即对裂隙的扩展影响形式表现为以围压为主,矿物赋存形态为辅。

Fractal Characteristics of Particle Size Distribution in Dynamic Flocculation Process

This study selected polyaluminum chloride（PAC） coagulant to remove suspended particles in Kaolin suspension solution and used a turbidimeter and particle counter to monitor the flocculation process online and collected the experiment data. The experiments were conducted to study the dynamic distribution characteristics of suspended particles under different hydrodynamic conditions. The results show the self-similarity and scale invariance of particle size distribution. The study further proposed the concept of fractal dimension of particle size distribution and found out that fractal dimension changed in a similar way as residual turbidity did and could excellently indicate the variation of coagulation effect. Therefore, fractal dimension could be adopted to optimize the addition of coagulants and the quality of outflow could be further improved to reduce production costs.

2种水土保持林土壤微团聚体组成及其在不同坡位和不同土层间的分布特征

2022年8月份,在黑龙江省齐齐哈尔市克山县境内的克山农场,选择位置相邻,坡度、坡向、坡长、林龄基本一致的樟子松水土保持林、杨树水土保持林、坡耕地(对照)为研究对象;在选定的坡面上沿着和坡面等高线垂直的方向分别布设3条样线作为3个重复,每2条样线之间间隔3 m,每条样线从坡顶至坡底分别设置10个取样点,每个取样点之间间隔30m;使用环刀法,按照土层深度(h)采集土壤表层(0<h≤15 cm)、下层(15 cm<h≤30 cm)土样,放在通风处自然风干后过2.00、0.15 mm土壤筛,测定土壤微团聚体的粒径分布、比表面积、土壤理化性质;运用体积分布模型计算不同粒径土壤颗粒体积分形维数(D值),比较不同树种水土保持林的土壤微团聚体粒径组成、微团聚体分形维数的坡面分布特征,分析土壤理化性质与土壤微团聚体粒径组成、微团聚体分形维数之间的相关性。结果表明:坡面主要土壤养分质量分数,全磷质量分数(土壤表层、下层),由大到小依次为耕地、杨树林地、樟子松林地;有效磷质量分数(土壤表层、下层),由大到小依次为耕地、樟子松林地、杨树林地;有机质质量分数,土壤表层由大到小依次为杨树林地、樟子松林地、耕地,土壤下层由大到小依次为杨树林地、耕地、樟子松林地。分形维数,与有效磷质量分数、全磷质量分数、微团聚体颗粒比表面积显著相关;分形维数在一定程度上可用于表征土壤的养分状况;土壤下层整个坡面,坡耕地的分形维数明显小于樟子松林地、杨树林地的分形维数,说明水土保持林的林下土壤的土质优于耕地;根据坡面土壤微团聚体分布特征及其趋势、坡面养分分布特征综合对比,杨树林地土质优于樟子松林地。

黑河源区不同植被类型土壤粒径分形特征研究

本研究以黑河源区为研究区,运用分形理论研究了该区域3种主要植被类型土壤粒径分形特征,并分析了土壤粒径分形与环境因子的关系。结果表明:草地砂粒含量最大(38.83%),灌木林地次之(26.11%),乔木林地砂粒含量最低(22.76%),土壤单重分形维数(Single fractal dimension,D)大小表现为草地(2.60)<灌木林地(2.64)<乔木林地(2.65);乔木林地、灌木林地和草地的土壤粒径均呈非均匀性分布,与乔木林地和灌木林地相比,草地的土壤粒径分布非均匀性最高;D与土壤粘粒、粉粒含量呈极显著正相关关系,与砂粒含量呈极显著负相关关系,而容量维(D 0),信息维(D 1),关联维(D 2)与土壤各粒级含量的关系与D相反。此外,地形、植被盖度和土壤理化因子对3种植被类型土壤分形维数产生不同程度的影响。综上,不同植被类型土壤粒径分形特征差异明显,分形维数主要受土壤粒径影响,其它因子通过影响土壤颗粒组成从而对分形维数产生影响。研究结果可为黑河源区土地资源的科学管理和合理利用提供参考。

乌鲁木齐市城市化梯度带土壤粒度分布差异性研究

从新疆乌鲁木齐市城市化梯度带共采集88个表层(0 cm~20 cm)土壤样品,利用激光衍射技术测定土壤粒度组成,采用分形维数(Dv)、平均粒径(MG)、分选系数(σG)、偏度(SKG)和峰态(KG)等参数对比分析不同梯度带土壤粒度分布特征及各粒度参数之间的关系。结果表明:研究区乡村土壤粒度组成最粗,荒地土壤粒度组成最细;各梯度带土壤平均Dv值从大到小依次为荒地>郊区>城区>乡村;各梯度带表层土壤σG值均> 4.0,分选性均属于极差水平;土壤Dv和MG值能反映不同梯度带表层土壤粒度分布特征;各梯度带土壤Dv值的大小受土壤粒度组成的影响作用强烈,其中土壤黏粒含量起主导作用。

基于图像处理判断水混凝中矾花性能的研究及应用进展

原水预处理主要分为混凝、沉淀和过滤3个阶段,混凝中的絮凝过程直接影响矾花结构与出水浊度;目前多采用检测出水浊度方法来控制混凝剂加药量,但因时间滞后无法快速反映混凝效果与反馈调节加药量。随着计算机技术的快速发展,利用矾花图像处理技术能够实现快速、准确、实时检测絮凝状态,从而更准确控制加药量,提高混凝效果。从计算机视觉技术角度,概述了絮凝中矾花图像采集与处理的技术特点,介绍了实时跟踪和计算矾花结构特征参数如等效粒径、分形维数等方法,并给出了部分试验结果,通过这些参数可以判断最佳混凝效果,为混凝控制与加药提供依据。

正态分布矸石侧限压缩特征与声发射特征研究

为研究矸石集料的承载力学特征及声发射特征规律,通过采用岩石力学伺服加载系统和声发射系统对矸石集料进行侧限压缩试验和声发射信息采集,考虑采空区破碎矸石粒径分布特征和受力状态,以平均级配矸石集料为对比,研究正态分布矸石集料在不同轴向应力加载过程中的应力应变关系、声发射能量、粒径级配和分形维数的变化。结果表明:矸石集料应力应变曲线呈指数函数关系,正态分布矸石集料在承载过程中产生的应变更大;较平均级配,正态分布矸石集料先发生大范围破碎现象,且频率更高,分布更均匀,但其最高声发射能量小于平均级配;分形维数与加载应力呈对数函数关系,正态分布矸石集料分形维数增长率高于平均级配,具有更大的跨度区间。

基于颗粒分布分形模型毛细水上升高度计算分析

由表面张力引起的弯液面两侧压力差推动毛细水上升,造成低路堤路基产生毛细水病害,毛细水上升高度是防治路基毛细水病害的关键所在。克服了毛细水上升高度测量试验的缺陷,基于土粒分布的分形模型,提出毛细水上升高度的计算方法。采用筛分试验计算粉土颗粒分布分维,建立粉土颗粒级配的分形模型,系统地分析分维、进气值、孔隙率、毛细水最大上升高度和饱和渗透系数对毛细水上升高度和速度的影响。计算结果表明:毛细水上升高度与时间呈幂函数正相关关系,毛细水上升高度随颗粒分布分维、进气值、毛细水最大上升高度和饱和渗透系数增大而增大,随孔隙率增大而减小;毛细水上升速度只与颗粒分布的分维有关,随颗粒分布分维增大而增大,不受进气值、孔隙率、毛细水最大上升高度和饱和渗透系数的影响。

冲击荷载下颗粒破碎分维变化及能量耗散研究

颗粒受冲击荷载,发生破碎现象,改变颗粒粒径分布,影响颗粒力学性能。随着颗粒破碎程度的增加,最终颗粒分布会趋向自相似分布,称为分形分布。为研究冲击对颗粒破碎粒度分布的影响,通过试验,得到了炉渣颗粒和大理岩颗粒受冲击破碎的颗粒分布曲线及分形维数的变化规律。研究发现,颗粒受冲击破碎后,不会无限制的破碎;粒度分布符合分形模型;分形维数随破碎程度加深逐渐增大,但存在极限。最终的分形维数可以与颗粒力学特性建立联系以推导颗粒破碎能耗和颗粒弹性应变能。考虑颗粒间不同的接触类型,忽略颗粒间摩擦,根据断裂力学理论,建立的颗粒破碎的能量平衡方程可以很好地描述颗粒破碎过程中能量转化的规律。

Cu^(2+)污染原状黄土的物化及结构特性

为制定环境保护和土壤污染防治和修复策略,以及为污染场地工程建设提供理论支撑,该文研究了Cu^(2+)对原状黄土物化特性及结构特性的影响。通过制备不同掺量的Cu^(2+)污染黄土试样,进行了粒径分布、CaCO_(3)含量和pH值的测定。利用扫描电镜和激光粒度仪获得试样的SEM图像和粉粒各粒径含量,并借助分形理论深入分析了Cu^(2+)对原状黄土微观结构的影响机理。对Cu^(2+)污染的原状黄土试样进行了压缩试验,并对试样的综合结构势进行了分析。结果表明,随着Cu^(2+)掺量的增大,黏粒含量表现为先增后减,再增再减的趋势,粉粒含量则表现为先减后增,再减再增,砂粒含量保持不变;CaCO_(3)的含量呈线性减小;pH值先迅速减小,后保持不变;污染黄土试样的综合结构势先增大后减小,之后再增大再减小。总体而言,重金属Cu^(2+)的掺入,导致土壤pH值降低,主要胶结物质碳酸钙被溶解,而又因黏粒之间的静电引力和范德华力,黏粒聚集体的形态和成分发生变化,从而影响了土体的密实度和结构强度。

黑河中游荒漠-绿洲过渡带固沙植物根区土壤颗粒组成及分形特征

探究荒漠-绿洲过渡带固沙植物根区土壤颗粒分布及分形特征,可对区域生态植被建设和荒漠化防治提供一定理论依据。选取黑河中游的荒漠-绿洲过渡带内3种固沙植物作为研究对象,采集固沙植物根区0~120 cm土层的土壤样品,测定了土壤粒度组成,并计算了土壤颗粒分形维数D。结果显示:3种固沙植物根区土壤的颗粒以中砂粒(0.25~0.5 mm)和细砂粒(0.1~0.25 mm)为主,占比75%以上,除中砂粒和细砂粒外,不同粒级土壤颗粒质量分数由高到低为极细砂粒>粗砂粒>粉粒>黏粒;3种固沙植物根区的土壤颗粒组成存在显著差异(P<0.05),沙拐枣根区土壤细砂粒和极细砂粒质量分数显著高于泡泡刺和梭梭,泡泡刺根区土壤中粉粒和黏粒质量分数显著高于梭梭和沙拐枣;3种固沙植物根区土壤颗粒分形维数D也存在显著差异(P<0.05),泡泡刺(2.00)>梭梭(1.94)>沙拐枣(1.91),且浅层(0~60 cm)土壤易受外界因素干扰,土壤颗粒分形维数D变化幅度较大;土壤颗粒分形维数D与土壤颗粒中的黏粒和粉粒质量分数呈极显著的正相关关系,与土壤中颗粒的砂粒质量分数呈极显著负相关关系,土壤颗粒分形维数D能较好地体现研究区固沙植物根区的土壤颗粒组成。提高固沙植物数量和覆盖率对于沙化土壤固定,改善土壤质量,防止风蚀的发生均具有重要意义。

不同变质程度煤体微孔多重分形特征研究

为研究不同变质程度煤体微孔孔径多重分形的特征,根据低温液氮吸附实验数据,运用多重分形理论对4种不同变质煤体样品微孔的多重分形特征、以及孔隙特征与变质程度之间的关联展开研究。结果表明:4种煤样微孔均具备了多重分形的典型特征,变质程度越高煤样的微孔分布非均质性越强,其微小孔拥有更大的比表面积,将会为瓦斯气体提供更多的吸附位,拥有更大的解吸量;4种煤样的微孔孔径多分布在孔隙空间较为狭小的区域中,约为7~9 nm;微孔结构在弱变形作用下的非均质性明显,在此区域内,较大的孔径分布均一;但从整体看,其连通性与变质程度关系不明显且孔隙以聚集和分布不均匀为主导。

北京平原地区不同土地利用类型对土壤颗粒组成及其分形特征的影响

选取农田、撂荒草地、人工乔木林、人工灌木林和次生林5种不同土地利用类型土壤颗粒为研究对象,采用Microtrac S3500激光粒度仪测定土壤样品粒径,利用土壤分形学理论和方法,分析不同土地利用类型对土壤颗粒组成及其分形特征的影响。结果表明,土壤粒径在不同土地利用方式下存在显著差异,其中撂荒草地以砂粒为主,农田、人工乔木林、人工灌木林和次生林以粉粒为主;次生林、人工乔木林黏粒体积分数最大,且显著大于其他土地利用类型,撂荒草地最小;次生林、人工乔木林、人工灌木林粉粒体积分数最大,且显著大于农田与撂荒草地;砂粒体积分数则与粉粒相反。土壤分形维数的大小依次为撂荒草地<农田<人工灌木林<次生林<人工乔木林;土壤分形维数与土壤黏粒含量、粉粒含量均呈显著正相关,与土壤砂粒含量呈显著负相关。

喀斯特石漠化区不同植被恢复下土壤颗粒分形特征

【目的】研究喀斯特石漠化地区的土壤颗粒分布和分形特征,为石漠化地区水土保持和土壤评价提供科学依据。【方法】在贵州师范大学喀斯特野外观测研究站,选取石漠化治理区中火龙果(Hylocereus undulatus)、玉米(Zea mays)、核桃(Juglans regia)、柚木(Tectona grandis)和种植于坡上和坡谷的花椒(Zanthoxylum bungeanum)等6种植被作为研究对象,分析了雨、旱两季的土壤粒径分布,并基于单重和多重分形理论计算了土壤颗粒分形参数。【结果】(1)研究区土壤粒径集中在1.5~300μm,质地较细以粉粒为主,黏粒含量最少,粒径分布呈非均匀性;(2)植被和季节对单重体积分形维数D_(v)均存在显著影响(P<0.05),决定系数R^(2)表明D_(v)与黏粒关系最为密切。旱季D_(v)的均值(2.56)较雨季(2.64)相比有所下降,细粒物质流失程度在不同植被之间存在显著差异(P<0.05);(3)各样地土壤粒径分布以体积分数占比较大的颗粒为主,广义维数谱D_(q)的递减程度在指数q<0时要大于q>0时,稀疏区土壤颗粒对环境因子的影响更敏感;(4)D_(v)与黏粒和粉粒呈极显著正相关,与砂粒呈极显著负相关。容量维数D_(0)、信息熵维数D_(1)、D_(1)/D_(0)、关联维数D_(2)和土壤颗粒的相关性与D_(v)相反。土壤有机碳/全氮(SOC/TN)与粉粒呈显著正相关,而与砂粒呈显著负相关,这说明粉粒组分在发挥固碳功能方面发挥主导作用。【结论】土壤分形维数能够作为喀斯特石漠化区土壤物理结构改善效果的指标,为石漠化水土保持和土壤评价提供科学理论支持。