Particle Size Fractal Dimension Research Articles

Experimental Study on the Effect of Coarse Grain Content on the Dilatancy and Particle Breakage Characteristics of Coarse-Grained Soils

The dilatancy deformation and particle breakage effects of coarse-grained soil have a significant influence on the safety and stability of high earth and rock-fill dams. To study the shear deformation and particle breakage characteristics of coarse-grained soil, four groups of soil sample with different coarse grain contents were to conduct consolidated drained triaxial compression tests by DJSZ-150 large-scale triaxial compression test machine. The results showed that the volume of coarse-grained soil changes significantly under deviation stress. The soil samples underwent positive dilatancy under the confining pressures of 200 kPa and 400 kPa but negative dilatancy under the confining pressures of 600 kPa and 800 kPa. When increasing the coarse grain contents in the soil sample under the same confining pressure, the positive dilatancy was more significant. A three-parameter dilatancy equation of coarse-grained soil considering confining pressure was established, in which the parameter L = 4 could serve as a criterion for whether the coarse-grained soil underwent positive dilatancy. Under the load, the coarse-grained soil showed three particle breakage modes: abrasion, attrition, and fracture. The coarse-grained soil particle size distribution before and after breakage conformed to the fractal characteristics, and the particle breakage rate increased significantly with larger soil particle size fractal dimension differences before and after the test. The coarse grain content and the confining pressure are two important factors affecting the mechanical properties of coarse-grained soil, and they control the shear deformation of soil.

Grain size and shape fractal characteristics of gangue in the process of 'jaw breaking-ball milling'.

This study investigates the fractal characteristics of the particle size and shape distribution of gangue powder in the "jaw crushing-ball milling" process using mudstone gangue. For this, fractal theory, laser particle size analyzer, scanning electron microscope and other mesoscopic research methods were introduced. This study has several main factors, including the discharge port width in the jaw crushing stage, the grinding particle size, ball-to-powder ratio in the ball milling stage, and the fractal dimension changes of the gangue in different crushing stages. The results indicate that in the process of "jaw crushing-ball milling", gangue's particle size and shape fractal dimension values changed periodically. During the jaw crushing stage, the particle size fractal dimension increases with the width of the discharge opening, ranging from 1.85 to 1.92. The value of the shape fractal dimension varies from 2.65 to 2.84. Ball milling causes the fractal dimension value of gangue particle size to increase with time before agglomeration and decrease after agglomeration. By comparing different in-grinding particle sizes and ball-to-powder ratio, it is found that the fractal dimension value of gangue particle size decreases with the increase of in-grinding particle size and increases with the increase of ball-to-powder ratio. The final gangue's particle size fractal dimension value is concentrated between 2.5 and 2.8. The fractal dimension of particle shape increases with the increase of the grinding particle size, and decreases with the increase of ball-to-powder ratio. A ball-to-powder ratio greater than 6 gradually reduces its influence on fractal dimensions, and the final shape dimension lies between 1.06 and 1.16. In addition, the increase/decrease range of particle size and shape fractal dimension decreases with the increase of ball milling time, which is also consistent with the grinding kinetics theory. As a result of the changes in particle size and shape fractal dimensions, parameters such as jaw crusher discharge port width, grinding particle size, and ball-to-powder ratio are calculated to provide a theoretical basis for the entire crushing process in the "jaw crusher-ball milling" crushing process.

STUDY ON THE INFLUENCE OF DRY DENSITY AND PARTICLE SIZE FRACTAL DISTRIBUTION ON THE RADON CONTROL PERFORMANCE OF OVERLYING SOIL IN URANIUM TAILINGS POND.

In order to explore the influence of dry density and particle size fractal distribution on the radon control performance of overlying soil in uranium tailings pond, overlying soil samples with different particle size fractal dimension and dry density were prepared for radon exhalation experiments. According to the principle of radon generation and diffusion, a set of radon measuring device was designed independently. In addition, the radon concentration on the surface of different overlying soil layers was measured by local static method, and the radon exhalation rate was further calculated. The relationship between radon exhalation law, dry density and fractal dimension of overlying soil was studied by correlation analysis method. Furthermore, a piecewise linear function between radon exhalation rate, dry density and fractal dimension was constructed. Then, the average value of the experimental data was compared with the calculated results. Results show that: at the same dry density and different fractal dimension, the radon exhalation rate decreased with the increase of fractal dimension. When the fractal dimension increased to a certain value, the radon exhalation rate tended to be stable. At the same fractal dimension and different dry density, the radon exhalation rate decreased with the increase of dry density. The calculated results of piecewise linear function were relatively close to the experimental data, which verified the practicability of the formula.

Microscopic Mechanism of the Macroscopic Mechanical Properties of Cement Modified Subgrade Silty Soil Subjected to Freeze-Thaw Cycles

In order to study the effects of the microstructure parameters of cement modified subgrade silty soil (CMSS) in a frozen area under freeze-thaw (F-T) cycles on the macroscopic mechanical properties, the static triaxial test, scanning electron microscopy (SEM), and grey relation analysis (GRA) were implemented on silty soil modified with 0% and 2% cement at optimum moisture content from the northwest in Jilin Province in China. The results showed that the shear strength, the cohesion of 0% and 2% CMSS, decreased with the increase of F-T cycles, while the internal friction angle was not obviously changed. The shear strength and its parameters of 2% CMSS doubled compared to that of 0% CMSS. The micro-parameters, representing the particle morphological characteristics, particle arrangement, and pore characteristics of CMSS, changed differently under F-T cycles. If the cement was not added, the cohesion and the internal friction angle were most sensitive to the average particle diameter (Dp) and the average particle abundance (C), respectively. When the cement content was 2%, the cohesion was chiefly affected by the particle size fractal dimension (Dps), while the internal friction angle was mainly related to the average pore diameter (Dh). The main principle of cement improvement was to decrease Dh of soil under F-T cycles.

A New Method for the Process Division and Effect Evaluation of Coagulation Based on Particle Size Fractal Dimension

To divide, control, and predict the effects of the coagulation process in water treatment, a characteristic analysis of the change in particle size distribution (particle number and fractal dimension) during aided coagulation with hydrated MnO2 was performed. The results showed that the process of coagulation could be divided into three characteristic stages based on the first derivative of the particle size fractal dimension. In the primary stage, most of the microflocs aggregated to form small flocs; in the growth stage, most of the small flocs aggregated to form large flocs; and in the stable stage, some large flocs broke apart and reformed. The first derivative of the particle size fractal dimension had a good linear relationship with the coagulation time in the primary stage and growth stage, and its slope had a power function relationship with the particle number in settled water; the first derivative could thus be used to evaluate the coagulation effect. In the stable stage, the rate of change in particle size fractal dimension fluctuated along the fitted line, and the mean residual sum of squares had a linear relation with the particle number in settled water; therefore, this parameter could be used as an indicator of the coagulation effect.

Quantitative Analysis of the Relationship Between Shear Strength and Fractal Dimension of Solidified Dredger Fill with Different Fly Ash Content Under Monotonic Shear

Abstract The dredger fill of Shanghai Hengsha Island Dongtan is solidified by curing agents with different fly ash content, and the shear strength index of solidified dredger fill is measured by the direct shear test. The microscopic images of solidified dredger fill are obtained by using SEM. The microscopic images are processed and analyzed by using IPP, and the fractal dimension including particle size fractal dimension Dps, aperture fractal dimension Dbs and particle surface fractal dimension Dpr is calculated by fractal theory. The quantitative analysis of the relationship between shear strength index and fractal dimension of solidified dredger fill is done. The research results show that the internal friction angle and the cohesion are closely related to the fly ash content λ and the curing period T, and the addition of fly ash can improve the effect of curing agent; There is no obvious linear relationship between the internal friction angle and the three fractal dimensions; The smaller particle surface fractal dimension Dpr and particle size fractal dimension Dps, the larger aperture fractal dimension Dbs, the greater the cohesion, and the cohesion has a good linear relationship with three fractal dimensions, and the correlation coefficient R2 is above 0.91.

Analysis of the Engineering Characteristics of Solidified Saline Soil Based on the Microstructure Index Using Response Surface Methodology

Selection of experimental factors such as particle size fractal dimension Dps, particle orientation fractal dimension Ddi, equivalent diameter De , design the experiments using response surface method, Study on the relationship between the mechanical strength index and the optimal microstructure parameters of lime solidified saline soil ,and is verified. The results show that the microstructure of the solidified soil is the best index of particle size fractal dimension Dps 0.8, particle orientation fractal dimension Ddi 0.93, equivalent diameter De 1.75, The mechanical strength of solidified saline soil reached the maximum. The model can be used to analyze and predict the mechanical properties of solidified soil.