The Correlation Between the Fractal Dimension and Internal Friction Angle of Different Granular Materials

Gori, Umberto; Mari, Milena

doi:10.3208/sandf.41.6_17

Cited by 38 publications

(14 citation statements)

References 13 publications

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“…Wadell [52] defined roundness (R) as D i−ave /D max−insc , where D i−ave is the average diameter of the inscribed circle for each corner of the grain. Besides, in recent years, fractal geometry techniques have few applications on engineering properties of soils [30,51,53]. The concept of fractals developed by Mandelbroth [40] is a relatively new mathematical approach for describing the geometry of irregular shape objects in terms of frictional numbers [8].…”

Section: Introductionmentioning

confidence: 99%

Stress fluctuations in granular material response during cyclic direct shear test

Çabalar

2015

Granular Matter

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This paper presents the results of an intensive series of experiments on various types of sands using cyclic direct shear testing apparatus. Two different grain shapes (rounded and angular) of sands having distinct sizes (0.25-0.5 and 1.0-2.0 mm) were tested in an automated constant normal load cyclic direct shear testing apparatus at an 100 kPa vertical effective stress, and two rates of shearing (2.0 and 0.025 mm/min). Experiments on the specimens resulted in sharp decreases followed by gradual increases in shear stress values. The results suggest that these successive drops and formations give a stick-slip nature to the fluctuations, which might be attributed mainly to the rate of loading, shape of grains, size of grains, and fines contents.

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Section: Introductionmentioning

confidence: 99%

Stress fluctuations in granular material response during cyclic direct shear test

Çabalar

2015

Granular Matter

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“…Mathematically, however, the strength of these relationships was poor, even though the particle size was kept constant and the q values determined from tests on sands of diŠerent relative densities were separated. Contrary to the study by Gori and Mari (2001), which includes the results of shear box tests carried out under lower normal stress levels, the dependence of q on Dtot and D2 parameters was not explanatory. In coarse sands, parameter D1 was capable of explaining variations in q.…”

Section: Relationships Between the Fractal Dimension And The Internalmentioning

confidence: 70%

“…In this context, geometric multifractals and distribution-based analyses are the most common fractal models for modeling the variability in the shape of soil grains (Perfect and Kay, 1990;Bitelli et al, 1999;Wang et al, 2006). Although roundness, sphericity, and other shape parameters seem to represent the various aspects of particle shape, fractal geometry is capable of representing these parameters as a whole (Gori and Mari, 2001).…”

Section: Particle Shape Identiˆersmentioning

confidence: 99%

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Relationships between Shape Characteristics and Shear Strength of Sands

Sezer

Altun

Göktepe³

2011

Soils and Foundations

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In the Mohr-Coulomb criterion, the shear strength of sands is typically characterized by the internal friction angle, which depends on many factors such as grain size and distribution, the mineralogical origin of the particles, particle shape, unit weight, geological history, cementation, saturation, and overburden pressure. In this study, the empirical relationships among three particle shape indices, diŠerent fractal dimension deˆnitions, and internal friction angles were investigated. Within this context, direct shear tests were conducted on 38 diŠerent types of sands from diŠerent origins and with various grain sizes. For each type of sand, image analyses were performed toˆnd out the roundness, sphericity, regularity parameters belonging to individual grains. Additionally, several statistics of these parameters for diŠerent types of sands were determined. The results revealed that particle shape has a limited eŠect on the friction angle of sands in comparison to grain size distribution. Furthermore, it was found that decreasing regularity in particle shape caused an increase in the internal friction angle of uniform sands. Theseˆndings agree with the empirical relationship between the internal friction angle and particle shape suggested in the literature.

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“…Other methods express the proportions of the geometrical sizes of particles obtained through direct measurement (Domokos et al, 2011) or through the measurement of images obtained with use of advanced equipment. This device may be the light microscope (Gori and Mari, 2001;Vallejo, 1995), scanning electron microscope SEM (Cox and Badhu, 2008;Thomas et al, 1995), computed tomography X-ray (Cox and Badhu, 2008;Masad, 2005) or 3D laser (Garboczi et al, 2006;Sinecen et al, 2011). More complex approaches to shape analysis include calculation methods, such as Fourier analysis (Bowman et al 2001;Thomas et al, 1995), the fractal method (Arasan et al, 2011;Gori and Mari, 2001;Vallejo, 1995) and the use of neural networks (Sinecen et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Influence of soil particle shape on saturated hydraulic conductivity

Zięba

2016

Journal of Hydrology and Hydromechanics

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Abstract:The aim of this paper is to define the correlation between the geometry of grains and saturated hydraulic conductivity of soils. The particle shape characteristics were described by the ζ 0C index (Parylak, 2000), which expresses the variability of several shape properties, such as sphericity, angularity and roughness.The analysis was performed on samples of four soils, which were characterised by the same grain size distribution and extremely different particle structure. The shape characteristics varied from ideally spherical, smooth grains (glass microbeads GM) to highly irregular and rough particles (fly ash FA).For each soil, laboratory tests of saturated hydraulic conductivity (constant head test CHT and falling head test FHT) were performed. Additionally, an empirical analysis of effective pore diameter was conducted with use of the analytical models developed by Pavchich (Wolski, 1987) and Indraratna and Vafai (1997). The models were modified by introducing the ζ 0C index.Experiments have shown that saturated hydraulic conductivity depends on grains shape and surface roughness. This parameter decreases with the increase in the irregularity of soil particles. Moreover, it was proven that the ζ 0C reflects the relationship between effective pore diameter and grain shape characteristics.

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The Correlation Between the Fractal Dimension and Internal Friction Angle of Different Granular Materials

Cited by 38 publications

References 13 publications

Stress fluctuations in granular material response during cyclic direct shear test

Stress fluctuations in granular material response during cyclic direct shear test

Relationships between Shape Characteristics and Shear Strength of Sands

Influence of soil particle shape on saturated hydraulic conductivity

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