Fractal Dimension Analysis of the Fine Aggregate Gradation of Interlocking Skeleton Asphalt Mixture

By analyzing the fine aggregate gradation scales from standards,fine aggregate in the asphalt mixture is regarded as a whole research object and fractal dimensions X of the samples were obtained by linear regression and（AC-13）is 2.43-2.56,Sup-13 is 2.28-2.54,SMA-13 is 2.66-2.88 and SAC-13 is 2.54-2.73.In the dense gradation mixture,there are little different between fractal dimensions of coarse and fine aggregates but it makes sense for skeleton asphalt mixture.For a given coarse aggregate gradation and the same percentage of coarse aggregates,the compressive strengths and splitting strengths of the asphalt mixture are studied when the fractal dimensions are selected as 2.60,2.65 and 2.70,respectively.When asphalt-stone ratio is less than optimal asphalt-stone ratio,the higher compressive strength is,the bigger X can be gotten.When asphalt-stone ratio is larger than optimal asphalt-stone ratio,little difference of compressive strength can be observed under these three conditions.The largest splitting strength can be got when X is 2.65,and larger splitting strength can be observed with the ascending of the asphalt-stone ratio.

Soil Aggregates and Fractal Features under Different Land Use Types in a Frequent Debris Flow Area

The stability of soil aggregates and the fractal characteristics of four typical land use types(farmland,grassland,woodland,and bare land) in the Jiangjiagou Ravine(Yunnan,China),a frequent debris flow occurring area,were studied according to the normal mean mass diameter and fractal theory.The present research showed that the stability of the soil aggregates was different for the different land use types.When the soil depth was 0-30 cm,farmland soil formed more aggregates with diameters greater than 0.25 mm,i.e.,the farmland soil was more stable than that of the other three land uses.When the soil depth was 30-45 cm,the order of stability of the soil aggregates was woodland > grassland > farmland > bare land.The fractal dimensions had a significant linear positive correlation with the amount of soil particles with diameters of <0.25 mm,and a significant negative linear correlation with the amount of soil particles with diameters of 0.25-0.5 mm,0.5-1 mm and 1-2 mm.Smaller fractal dimensions of the soil particles correlated with more stable soil aggregates.The fractal dimensions had a positive linear correlation with the soil bulk density and a negative correlation with the concentration of organic matter.These results showed that soil aggregates can be used as a parameter for characterizing the soil structures and properties.According to these results,the soil particle fractal dimensions could not only objectively characterize the stability of the soil structure but also could be used to indicate soil structure and properties.In addition,these results have great significance for the discussion of the comprehensive evaluation of soil.

Coercivity of fractal aggregates formed by single-domain particles

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Influence of Conservation Tillage on Soil Aggregates Features in North China Plain

Tillage greatly influences the aggregation and stability of soil aggregates. This study investigated the effects of conservation tillage on soil aggregate characteristics. During a four-year study period （2001-2005）, soils were sampled from no-tillage （NT）, rotary tillage （RT）, and conventional tillage （moldboard tillage, CT） plots at the Luancheng Agriculture and Ecology Experimental Station in Hebei Province, China, and the amount, size distribution, and fractal dimension of the aggregates were examined by dry and wet sieving methods. The results indicated that NT significantly increased the topsoil （0-5 cm） bulk density （BD）, while RT maintained a lower BD as CT. Dry sieving results showed that NT had higher macro-aggregate content （R0.25）, and a larger mean weight diameter （MWD） and geometric mean diameter （GMD） than other treatments in the 0-10 cm layer, while RT showed no difference from CT. In wet sieving, results showed that most of the aggregates were unstable, and the MWD and GMD of water-table aggregates showed the trend of NT 〉 RT 〉 CT. At 0-5 cm layer, the fractal dimension （D） of water-stable aggregates under NT was lower than it was under RT and CT. At 5-10 cm, RT yielded the highest D, and showed stability. After four years, NT increased the aggregation and the stability of soil aggregates; while due to intense disturbance, the aggregation and stability of the upper layer （0-10 cm） under RT and CT decreased.

The Influence of Different Land Use Manners on Soil Aggregate Characteristics of Consolidation and Returning to Field in Hollow Village of Hilly Area

The research aimed to explore the influence of different land use manners on soil aggregate,and provide scientific basis for improving soil stability and production performance of consolidation and returning to field in hollow village of hilly area. After consolidation and returning to field in hollow village of hilly area of Chengcheng County,Shaanxi,5 kinds of land use manners were set for 1-year plantation test,and they were corn( C treatment),wheat( W treatment),vegetable( V treatment),medicinal material( M treatment) and control( no plantation: CK treatment). Soil aggregate distribution,mean mass diameter( WMD),geometric mean diameter( GMD),aggregate failure rate( PAD),unstable aggregate number( ELT) and fractal dimension( D) at 0-40 cm of soil layer were measured and analyzed by dry and wet sieving methods. The results showed that( i) soil aggregate number and size at 0-40 cm of soil layer by each treatment were all significantly better than CK treatment,and > 0. 25 mm of aggregate content by dry sieving method( DR0. 25) and >0. 25 mm of aggregate content by wet sieving method( WR0. 25) at 0-40 cm of soil layer in each treatment showed declining trend with soil layer depth increased;( ii) MWD and GMD sequences of each treatment at 0-40 cm of soil layer by dry and wet sieving methods were both W treatment > C treatment > M treatment > V treatment > CK treatment,and C treatment was conducive to increasing large aggregate content of surface soil,while W treatment was conducive to increasing large aggregate content of lower soil;( iii) the analysis by wet sieving method showed that PAD and ELT at 0-40 cm of soil layer in each treatment both showed similar " Z" shape trend,and each treatment was significantly lower than CK;( iv) D sequence at 0-40 cm of soil layer in each treatment was C treatment < W treatment < M treatment < V treatment < CK treatment. D showed good linear relationship with> 0. 25 mm of aggregate content at 0-40 cm of soil layer by dry and wet sieving methods,and they were respectively R2= 0. 74 and R2= 0. 67. Corn and wheat plantation after consolidation and returning to field in hollow village was conducive to improving large aggregate content at 0-40 cm of soil layer,increasing the stability of soil layer and improving soil structure.

The fractal research of Ultrafine Fe particle aggregation

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A Fractal Method of Estimating Soil Structure Changes Under Different Vegetations on Ziwuling Mountains of the Loess Plateau,China

Fractal method is a new method to estimate soil structure. It has been shown to be a useful tool in studies related to physical properties of soil as well as erosion and other hydrological processes. Fractal dimension was used to study the soil structure in soil at different stages of vegetative succession on the Ziwuling Mountains. The land use and vegetation types included cultivated land, abandoned land, grassland, two types of shrub land, and three types of forests. The grassland, shrub land, and forested areas represented a continuum in vegetative succession that had occurred naturally, as the land was abandoned in 1862. Disturbed and undisturbed soil samples were collected from ten vegetation types from depths of 0-10, 10-20, and 20-30 cm on the Ziwuling Mountains, at a site with an elevation of about 1 500 m. Particle size distribution was determined by the pipette method and aggregate size distribution was determined by wet sieving. The results were used to calculate the particle and aggregate fractal dimension. The results showed that particle and aggregate fractal dimensions varied between vegetation types. There was a positive correlation between the particle fractal dimension and the weight of particles with diameter 〈 0.001 mm, but no relationship between particle fractal dimension and the other particle size classes. Particle fractal dimension was lower in vegetated soils compared to cropland and there was no consistent relationship between fractal dimension and vegetation type. Aggregate fractal dimension was positively correlated with the weight of 〉 0.25 mm aggregates. Aggregate fractal dimension was lower in vegetated soils compared with cropland. In contrast to particle fractal dimension, aggregate fractal dimension described changes in soil structure associated with vegetative succession. The results of this study indicate that aggregate fractal dimension is more effective in describing soil structure and function compared with particle fractal dimension.

Flocculation control study based on fractal theory

A study on flocculation control based on fractal theory was carried out. Optimization test of chemical coagulant dosage confirmed that the fractal dimension could reflect the flocculation degree and settling characteristics of aggregates and the good correlation with the turbidity of settled effluent. So that the fractal dimension can be used as the major parameter for floc-culation system control and achieve self-acting adjustment of chemical coagulant dosage. The fractal dimension flocculation control system was used for further study carried out on the effects of various flocculation parameters, among which are the dependency relationship among aggregates fractal dimension, chemical coagulant dosage, and turbidity of settled effluent under the conditions of variable water quality and quantity. And basic experimental data were obtained for establishing the chemical coagulant dosage control model mainly based on aggregates fractal dimension.

AN ATOMIC FORCE MICROSCOPY STUDY ON THE AGGREGATION OF ISOTACTIC POLY(METHYL METHACRYLATE)

Aggregation process of isotactic poly（methyl methacrylate） （i-PMMA） has been studied extensively for many years, and considerable progress has been made in both experimental and theoretical studies. They are, however, seldom sustained by real-space observations of the underlying morphology. In this paper, the aggregation process of i-PMMA in concentrated acetone solutions and the fractal structure of the resulting three-dimensional clusters were characterized on the basis of real-space AFM observations of their two-dimensional projection. It was found that spherical multiple-chain particles formed upon collapse and aggregation of the involving chains as a whole during quenching the solution to room temperature. By keeping the solution at room temperature, the initially formed particles stick together upon contact to form larger particles through reassembling very slowly. The succeeding collision of the enlarged spherical particles leads to the formation of small clusters. These newly formed small clusters grow when they meet with other clusters or single Brownian particles. This leads to the formation of large clusters with fractal dimension of 1.95 ± 0.05, which suggest a reaction-limited cluster aggregation of i-PMMA in a concentrated acetone solution. This is in accordance with the conclusion obtained by light scattering measurements.

Fractal Characteristics of Stagnic Anthrosols and the Relationship with Soil Micro-Structure

The Stagnic Anthrosols developed from quaternary yellow sedimentary parent material occupied an important position in Southwest China. Fractal dimensions of particle size and micro-aggregate size distributions of Stagnie Anthrosols and their relationship to soil micro-structure had been probed. Results showed that the soil particle size distributions were dominated by clay, the fractal dimensions of particle size distributions （Ds） were high and between 2.676-2.925, as the fractal dimensions of micro-aggregate size distributions （Da） were between 2.354-2.853. The fractal dimensions of particlesize distributions were preferably related with the ratio of coarse particles and fine particles （c/f20 ,m） and the micromorphological feature of skeleton grains. The evolution degree of micro-structure among horizons were reflected by the coefficient of variation of Ds within the profile. The fractal dimensions of micro-aggregate size distributions were related with the quantities, distributions of micro-aggregates and micro-pores. Results revealed that the soil micro-structures could be quantified by fractal dimensions preliminarily.

Effect of particle gradation on pore structure and seepage law of solution in weathered crust elution-deposited rare earth ores

Both CT and Avizo software were used to explore the effect of particle gradation on the evolution characteristics of pore structure and seepage paths in weathered crust elution-deposited rare earth ores during leaching.The results showed that the pore areas in four kinds of ore samples before leaching were mainly concentrated in 10^(4)–10^(7)μm^(2),whose pore quantities accounted for 96.89%,94.94%,90.48%,and 89.45%,respectively,while the corresponding pore volume only accounted for 30.74%,14.55%,7.58%,and 2.84%of the total pore volume.With the decrease of fractal dimension,the average pore throat length increased,but pore throat quantities,the average pore throat radius and coordination number decreased.Compared with that before leaching,the change degree of pore structure during leaching increased with the fractal dimension decreasing.For example,the reduction rate of the average coordination number of ore samples was 14.36%,21.30%,28.00%,and 32.90%,respectively.Seepage simulation results indicated that seepage paths were uniformly distributed before leaching while the streamline density and seepage velocity increased with the fractal dimension decreasing.Besides,the phenomenon of the streamline interruption gradually reduced during leaching while preferential seepage got more obvious with the decrease of the fractal dimension.

Mathematical and Physical Fractals

A review of the concepts developed about mathematical and physical fractals is presented followed by experimental results of the latter, considered to be a fourth state of matter which pervades the universe from galaxies to submicroscopic systems. A model of multiple fractal aggregation via a computer code is shown to closely simulate physical fractals experiments carried out in simulated and in real low gravity.

具有分形级配的多分散颗粒体堆积特性研究

混凝土骨料或公路工程基层碎石常采用Fuller或Thompson分布作为设计级配,具有分形特性的多分散颗粒堆积体容易形成相对较大的堆积密度,作为理想的设计级配,其作用机理尚没有详细地解释。采用颗粒离散元仿真技术获取了多种具有分形级配的颗粒体在各向同性压缩条件下的堆积密度,颗粒体由光滑(无摩擦)的球形颗粒构成,分形级配曲线的形状由粒径区间和分形维数指标控制。在此基础上,研究了分形级配指标与堆积密度和配位数等宏细观指标的相关性,得出分形维数及粒径区间对堆积密度有重要影响。当级配粒径区间较大时,最大的堆积密度对应的分形维数为2.5左右,与工程中常采用的Fuller和Thompson级配十分一致。通过对堆积体细观颗粒层面的配位数及局部堆积密度的研究得出,分形维数为2.5左右时,试样局部排序和接触分布得到优化。研究结果可为进一步优化混凝土、土石坝或路基等碎石填料的级配设计提供理论指导。

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。

茶树边坡抗冲性能影响因素分析

为研究茶树种植对边坡抗冲性能的作用并探究影响茶树边坡抗冲性能的因素,以远安县某茶场地域环境为对象设计边坡模型,进行冲刷试验、水稳性团聚体分布测定和根系分形扫描。结果显示:1)径流率先增大到峰值再波动并趋于稳定,最大径流率表现为茶树边坡(1.224)<原生植被边坡(1.280)<素土边坡(1.398);2)茶树边坡抗冲系数比原生植被边坡和素土边坡分别提升12.8%和53.2%;3)边坡土壤水稳性团聚体含量表现为茶树边坡>原生植被边坡>素土边坡;4)茶树发育情况整体优于原生植被,具体表现在覆盖度(茶树95%>原生植被87%)和分形维数2方面。经分析,茶树种植有利于提升边坡抗冲性能,抗冲性能受植被覆盖度、根系发育情况、水稳性团聚体含量、冲刷时间和冲刷深度的影响。

骨料特征对水下不分散混凝土性能的影响

利用分形理论结合图像处理方法对骨料的级配和粒形特征进行了定量评价,研究了不同分形维数下骨料特征对水下不分散混凝工作性、抗分散性能、力学性能、气泡特征、抗冻性能的影响。结果表明:随着级配分形维数的增加,水下不分散混凝土的工作性和抗压强度先提高后降低,抗分散性能提高,但抗冻性能降低,气泡间距系数与抗冻性能间存在良好的对应关系;当级配分形维数为2.5时,综合性能相对最佳;随着粒形分形维数的增加,水下不分散混凝土的工作性略有提高,但对抗分散性能、抗压强度、抗冻性能的提高效果不显著。

路用集料形貌特征参数分析与性能评价

沥青路面的长期抗滑性能取决于集料的抗磨光/耗性能,准确快速计算集料的形貌特征十分重要。本文引入一种新型高抗滑路用集料——88#煅烧铝矾土,采用Image-Pro-Plus 6.0(IPP)、IBM SPSS Statistics 26.0(SPSS)等数字图像处理软件对集料形貌特征进行分析评价。同时对不同磨光次数下集料形貌特征参数的变化进行灰熵关联分析,得到各集料形貌特征参数与其磨光值(PSV)的灰熵关联度。结果表明,采用IPP软件能够准确获得各集料的形貌特征参数,并且,相较于传统路用集料,88#煅烧铝矾土具有更加丰富的棱角特性及较高的粗糙度。通过灰熵关联分析得到,分形维数与PSV之间的相关性最显著。

沥青混合料细观分形特征研究

沥青混合料的集料骨架和空隙结构与路面性能高度相关。然而,沥青混合料内部复杂的几何结构和非均质特性,给其细观结构表征和分析带来了极大的困难。为探究不同级配类型沥青混合料的细观结构特征,选用两种压实方法和三种设计指标制备试件,并进行CT扫描和三维重构。采用分形维数D和多重分形理论的相关参数,描述沥青混合料的内部结构。分析结果表明,多重分形谱参数相较于分形维数D,更能反映沥青混合料的细观结构;三种沥青混合料随着平均粒径增加,其细观结构特征趋于相同;压实度对沥青混合料简单分形和多重分形特征影响较小。

保护性耕作对华北平原土壤团聚体特征的影响

【目的】研究华北平原保护性耕作制度对土壤团聚数量、大小和稳定性的影响。【方法】本文采集了华北平原河北栾城试验站经过4年保护性耕作(旋耕和免耕)与传统耕作(翻耕)处理下原状土壤样品,测定了土壤容重、有机质和粘粒含量等物理性质,重点应用干筛和湿筛法分析了土壤团聚体数量、分布和分形维数。【结果】表层(0～5cm)土壤容重的大小顺序为免耕>旋耕>翻耕,免耕使表层土壤的容重显著增加;旋耕与翻耕的表层土壤容重差异不显著,但旋耕使10～20cm的土壤容重明显增加。干筛法分析表明,免耕处理下0～10cm土层大于0.25mm团聚体含量、平均重量直径(mean weight diameter,MWD)和几何平均直径(geometric mean diameter,GMD)均高于旋耕处理和翻耕处理,而旋耕与翻耕处理间没有显著的差异;湿筛法分析表明,土壤中的团聚体以非水稳性团聚体为主,水稳性团聚体的MWD和GMD大小顺序为免耕>旋耕>翻耕;在0～5cm土层内免耕处理的水稳性团聚体分形维数(D)最小,而旋耕处理下5～10cm的分形维数D值显著高于翻耕、免耕处理,说明旋耕使得该层内土壤团聚体的稳定性降低。【结论】免耕处理促进表层土壤团聚体的形成,并提高了其稳定性;旋耕和翻耕处理由于对土壤的强烈扰动,降低了耕作深度内土壤团聚体的团聚度和稳定性;在10～30cm3种耕作处理间没有显著差异。

PAM对黄土高原主要土壤类型水稳性团聚体的改良效果及机理研究

通过室内土柱培养,研究PAM对黑垆土、黄绵土、风沙土水稳性团聚体的改良效果,并探讨其作用机理和合理的施用浓度。结果表明,在浓度为0.05%～0.4%,PAM均可促进3种土壤>0.25 mm水稳性团聚体的形成,并有效降低3种土壤团聚体分形维数,改善土壤结构;方差分析表明,PAM改良3种土壤结构的机理是一致的,将<1 mm的水稳性团聚体聚合为更大粒径的水稳性团聚体,使>1 mm的水稳性团聚体含量增加。PAM改良黑垆土、黄绵土和风沙土土壤水稳性团聚体达到显著水平时的浓度也不相同,其适宜浓度分别为0.2%～0.4%,0.05%,0.05%。3种土壤的黏粒含量和有机质含量的差异,可能是影响PAM对不同土壤的水稳性团聚体的改良效果差异的主要原因。