Fractal Analysis of Particle Distribution and Scale Effect in a Soil–Rock Mixture

Fu, Xiaodong; Ding, Hongwei; Sheng, Qian; Zhu, Zhenping; Yin, Dawei; Chen, Fei

doi:10.3390/fractalfract6020120

Cited by 29 publications

(11 citation statements)

References 43 publications

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“…Under the double logarithmic coordinate, the lg[M(d<d i )/M t ]lg[(d i /d max )] distribution function of the gangue under different discharge opening widths is in good line with the linear relationship[26,27]. The regression curves of the scatter plots under any width of the discharge opening are all straight lines, and the R 2 of the regression coefficient is at least 0.98, indicating that the gangue has an obvious fractal characteristic in the jaw crushing process.…”

supporting

confidence: 53%

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

Zhu

Liu

et al. 2023

PLoS ONE

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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.

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confidence: 53%

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

Zhu

Liu

et al. 2023

PLoS ONE

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“…In particular, the vibration characteristics of a rock hold significant importance in investigating the fracture mechanism under harmonic excitation forces. Considering the complexity of porous structures of the rock, many previous results have confirmed that the mechanical properties and fracture behaviors of rocks are scale dependent (Fu et al 2022;Chen et al 2023;Wang et al 2023c) and sensitive to the loading rate (De Almeida et al 2020;Wang et al 2023a;Lai et al 2023). Hence, an in-depth understanding of the relationship between the porosity and natural frequency of a rock is an important task for us.…”

Section: Introductionmentioning

confidence: 98%

Effect of rock porosity on the natural frequency of the sample: theoretical model and experiment

Zhang,

Gu,

Kong

et al. 2024

Preprint

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Not confined to static effects such as permeability, the effect of porosity on the natural frequency of a rock is crucial to explore its dynamic behaviors. In the present work, a cylinder vibration model governed by the Lame-Navier equation is developed to clarify the mechanism of porosity-effect on the natural frequency of a rock. Focusing on the structural difference of the pore, the porosity-effect on the natural frequency for a cylinder model is preliminarily investigated by finite element (FE) simulations, in consideration of ideal straight and conical hole structures. To probe the distribution of real pores, the micro-computed tomography (micro-CT) technique is used to extract the accurate geometry of pores of the digital core, and the results are imported into the FE model for simulation. By introducing the Nur’s model and Krief’s model, the improved cylinder vibration model is able to predict multiple orders of the natural frequency of real rock samples with various porosities, and therefore overcomes the defects of the conventional spring-dashpot model. Verified by the resonant experiment on various rock samples, the results of the FE model and the improved cylinder vibration model show a basically consistent trend, i.e. the natural frequency decreases with the increase of porosity. These findings are beneficial to a wide range of engineering applications such as resonance enhanced drilling (RED) of rocks, high-speed processing of novel porous materials, and oil or gas explorations.

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“…Soil-rock mixture (S-RM), defined as the combination of the soil matrix with rock blocks of various sizes, presents a large distribution in southwestern China (Fu et al, 2021a;Ji et al, 2021;Zhou et al, 2022). The inclination to use S-RM, for example as the fill material for the high-fill deposit slope and rock-fill dam, is growing in the geotechnical engineering projects due to the expansion of the highway and building in the mountainous region of southwestern China (Zhang et al, 2021;Du et al, 2022;Fu et al, 2022). The natural S-RM can be divided into landslide deposit, collapse deposit, residual deposit, and other categories depending on how they formed (Xu et al, 2007;Yang et al, 2021).…”

Section: Introductionmentioning

confidence: 99%

A determination method for the shear strength of soil-rock mixture considering the size effect and its application

et al. 2022

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The shear strength of the soil-rock mixture (S-RM) is the primary mechanical factor influencing the stability of the deposit slope. The particle size range inside the test sample, however, is not the same as that of the S-RM in the deposit slope due to the limitations of the test device, which results in a variation in the mechanical properties. In this study, computer simulation tests were conducted to examine the impact of particle size on mechanical behaviors under the uniaxial compressive condition, and the size effect was analyzed from both macroscopic and mesoscopic perspectives. Results indicate that when the particle size increases, the anisotropy levels of the S-RM sample also rise, causing the particle displacement difference inside the sample to increase and the rounding rock effect to become more pronounced. The quantitative relationship between the uniaxial compressive strength (UCS) and the maximum particle size (dmax) was proposed, and the accuracy of the prediction formula for the UCS value of S-RM that takes the size effect into account has been confirmed. The improvement of the shear strength determination method was achieved by unifying the particle size range corresponding to the uniaxial compressive and shear test results used in the approach, and the determination method was used to evaluate the stability of a typical deposit slope. The study results can be used as a guide for estimating strength parameters of S-RM throughout the design and construction process of the deposit slope.

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Fractal Analysis of Particle Distribution and Scale Effect in a Soil–Rock Mixture

Cited by 29 publications

References 43 publications

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

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

Effect of rock porosity on the natural frequency of the sample: theoretical model and experiment

A determination method for the shear strength of soil-rock mixture considering the size effect and its application

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