Applicability of Fractal Models in Estimating Soil Water Retention Characteristics from Particle-Size Distribution Data

Soil water retention characteristics are the key information required in hydrological modeling. Frac-tal models provide a practical alternative for indirectly estimating soil water retention characteristics fromparticle-size distribution data. Predictive capabilities of three fractal models, i.e, Tyler-Wheatcraft model,Rieu-Sposito model, and Brooks-Corey model, were fully evaluated in this work using experimental datafrom an international database and literature. Particle-size distribution data were firstly interpolated into20 classes using a van Genuchten-type equation. Fractal dimensions of the tortuous pore wall and the poresurface were then calculated from the detailed particle-size distribution and incorporated as a parameter infractal water retention models. Comparisons between measured and model-estimated water retention cha-racteristics indicated that these three models were applicable to relatively different soil textures and pressurehead ranges. Tyler-Wheatcraft and Brooks-Corey models led to reasonable agreements for both coarse- andmedium-textured soils, while the latter showed applicability to a broader texture range. In contrast, Rieu-Sposito model was more suitable for fine-textured soils. Fractal models produced a better estimation of watercontents at low pressure heads than at high pressure heads.

Spatial Density Distributions and Correlations in a Quasi-one-Dimensional Polydisperse Granular Gas

By Monte Carlo simulations, the effect of the dispersion of particle size distribution on the spatial density distributions and correlations of a quasi one-dimensional polydisperse granular gas with fractal size distribution is investigated in the same inelasticity. The dispersive degree of the particle size distribution can be measured by a fractal dimension dr, and the smooth particles are constrained to move along a circle of length L, colliding inelastically with each other and thermalized by a viscosity heat bath. When the typical relaxation time τ of the driving Brownian process is longer than the mean collision time To, the system can reach a nonequilibrium steady state. The average energy of the system decays exponentially with time towards a stable asymptotic value, and the energy relaxation time τB to the steady state becomes shorter with increasing values of df. In the steady state, the spatial density distribution becomes more clusterized as df increases, which can be quantitatively characterized by statistical entropy of the system. Furthermore, the spatial correlation functions of density and velocities are found to be a power-law form for small separation distance of particles, and both of the correlations become stronger with the increase of df. Also, tile density clusterization is explained from the correlations.

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.

Fractal analysis on the spatial distribution of acoustic emission in the failure process of rock specimens

The spatial distribution of acoustic emission （AE） events in the failure process of several rock specimens was acquired using an advanced AE acquiring and analyzing system. The box counting method （BCM） was employed to calculate the fractal dimension （FD） of AE spatial distribution. There is a similar correlation between the fractal dimension and the load strength for different rock specimens. The fractal dimension presents a decreasing trend with the increase of load strength. For the same kind of specimens, their FD values will decrease to the level below a relatively same value when they reach failure. This value can be regarded as the critical value, which implies that the specimen will reach failure soon. The results reflect that it is possible to correlate the damage of rock with a macroscopic parameter, the FD value of AE signals. Furthermore, the FD value can be also used to forecast the final failure of rock. This conclusion allows identifying or predicting the damage in rock with a great advantage over the classic theory and is very crucial for forecasting rockburst or other dynamic disasters in mines.

DESCRIPTION OF G-S PARTICLE SIZE DISTRIBUTION OF ROCK COMMINUTION WITH FRACTAL GEOMETRY

The fractal model of rock comminution is presented with Mandelbrot's fractal geometry.The results show that it is difficult for those with only a linear similarity ratio to fit practical situations.The comminution prob ability of the central part should be considered so the geometric meaning of the constant in Gaudin-Schuhmann's distribution function can be explained more clearly.

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.

Influence of Processing Parameters on Granularity Distribution of Superalloy Powders during PREP

In order to investigate the influence of processing parameters on the granularity distribution of superalloy powders during the atomization of plasma rotating electrode processing (PREP), in this paper FGH95 superalloy powders is prepared under different processing conditions by PREP and the influence of PREP processing parameters on the granularity distribution of FGH95 superalloy powders is discussed based on fractal geometry theory. The results show that with the increase of rotating velocity of the self-consuming electrode, the fractal dimension of the granularity distribution increases linearly, which results in the increase of the proportion of smaller powders. The change of interval between plasma gun and the self-consuming electrode has a little effect on the granularity distribution, also the fractal dimension of the granularity distribution changed a little correspondingly.

STATISTICALLY FRACTAL STRENGTH THEORY FOR BRITTLE MATERIALS

Based on the hypothesis of the fractal distribution of crack sizes in brittle materials and the weakest link principle, the relationship between the fractal dimension of the size-frequency distribution of cracks and the Weibull Modulus is derived, which reveals the geometrical nature of the Weibull Modulus. The influences of the size distribution and the orientation distribution of cracks as well as the irregularity of the crack propagation on the strength are all taken into account. Finally, a general expression for the statistical strength of brittle materials in complex tensile stress state is obtained.

Characterizations of PSD Fractal of Porous Medium

A volume-based method for measuring particle-size distribution (PSD) fractal dimensions of porous mediums was developed by employing laser size-analyzing technology. Compared with conventional approaches of using hydrometer or screen to determine PSD, this method can avoid calculation errors and measure smaller size-scale porous medium. In this paper the experimental porous mediums were brown soil, kaolin and sand soil. A micro-order of magnitude (10 -5 m) in particle-size interval could be shown in PSD results of brown soil and kaolin. The experiments indicated that brown soil had a nearly mono-fractal PSD character, while kaolin and sand soil showed multi-fractal PSD characters. By the adsorption isotherm experiments, the PSD fractal dimensions of the sand soil were also found to keep a linearly increasing relation with the linear adsorptive parameters of the soils in different intervals to adsorb benzene from aqueous solution.

Fractal characteristics of cracks and fragments generated in unloading rockburst tests

True triaxial rockburst experiments with four different unloading rates were performed on four prism specimens of granite sampled from Beishan, China. The damage evolution in the rockburst test was investigated from two aspects including fracture surface crack and fragment characteristics. The scanning electron microscopy was used to observe the micro crack information on fragment surface. Combing binarization and box counting dimensions, the fractal dimensions of cracks were obtained. Meanwhile,the fragments were collected and a sieving experiment was conducted. We weighed the fragments qualities, counted the amount of fragments and measured the fragments length, width and thickness.Utilizing four methods to calculate damage fractal dimensions of fragments, the trend of fractal value changing with unloading rates can be roughly described. It can be concluded from these experiments that the fractal dimension either for crack or for fragment holds a decreasing trend with the decreasing unloading rate, indicating a reduction of damage level.

Classification of low-density EEG for epileptic seizures by energy and fractal features based on EMD

We are here to present a new method for the classification of epileptic seizures from electroencephalogram(EEG) signals.It consists of applying empirical mode decomposition(EMD) to extract the most relevant intrinsic mode functions(IMFs) and subsequent computation of the Teager and instantaneous energy,Higuchi and Petrosian fractal dimension,and detrended fluctuation analysis(DFA) for each IMF.We validated the method using a public dataset of 24 subjects with EEG signals from 22 channels and showed that it is possible to classify the epileptic seizures,even with segments of six seconds and a smaller number of channels(e.g.,an accuracy of0.93 using five channels).We were able to create a general machine-learning-based model to detect epileptic seizures of new subjects using epileptic-seizure data from various subjects,after reducing the number of instances,based on the k-means algorithm.

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.

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。

时序数据涨落分形维数测度研究——以股票市场为例

为了更好分析时序数据的规律与特征,文章基于分形理论设计时间序列数据的涨落分形维数的测度方法,并以中美股票交易市场的股价数据为例,从测度单一股票的分形维数到分析整个市场的分形维数分布特征,说明算法的应用方式。算法应用研究发现,中国股票市场上的股票涨落的分形维数数据服从两种正态分布的混合分布,符合“政府+市场”的中国特色,且股价涨落的分形维数还反映了中国的两个股票交易市场的差异化定位与功能,从侧面验证了算法的有效性。

西秦岭夏河-合作地区断裂构造分形结构特征及成矿预测

西秦岭夏河-合作地区是中国重要的金矿及多金属矿床开发地带,区内断裂构造复杂,构造控矿作用显著。文章利用分形理论方法对夏河-合作地区不同方向断裂构造作定量分析,统计计算断裂构造容量维和信息维,结合矿床空间分布分形特征和矿床Fry分析,探讨研究区构造分形特征及断裂与矿床的空间展布关系。研究结果表明,研究区全部断裂容量维1.2374,北东向断裂容量维0.8229,北西向断裂容量维1.2296,近东西向断裂容量维1.0312,全部断裂容量和北西向断裂容量维处于断裂分形临界值(1.22~1.38)区域,显示研究区断裂构造连通性较好。研究区全部断裂信息维1.1118,北东向断裂信息维1.018,北西向断裂信息维1.2296,近东西向断裂信息维1.0217,北西向断裂信息维处于断裂分形临界值区域,反映北西向对矿床的控制最强。断裂构造分形维数可以表征矿床的沉积部位,以容量维、信息维等值线图以及Fry图划分出3个有利成矿区。

青藏高寒区隆子县居民点空间分布及其与地形地貌关系

以青藏高寒区隆子县为研究对象,利用遥感高清影像,采取目视解译结合实地考察的方式,获取隆子县居民点数据,选取高程、坡度、坡向、地形起伏度、坡向变率、地面粗糙度、高程变异系数和地貌类型8个因子,运用空间热点探测分析居民点规模分布“冷热点”,利用分布指数和信息熵探讨了隆子县居民点分布格局,通过变维分形揭示了居民点分布与地形地貌的关系.结果表明:(1)隆子县居民点分布以集群型小型居民点为主要特征,规模分布“冷热点”分异明显,热点主要分布在隆子镇,冷点主要分布在雪萨乡;(2)居民点在其分布的优势地形位上,其有序程度也相对较高.居民点在高程3 500~4 000 m,坡度小于2°,北坡坡向,地形起伏度15 m以下,坡向变率5°~10°,地面粗糙度小于1.01、高程变异系数为0.001~0.005的地形位和砂砾质冲洪积平原地貌上的有序性最强,这些地形位大多是居民点分布的优势地形位;(3)地形地貌对隆子县居民点分布及其发展影响的降序排序依次为地貌类型>高程>坡度>高程变异系数>坡向变率>坡向>地形起伏度>地面粗糙度.

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。

Effects of Vegetation Cover and Rainfall Intensity on Sediment-Bound Nutrient Loss,Size Composition and Volume Fractal Dimension of Sediment Particles

Vegetation and rainfall are two important factors affecting soil erosion and thus resulting in nutrient loss in the Chinese Loess Plateau.A field experiment was conducted to investigate the effects of rainfall intensities(60,100 and 140 mm h-1) and vegetation(Caragana korshinskii) coverages(0%,30% and 80%) on soil loss,nutrient loss,and the composition and volume fractal dimension of eroded sediment particles under simulated rainfall conditions.The results showed that vegetation cover,rainfall intensity and their interaction all had significant effects on sediment transport and the sedimentbound nutrient loss.Higher rainfall intensity and lower coverage led to higher sediment and nutrient losses.Positive linear relationships were observed between soil loss and nutrient loss.The treatments showed more significant effects on the enrichment ratio(ER) of nitrogen(ERN) than organic matter(EROM) and phosphorus(ERP).Compared with the original surface soil,the eroded sediment contained more fine particles.Under the same coverage,the clay content significantly decreased with increasing rainfall intensity.The ER of sediment-bound nutrients was positively correlated with that of clay,suggesting that the clay fraction was preferentially eroded and soil nutrients were mainly adsorbed onto or contained within this fraction.There were increments in the fractal dimension of the sediment particles compared to that of the original surface soil.Moreover,the fractal dimension was positively correlated with clay,silt,and sediment-bound OM,N,and P contents,whereas it was negatively correlated with sand content.This study demonstrated that fractal dimension analysis can be used to characterize differences in particle-size distribution and nutrient loss associated with soil erosion.