Determination of the Fractal Dimension of the Fracture Network System Using Image Processing Technique

Basirat, Rouhollah; Goshtasbi, Kamran; Ahmadi, Morteza

doi:10.3390/fractalfract3020017

Cited by 25 publications

(10 citation statements)

References 26 publications

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“…As fractal theory is now widely used [15][16][17][18][19][20][21][22][23], many researchers [24][25][26][27][28][29][30][31] have found that geomaterials exhibit fractal characteristics, and the rock joints, particle distribution, and pores at different scales have self-similarity, which is also consistent with the evolution of geomaterials under natural conditions. Generally, geomaterials can be regarded as an open non-linear self-organizing system.…”

Section: Introductionmentioning

confidence: 67%

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

Ding

Sheng

et al. 2022

Fractal Fract

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A soil–rock mixture (SRM) is a type of heterogeneous geomaterial, and the particle distribution of SRM can be described by fractal theory. At present, it is difficult to quantify the fractal dimension of a particle size distribution and understand the scale effect in SRMs. In this study, the fractal theory and discrete element method (DEM) were introduced to solve this problem. First, the particle gradation of SRM was dealt with by using fractal theory. The fractal structure of particle distribution was studied, and a method of calculation of the fractal dimension is presented in this paper. Second, based on the fractal dimension and relative threshold, the particle gradations of SRMs at different scales were predicted. Third, numerical direct shear tests of SRM at different scales were simulated by using the DEM. The scale effects of shear displacement, shear zone, and shear strength parameters were revealed. Last, taking the maximum particle size of 60 mm as the standard value, the piece-wise functional relationship between shear strength parameters and particle size was established. The results are as follows: for SRM in a representative engineering area, by plotting the relationship between particle cumulative mass percentage and particle size, we can judge whether the SRM has a fractal structure; in Southwest China, the frequency of the fractal dimension of the SRM is in the normal distribution, and the median fractal dimension is 2.62; the particle gradations of SRMs at different scales calculated by fractal dimension and relative threshold can expand the study scope of particle size analysis; when the particle size is less than 70 mm, the strength parameters show a parabolic trend with the particle size increases, and if not, a nearly linear trend is found. The proposed method can describe the fractal characteristics of SRM in a representative engineering area and provides a quantitative estimation of shear strength parameters of SRM at different scales.

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Section: Introductionmentioning

confidence: 67%

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

Ding

Sheng

et al. 2022

Fractal Fract

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“…[26,29,30]. This method (i.e., calculating the fractal dimension by digital image processing) also was verified through manual and different methods by Basirat et al [31]. This process was applied in a macro-scale (outcrop photos) image and a micro-scale (CT-scan) image.…”

Section: Calculation Of Fractal Dimension (D) Using Digital Image Promentioning

confidence: 95%

Scaling Geological Fracture Network from a Micro to a Macro Scale

Basirat

Goshtasbi

Ahmadi

2019

Frattura Ed Integrità Strutturale

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Characterizing fracture systems at various scales, modeling fracture distributions, and clarifying scale relations that correlate total fracture systems are of paramount importance in geology, mining, civil engineering, and petroleum engineering. In this paper, the conditions of fracture network geometry are investigated in a field scale (about 100 m) and a core sample scale (several centimeters). To achieve this purpose, field surveys and coring of rock outcrops were performed in the Asmari Formation of Iran. Fractures were manually sampled from rock outcrops on the field scale while micro-fractures were surveyed using CT-scan images of core samples on a small scale. To compare the fracture network geometry, two perspectives of fractal dimensions and orientation of fractures were used. The results showed that the fractal dimension has the same value in both field and core scales and the orientation of the fractures is similar in both scales. Therefore, it can be claimed that in the Asmari Formation of Iran the structure of the fracture network is similar in two studied scales.

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“… Deposition, folding, shorelines, water flow, burial patterns below the surface [10].  Determining the relationship between lineaments and soil degradation processes [17]  Structural geology phenomenon [18].…”

Section: Fractalmentioning

confidence: 99%

The Comparative of Morphological and Gravity Anomaly Lineaments in West Progo Mountains, Indonesia The Comparative of Morphological and Gravity Anomaly Lineaments in West Progo Mountains, Indonesia

Winarti

Sukiyah

Syafri

et al. 2021

Int. J. Adv. Sci. Eng. Inf. Technol.

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In Yogyakarta Special Region, the West Progo Dome comprises the Nanggulan Formation and Old-Andesite Formation as the oldest formations. The Nanggulan Formation is composed of sedimentary rock with a density of 2.5 g/cm3, while the Old-Andesite Formation is composed of volcanic rock with a density of 2.7 g/cm3. Dome morphology is formed by vertical endogenous energy that radiates SE-NW, NE-SW, and E-W. This study aims to describe the correlation between the hill lineaments and gravity anomaly lineaments in the Nanggulan Formation and Old-Andesian Formation. Identification of the hill lineament uses Shuttle Radar Topography Mission (SRTM), while the gravity anomaly lineament uses gravity anomaly map. The standard used in the gravity survey concerning the American Society for Testing and Materials Standard (ASTM). The measurement system utilizes a looping distance of 200-350 meters. The lineaments of the hill and gravity anomaly show the same direction SE-NW. Both lineaments are calculated by fractal dimension (D) utilize the box-counting method. The result of overlaying the two lineaments' fractal dimension produces the same value and the different value. The same fractal dimension value (D=0.81-1.20) indicates whether the hill lineament and gravity anomaly lineament are correlated, while the different fractal dimension values indicate that the two lineaments are not correlated. The fractal dimension value is different due to small intrusions and faults.

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Determination of the Fractal Dimension of the Fracture Network System Using Image Processing Technique

Cited by 25 publications

References 26 publications

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

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

Scaling Geological Fracture Network from a Micro to a Macro Scale

The Comparative of Morphological and Gravity Anomaly Lineaments in West Progo Mountains, Indonesia The Comparative of Morphological and Gravity Anomaly Lineaments in West Progo Mountains, Indonesia

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