Numerical Simulation of Rockfill Materials Based on Fractal Theory

With the use of the particle flow code in two dimensions, a fractal model is established with the number of particles of different particle fractions used as the statistics to study the fractal characteristics of particle size distribution. Numerically simulated specimens obtained by four scale methods are subjected to the relative density test and the biaxial compression test to explore the influences of fractal dimension D on the macroscopic and mesomechanical properties of specimens, as well as to study the relationship between fractal dimension D and different mechanical performance indexes. Results show that the particle size distribution of each of the four groups after scale exhibits fractal characteristics, with the fractal dimension D ranging from 1.27 to 2.03. The number of fine particles in the specimen increases with the fractal dimension D, the particle aggregates become more compact, the macroscopic mechanical properties of the specimens are improved, and a linear relationship exists between the fractal dimension D and different mechanical performance indexes. A large fractal dimension D corresponds to a great mesoparticle coordination number.

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Green Preparation, Spheroidal, and Superior Property of Nano-1,3,5,7-Tetranittro-1,3,5,7-Tetrazocane

Journal of Nanomaterials ◽

10.1155/2018/5839037 ◽

2018 ◽

Vol 2018 ◽

pp. 1-8 ◽

Cited By ~ 5

Author(s):

Xinlei Jia ◽

Jingyu Wang ◽

Conghua Hou ◽

Yingxin Tan

Keyword(s):

Activation Energy ◽

Particle Size ◽

Fractal Dimension ◽

Particle Size Distribution ◽

Size Distribution ◽

Fractal Theory ◽

Crystal Form ◽

Decomposition Temperature ◽

Scanning Calorimetry ◽

The Impact

Herein, a green process for preparing nano-HMX, mechanical demulsification shearing (MDS) technology, was developed. Nano-HMX was successfully fabricated via MDS technology without using any chemical reagents, and the fabrication mechanism was proposed. Based on the “fractal theory,” the optimal shearing time for mechanical emulsification was deduced by calculating the fractal dimension of the particle size distribution. The as-prepared nano-HMX was characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), and differential scanning calorimetry (DSC). And the impact sensitivities of HMX particles were contrastively investigated. The raw HMX had a lower fractal dimension of 1.9273. The ideal shearing time was 7 h. The resultant nano-HMX possessed a particle size distribution ranging from 203.3 nm to 509.1 nm as compared to raw HMX. Nano-HMX particles were dense spherical, maintaining β-HMX crystal form. In addition, they had much lower impact sensitivity. However, the apparent activation energy as well as thermal decomposition temperature of nano-HMX particles was decreased, attributing to the reduced probability for hotspot generation. Especially when the shearing time was 7 h, the activation energy was markedly decreased.

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Evaluation of particle size distribution of granular blasting materials based on the fractal theory

Advances in Mechanical Engineering ◽

10.1177/1687814019881562 ◽

2019 ◽

Vol 11 (10) ◽

pp. 168781401988156 ◽

Cited By ~ 1

Author(s):

Jiejie Ji ◽

Qiang Yao ◽

Faming Wu ◽

Hongtao Li

Keyword(s):

Particle Size ◽

Fractal Dimension ◽

Particle Size Distribution ◽

Size Distribution ◽

Evaluation Method ◽

Fractal Theory ◽

Distribution Model ◽

Uniformity Coefficient ◽

Functional Relationships ◽

Fine Grain

The particle size distribution of granular blasting materials has a vital influence on the filling quality of earth-rockfill dams. The engineering experience-based method used to evaluate the particle size distribution has shortcomings at both the theoretical and practical aspects. This article proposes a new evaluation method based on the fractal theory. Grading sieve tests on granular materials, mass fractal analysis of particle size distribution, and a probability distribution model test of the characteristic parameters are used to revise the functional relationships between the fractal dimension D and the uniformity coefficient/curvature coefficient ( Cu/ Cc) of the grading curve. The feasibility of using D to evaluate the particle size distribution and the optimal fine grain content is then analyzed and determined. According to the results, the geometric shapes of the granular blasting materials have fractal characteristics, and their particle size distribution has a fractal distribution. The ranges of D where the rockfill and transition materials have a good particle size distribution are D = 2.254–2.529 and D = 2.358–2.559, corresponding to optimal fine grain content of 1.953%–11.805% and 10.268%–23.123%, respectively. Fractal dimension has a solid theoretical basis and strong practical applicability as an evaluation index for the particle size distribution of granular blasting materials.

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Analysis of the Correlation Between Strength and Fractal Dimension of Gravelly Soil in Debris-flow Source Areas

The Open Civil Engineering Journal ◽

10.2174/1874149501610010866 ◽

2016 ◽

Vol 10 (1) ◽

pp. 866-876 ◽

Cited By ~ 1

Author(s):

He Na ◽

Li Tao ◽

Zhong Wei ◽

Tom Cosgrove ◽

Zeng Mei

Keyword(s):

Particle Size ◽

Fractal Dimension ◽

Internal Friction ◽

Particle Size Distribution ◽

Debris Flow ◽

Size Distribution ◽

Fractal Theory ◽

Soil Samples ◽

Gravelly Soil ◽

Cohesion Force

Particle size distribution of gravelly soil plays a crucial role in debris flow initiation. For better understanding the mechanism of debris flow formation, two crucial mechanical property parameters of the gravelly soil are required to be studied meticulously: hydraulic conductivity and strength. With the aim of measuring the composition of the gravelly soil, 182 soil samples were taken from debris flow prone areas. With the aid of a sieve test, the particle size distribution of the samples can be obtained and analyzed. Then fractal theory was employed to compute the fractal dimension of the soil samples. By analyzing the results of sieve test (particle size distribution curves) and the results of the fractal theory calculations, the relationship between fractal dimension and particle size distribution can be explored. The results illustrate that the particle compositions of the gravelly soil tends to remain uniform as the fractal dimension increases. Moreover, as the coarse particle content increases, the fractal dimension decreases. To better understand the formation mechanism of debris flows, direct shear tests were conducted. Subsequently the experimental results were analyzed. By analysis, the following conclusions can be drawn: the soil strength decreases as the fractal dimension increases, and for soils with lower moisture content and identical dry density, a linear relationship between fractal dimension and cohesion force was identified. Moreover, cohesion force and internal friction force both decrease as the fractal dimension increases, but the internal friction angle decreases slightly while the cohesion force decreases greatly. Therefore we concluded that soil strength decreased mainly due to the reduction in cohesion force.

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Multi-fractal characteristics of particle size distribution of granular backfilling materials under different loads

Materials Testing ◽

10.3139/120.111127 ◽

2018 ◽

Vol 60 (2) ◽

pp. 202-208 ◽

Cited By ~ 4

Author(s):

Hao Yan ◽

Jixiong Zhang ◽

Jiaqi Wang ◽

Nan Zhou ◽

Sheng Zhang

Keyword(s):

Particle Size ◽

Particle Size Distribution ◽

Size Distribution ◽

Fractal Characteristics

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The Role of Particle Size Distribution in the Performance and Modelling of Filtration

Water Science & Technology ◽

10.2166/wst.1993.0199 ◽

1993 ◽

Vol 27 (10) ◽

pp. 19-34 ◽

Cited By ~ 9

Author(s):

R. I. Mackie ◽

R. Bai

Keyword(s):

Particle Size ◽

Particle Size Distribution ◽

Size Distribution ◽

Fine Particles ◽

Coarse Particles ◽

Large Particles

The paper examines the importance of size distribution of the influent suspension on the performance of deep bed filters and its significance with regard to modelling. Experiments were carried out under a variety of conditions using suspensions which were identical in every respect apart from their size distribution. The results indicate that the presence of coarse particles does increase the removal of fine particles. Deposition of fine particles leads to a greater headloss than deposition of large particles. Changes in size distribution with time and depth play an important role in determining the behaviour of a filter, and models of both removal and headloss development must take account of this.

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Slope scale spatial variability of fractal dimension of soil particle size distribution at multiple depths

Soil Science Society of America Journal ◽

10.1002/saj2.20178 ◽

2020 ◽

Author(s):

Xinyu Zou ◽

Zhuodong Zhang ◽

Mengyao Wu ◽

Yuanqiang Wan

Keyword(s):

Particle Size ◽

Fractal Dimension ◽

Particle Size Distribution ◽

Spatial Variability ◽

Size Distribution ◽

Soil Particle ◽

Soil Particle Size ◽

Soil Particle Size Distribution

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Fractal dimension of particle-size distribution and their relationships with alkalinity properties of soils in the western Songnen Plain, China

Scientific Reports ◽

10.1038/s41598-020-77676-w ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Yufeng Bai ◽

Yan Qin ◽

Xinrui Lu ◽

Jitao Zhang ◽

Guoshuang Chen ◽

...

Keyword(s):

Particle Size ◽

Fractal Dimension ◽

Particle Size Distribution ◽

Size Distribution ◽

Linear Regression Analysis ◽

Salt Content ◽

Clay Content ◽

Fine Sand ◽

Alkaline Soil ◽

Songnen Plain

AbstractThe purpose of this study was to identify the fractal dimension and their relationships with alkalinity properties of soils, and to evaluate the potential of fractal dimension as an indicator of alkalinity properties of soil. Six soils with an increasing salinity (electrical conductivity was 0.09, 0.18, 0.62, 0.78, 1.57 and 1.99 dS m−1, respectively) were selected from the western part of the Songnen Plain (China). Salt content, exchangeable sodium percentage, sodium adsorption ratio and other properties of the soils were determined and the soil particle-size distribution (0–2000 μm) was measured using a laser diffraction particle size analyser. Our results show that the overall fractal dimension of the selected soils ranged from 2.35 to 2.60. A linear regression analysis showed a significant negative correlation between fractal dimension and the amount of coarse sand and fine sand (r = − 0.5452, P < 0.05 and r = − 0.8641, P < 0.01, respectively), and a significant positive correlation with silt and clay (r = 0.9726, P < 0.01 and r = 0.9526, P < 0.01, respectively). Thus, soils with higher silt and clay content have higher fractal dimension values. Strong linear relationships between fractal dimension and salt content (P < 0.05), in particular a very significant positive relationship with HCO3− (P < 0.01), also exist. It is therefore possible to conclude that a soil’s fractal dimension could serve as a potential indicator of soil alkalization and the variability in alkaline soil texture.

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Performance Characteristics of Centrifugal Slurry Pumps

Journal of Fluids Engineering ◽

10.1115/1.1366322 ◽

2001 ◽

Vol 123 (2) ◽

pp. 271-280 ◽

Cited By ~ 37

Author(s):

B. K. Gandhi ◽

S. N. Singh ◽

V. Seshadri

Keyword(s):

Particle Size ◽

Particle Size Distribution ◽

Size Distribution ◽

Fine Particles ◽

Performance Characteristics ◽

Solid Concentration ◽

Solid Materials ◽

Power Characteristics ◽

Additional Losses

The performance of two centrifugal slurry pumps has been reported for three solid materials having different particle size distribution (PSD) in terms of head, capacity, and power characteristics. The results have shown that the values of head and efficiency ratios are not only dependent on solid concentration but are also affected by PSD of the solids and properties of the slurry. The addition of fine particles in the slurry of coarser material leads to reduction in the additional losses that occur in the pumps due to the presence of solids. It is also observed that with the increase in the pump size, the additional losses due to presence of solids reduce.

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