scholarly journals Development of Back-calculation Model for Aggregate Gradation Determination Using Fractal Theory

2018 ◽  
Vol 159 ◽  
pp. 01006
Author(s):  
Bagus Hario Setiadji ◽  
Supriyono ◽  
Djoko Purwanto
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Fractal Dimensions ◽  
Calculation Model ◽  
Careful Consideration ◽  
Upper And Lower Bounds ◽  
Aggregate Gradation ◽  
Fractal Characteristic ◽  
Fractal Characteristics

Several studies have shown that fractal theory can be used to analyze the morphology of aggregate materials in designing the gradation. However, the question arises whether a fractal dimension can actually represent a single aggregate gradation. This study, which is a part of a grand research to determine aggregate gradation based on known asphalt mixture specifications, is performed to clarify the aforementioned question. To do so, two steps of methodology were proposed in this study, that is, step 1 is to determine the fractal characteristics using 3 aggregate gradations (i.e. gradations near upper and lower bounds, and middle gradation); and step 2 is to back-calculate aggregate gradation based on fractal characteristics obtained using 2 scenarios, one-and multi-fractal dimension scenarios. The results of this study indicate that the multi-fractal dimension scenario provides a better prediction of aggregate gradation due to the ability of this scenario to better represent the shape of the original aggregate gradation. However, careful consideration must be observed when using more than two fractal dimensions in predicting aggregate gradation as it will increase the difficulty in developing the fractal characteristic equations.

Application of Fractal Theory in Aggregate Gradation Research

2012 ◽  
Vol 204-208 ◽  
pp. 1923-1928
Author(s):  
Bo Tan ◽  
Rui Hua Yang ◽  
Yan Ting Lai
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Fractal Dimensions ◽  
Aggregate Gradation ◽  
Structure Characteristics ◽  
Aggregate Distribution ◽  
Dimension Formula ◽  
Mass Fractal ◽  
Fractal Characteristics

The paper presents the fractal dimension formula of distribution of asphalt mixture aggregate diameter by the deducing mass fractal characteristics function. Taking AC-20 and SMA-20 as examples, selected 6 groups of representative grading curves within the grading envelope proposed by the present specification, and calculated their fractal dimensions. The asphalt mixture gradation has fractal dimension D (D∈(1,3)), and the fractal of continuous gradation is single while the fractal of gap-gradation shows multi-fractal with 4.75 as the dividing point. Fractal dimension of aggregate gradation of asphalt mixture reflect the structure characteristics of aggregate distribution, that is, finer is aggregate, bigger is the fractal dimension.

Relationship of High-Temperature Performance and Aggregate Gradation of Asphalt Mixtures Based on Fractal Theory

2012 ◽  
Vol 204-208 ◽  
pp. 3795-3798 ◽  
Author(s):  
Jing Bo Huang ◽  
Xun Yu
Keyword(s):  
Fractal Dimension ◽  
High Temperature ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Temperature Stability ◽  
Asphalt Mixtures ◽  
High Temperature Stability ◽  
Aggregate Gradation ◽  
Fractal Characteristics ◽  
Relationship Of

Fractal theory was introduced to study the asphalt mixture aggregate gradation which shows visible fractal characteristics, and the fractal dimension of seven different gradations of ATB-25 were calculated quantitatively. Then the rutting test was carried out, and the results show that the fractal dimension of aggregate gradation has a good correlation with the dynamic stability of asphalt mixture. Finally, the paper proposes a multiple linear regression formula which may more accurately predict the high-temperature stability of the asphalt mixture with different gradations.

scholarly journals Review about the Application of Fractal Theory in the Research of Packaging Materials

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 860
Author(s):  
Qingshan Duan ◽  
Jiejie An ◽  
Hanling Mao ◽  
Dongwu Liang ◽  
Hao Li ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Theory ◽  
Inorganic Materials ◽  
Packaging Materials ◽  
Analysis Method ◽  
Characteristic Parameters ◽  
Fractal Characteristic ◽  
Fractal Characteristics ◽  
The Relationship

The work is intended to summarize the recent progress in the work of fractal theory in packaging material to provide important insights into applied research on fractal in packaging materials. The fractal analysis methods employed for inorganic materials such as metal alloys and ceramics, polymers, and their composites are reviewed from the aspects of fractal feature extraction and fractal dimension calculation methods. Through the fractal dimension of packaging materials and the fractal in their preparation process, the relationship between the fractal characteristic parameters and the properties of packaging materials is discussed. The fractal analysis method can qualitatively and quantitatively characterize the fractal characteristics, microstructure, and properties of a large number of various types of packaging materials. The method of using fractal theory to probe the preparation and properties of packaging materials is universal; the relationship between the properties of packaging materials and fractal dimension will be a critical trend of fractal theory in the research on properties of packaging materials.

Fractal Characteristics of Microstructure in Semisolid A356 Alloy

2011 ◽  
Vol 204-210 ◽  
pp. 1575-1578 ◽  
Author(s):  
Zheng Liu ◽  
Xiao Mei Liu
Keyword(s):  
Fractal Dimension ◽  
A356 Alloy ◽  
Fractal Dimensions ◽  
Fractal Characteristic ◽  
Compound Process ◽  
Fractal Characteristics

The fractal characteristic of microstructure in semisolid A356 alloy was researched by the calculating program written to calculate the fractal dimensions. The results indicated that the morphology of primary grain in semisolid A356 prepared by compound process is characterized by fractal dimension, and the morphology of primary grain at the different position of ingot had the different fractal dimensions, which reflected the effect of solidified conditions at different position in the same ingot on the morphology of semisolid primary grain.

scholarly journals Fractal Analysis on Asphalt Mixture Using a Two-Dimensional Imaging Technique

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Yue Hou ◽  
Yucheng Huang ◽  
Fengyan Sun ◽  
Meng Guo
Keyword(s):  
Fractal Dimension ◽  
Asphalt Concrete ◽  
Imaging Technique ◽  
Asphalt Pavement ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Self Similarity ◽  
Topological Dimension ◽  
Aggregate Gradation ◽  
Pavement Surface

Fractal is a mathematical set that has a fractal dimension which usually exceeds its topological dimension and may be nonintegral. Since the asphalt pavement texture has limitations of randomness and self-similarity, fractal theory has been explored to quantify the asphalt pavement texture and employs good applicability in processing and analyzing the complex details of research object. In this paper, the 2D digital image of the pavement surface is measured in terms of area fractal dimension and contour fractal dimension, which are used to correlate with aggregate gradation and British Pendulum Number (BPN) value, respectively. It turns out the area fractal dimension of aggregate provides a simple way to acquire the continuous gradation of asphalt concrete sample and the contour fractal dimension is an available parameter to characterize roughness and friction of pavement surface texture.

scholarly journals A study on the effects of the fractal characteristics of aggregates on the mechanical behavior of cemented sand and gravel

2021 ◽  
Vol 71 (342) ◽  
pp. e250
Author(s):  
L. Guo ◽  
S. Li ◽  
L. Zhong ◽  
L. Guo ◽  
L. Wang ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Elastic Modulus ◽  
Fractal Theory ◽  
Peak Stress ◽  
Aggregate Gradation ◽  
Cemented Sand ◽  
Ordinary Concrete ◽  
Fractal Characteristics ◽  
Sand And Gravel ◽  
The Relationship

Owing to complex aspects of cemented sand and gravel (CSG), such as included unscreened aggregates, CSG properties differ from those of ordinary concrete. Fractal theory is introduced to study the effects of aggregate characteristics on CSG properties, quantifying aggregate gradation and shape. Numerical simulation and analyses show that: (1) improved aggregate gradation decreases the gradation fractal dimension and increases the CSG peak stress and elastic modulus; (2) more irregularly shaped aggregates increase the shape fractal dimension and decrease the CSG peak stress and elastic modulus; (3) the relationship quantified between aggregate characteristics and CSG mechanical properties provides a theoretical basis for aggregate allocation in engineering design and construction. Mixing artificial aggregates can improve aggregate gradation but reduces CSG performance. Appropriately blending artificial and on-site aggregates achieves optimal CSG performance; in this study, this is attained using 20% artificial aggregates added under standard gradation.

Studies on the Time-Varying Effect of Root Morphology and Soil Reinforcement of Two Kinds of Herbs

2012 ◽  
Vol 193-194 ◽  
pp. 323-328
Author(s):  
Bing Qin Zhao ◽  
Zhen Yao Xia ◽  
Wen Nian Xu ◽  
Zheng Jun Zhou
Keyword(s):  
Medicago Sativa ◽  
Cynodon Dactylon ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Growth Period ◽  
Soil Reinforcement ◽  
Time Varying ◽  
Fractal Characteristic ◽  
Fractal Characteristics ◽  
New Perspective

The roots can significantly increase the soil reinforcement of vegetation, and the fractal theory provides a new perspective for vegetation roots studies. This article applied the Fractal Fox software to calculate the fractal dimension of medicago sativa and cynodon dactylon roots in different growth periods and proved that the two species show fractal characteristics. The conclusions from the analysis are as follows: ①The fractal dimensions of the two plant roots tend to be stable with the increase of growth period; ②The fractal characteristic value of cynodon dactylon root is more significant than medicago sativa root; ③Compared with medicago sativa root, cynodon dactylon root is more effective in increasing the shear strength of soil.

Study on Fractal Characteristics of Primary Phase Morphology in Semi-Solid A356 Alloy

2010 ◽  
Vol 139-141 ◽  
pp. 653-656
Author(s):  
Zheng Liu ◽  
Xiao Mei Liu
Keyword(s):  
Fractal Dimension ◽  
A356 Alloy ◽  
Fractal Dimensions ◽  
Primary Phase ◽  
Phase Morphology ◽  
Fractal Characteristic ◽  
Box Counting ◽  
Compound Process ◽  
Fractal Characteristics ◽  
Semi Solid

Semi-solid A356 slurry was prepared by compound process, and the fractal characteristic of primary phase morphology was researched. The fractal dimensions of primary phase morphology in semi-solid A356 alloy were calculated by the calculating program written to calculate the fractal dimensions of box-counting in the imagine of morphology of semi-solid primary phase in A356 alloy. The results indicated that the primary phase morphology in semi-solid A356 prepared by compound process is characterized by fractal dimension, and the primary phase morphology prepared by the different technology parameters had different fractal dimensions. The primary phase morphology at the different position of ingot had the different fractal dimensions, which reflected the effect of solidified conditions at different position in the same ingot on the morphology of semi-solid primary phase

Fractal Research on Cracks of Reinforced Concrete Beams with Different Aggregates Sizes

2011 ◽  
Vol 250-253 ◽  
pp. 1818-1822 ◽  
Author(s):  
Hong Quan Sun ◽  
Jun Ding ◽  
Jian Guo ◽  
Dong Liang Fu
Keyword(s):  
Fractal Dimension ◽  
Reinforced Concrete ◽  
Theoretical Basis ◽  
Concrete Beams ◽  
Fractal Theory ◽  
Aggregate Size ◽  
Fractal Dimensions ◽  
Reinforced Concrete Beams ◽  
Crack Evolution ◽  
Fractal Characteristics

Under the concentrated loads, the crack evolutions of reinforced concrete experimental beams (RCEB) with three different aggregate sizes are studied. Using fractal theory, the generation, development and distribution of the cracks on the RCEB are analyzed. The results show that the cracks on the RCEB have fractal characteristics obviously. By studying the fractal dimension of the cracks, the aggregate sizes have significant effect to the cracks on the RCEB. The relationships of the fractal dimensions of the crack evolution in loading processing and loads meet the power function laws. The researching results of this paper provide a new theoretical basis for selecting the appropriate aggregate size to improve the strength of reinforced concrete beams.

scholarly journals Dynamic characteristics and fractal representations of crack propagation of rock with different fissures under multiple impact loadings

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bing Sun ◽  
Shun Liu ◽  
Sheng Zeng ◽  
Shanyong Wang ◽  
Shaoping Wang
Keyword(s):  
Fractal Dimension ◽  
Crack Propagation ◽  
Crack Growth ◽  
Impact Test ◽  
Fractal Theory ◽  
Dynamic Change ◽  
Fractal Dimensions ◽  
Peak Stress ◽  
Dynamic Mechanical Properties ◽  
Gravitational Potential Energy

AbstractTo investigate the influence of the fissure morphology on the dynamic mechanical properties of the rock and the crack propagation, a drop hammer impact test device was used to conduct impact failure tests on sandstones with different fissure numbers and fissure dips, simultaneously recorded the crack growth after each impact. The box fractal dimension is used to quantitatively analyze the dynamic change in the sandstone cracks and a fractal model of crack growth over time is established based on fractal theory. The results demonstrate that under impact test conditions of the same mass and different heights, the energy absorbed by sandstone accounts for about 26.7% of the gravitational potential energy. But at the same height and different mass, the energy absorbed by the sandstone accounts for about 68.6% of the total energy. As the fissure dip increases and the number of fissures increases, the dynamic peak stress and dynamic elastic modulus of the fractured sandstone gradually decrease. The fractal dimensions of crack evolution tend to increase with time as a whole and assume as a parabolic. Except for one fissure, 60° and 90° specimens, with the extension of time, the increase rate of fractal dimension is decreasing correspondingly.

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