scholarly journals Effect of the Concrete Mesostructure Geometric Form on Its Elastic Modulus

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xu Yang
Keyword(s):  
Fractal Dimension ◽  
Elastic Modulus ◽  
Euclidean Geometry ◽  
Coarse Aggregate ◽  
Fractal Dimensions ◽  
Macroscopic Behavior ◽  
Fractal Modeling ◽  
Aggregate Content ◽  
Random Fractal ◽  
Geometrical Form

A comprehensive understanding of the geometrical form of the concrete mesostructure is important because it is associated with the complex and random mechanical behavior of the concrete. There is still uncertainty about how to characterize the geometrical form of the concrete mesostructure and its effect on the observed macroscopic behavior. The coarse aggregate content and fractal dimension were used in this study to indicate the geometrical form of concrete at the mesolevel. Taking the mechanical parameters measured in experiments, a group of mesomodels with various fractal dimensions and coarse aggregate contents was simulated by using the random fractal modeling method and then was studied and discussed. The analytical solution, simulation, and experimental data all suggested that the elastic modulus increased with the increasing coarse aggregate content. Meanwhile, the fractal dimension can cause the elastic modulus to decline slightly. The comprehensive consideration of both fractal geometry and classical Euclidean geometry can aid in predicting the macroscopic behavior of concrete.

Analysis and optimization of mechanical properties of recycled concrete based on aggregate characteristics

2021 ◽  
Vol 28 (1) ◽  
pp. 516-527
Author(s):  
Jiangwei Bian ◽  
Wenbing Zhang ◽  
Zhenzhong Shen ◽  
Song Li ◽  
Zhanglan Chen
Keyword(s):  
Mechanical Properties ◽  
Elastic Modulus ◽  
Coarse Aggregate ◽  
Aggregate Size ◽  
Peak Stress ◽  
Recycled Concrete ◽  
Maximum Aggregate Size ◽  
Coarse Aggregates ◽  
Aggregate Content ◽  
Aggregate Shape

Abstract The most significant difference between recycled and natural concretes lies in aggregates. The performance of recycled coarse aggregates directly affects the characteristics of recycled concrete. Therefore, an in-depth study of aggregate characteristics is of great significance for improving the quality of recycled concrete. Based on the coarse aggregate content, maximum aggregate size, and aggregate shape, this study uses experiments, theoretical analysis, and numerical simulation to reveal the impact of aggregate characteristics on the mechanical properties of recycled concrete. In this study, we selected the coarse aggregate content, maximum aggregate size, and the aggregate shape as design variables to establish the regression equations of the peak stress and elastic modulus of recycled concrete using the response surface methodology. The results showed that the peak stress and elastic modulus of recycled concrete reach the best when the coarse aggregate content is 45%, the maximum coarse aggregate size is 16 mm, and the regular round coarse aggregates occupy 75%. Such results provide a theoretical basis for the resource utilization and engineering design of recycled aggregates.

THE RELATIONSHIP BETWEEN FRACTIONAL CALCULUS AND FRACTALS

Fractals ◽  
1995 ◽  
Vol 03 (01) ◽  
pp. 217-229 ◽  
Author(s):  
FRANK B. TATOM
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Fractional Calculus ◽  
Fractal Dimensions ◽  
Linear Functions ◽  
Fractal Curve ◽  
Random Fractal ◽  
Fractal Functions ◽  
Decay Exponent ◽  
The Relationship

The general relationship between fractional calculus and fractals is explored. Based on prior investigations dealing with random fractal processes, the fractal dimension of the function is shown to be a linear function of the order of fractional integro-differentiation. Emphasis is placed on the proper application of fractional calculus to the function of the random fractal, as opposed to the trail. For fractional Brownian motion, the basic relations between the spectral decay exponent, Hurst exponent, fractal dimension of the function and the trail, and the order of the fractional integro-differentiation are developed. Based on an understanding of fractional calculus applied to random fractal functions, consideration is given to an analogous application to deterministic or nonrandom fractals. The concept of expressing each coordinate of a deterministic fractal curve as a “pseudo-time” series is investigated. Fractional integro-differentiation of such series is numerically carried out for the case of quadric Koch curves. The resulting time series produces self-similar patterns with fractal dimensions which are linear functions of the order of the fractional integro-differentiation. These curves are assigned the name, fractional Koch curves. The general conclusion is reached that fractional calculus can be used to precisely change or control the fractal dimension of any random or deterministic fractal with coordinates which can be expressed as functions of one independent variable, which is typically time (or pseudo-time).

scholarly journals Fractal characteristic of recycled aggregate and its influence on physical property of recycled aggregate concrete

2021 ◽  
Vol 60 (1) ◽  
pp. 663-677
Author(s):  
Song Gao ◽  
Qiuyi Li ◽  
Jianlin Luo
Keyword(s):  
Fractal Dimension ◽  
Coarse Aggregate ◽  
Physical Property ◽  
Fractal Dimensions ◽  
Recycled Concrete ◽  
Recycled Aggregate Concrete ◽  
Recycled Aggregate ◽  
Boundary Line ◽  
Type I ◽  
Recycled Coarse Aggregate

Abstract Fractal dimension is introduced to describe the complicated characteristics of recycled aggregate and their influence on properties of recycled concrete as an integrated indicator. The fractal dimensions of both particle outline and distribution of recycled aggregate have obvious self-similarity and fractal characteristics. The order of the bulk density, water absorption, and crushing index of recycled aggregate in particle group state is clearly and directly related to the fractal dimension of boundary line. Additionally, the fractal dimension of the distribution of recycled coarse aggregate in concrete decreases in order of natural aggregate, Type I, Type II, and Type III recycled coarse aggregate; smaller distribution dimension value represents more concentrated distribution of aggregate, and 7 and 28 days compressive strength of the corresponding recycled concrete increases. The fractal dimension method is an effective process to assess comprehensive performances of recycled aggregate and helpful to establish a quantitative evaluation criterion for its wide applications.

scholarly journals From rock microstructure to macromechanical properties based on fractal dimensions

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983636 ◽  
Author(s):  
Dongmei Huang ◽  
Xikun Chang ◽  
Yunliang Tan ◽  
Kai Fang ◽  
Yanchun Yin
Keyword(s):  
Compressive Strength ◽  
Fractal Dimension ◽  
Elastic Modulus ◽  
Uniaxial Compressive Strength ◽  
Fractal Dimensions ◽  
Compression Tests ◽  
Scanning Electronic Microscopy ◽  
Electronic Microscopy ◽  
Rock Types ◽  
Rock Microstructure

Basic rock mechanical parameters, that is, the uniaxial compressive strength σc and elastic modulus E, have close relationships with the fractal dimension and inhomogeneity. Scanning electronic microscopy and fractal dimension calculations are applied to four different rock types (mudstone, sandstone, limestone, and basalt) in order to investigate the relationships between the rock mechanical properties, fractal dimensions, and homogeneity. The results show that the fractal dimension of each rock type fluctuates as the scanning electronic microscopy magnification increases. Rocks with different uniaxial compressive strength and elastic modulus values possess different self-similarity properties, and when the uniaxial compressive strength or elastic modulus increases, the fractal dimension of the rock microstructure decreases. The rock homogeneity is consistent with the fractal dimension, that is, the higher the homogeneity is, the larger the fractal dimension. Generally, homogeneity refers to the macroscale, and fractal dimension refers to the microscale. Overall, this research provides an innovative and effective approach for researching the mechanical behavior of rocks through a combination of uniaxial compression tests, homogeneity, and fractal dimensions.

FRACTAL DIMENSION, PRIMES, AND THE PERSISTENCE OF MEMORY

2003 ◽  
Vol 06 (02) ◽  
pp. 241-249
Author(s):  
JOSEPH L. PE
Keyword(s):  
Number Theory ◽  
Fractal Dimension ◽  
Fractal Dimensions ◽  
Distinguishing Characteristic ◽  
Local Behavior ◽  
Remarkable Similarity ◽  
Recursive Procedures

Many sequences from number theory, such as the primes, are defined by recursive procedures, often leading to complex local behavior, but also to graphical similarity on different scales — a property that can be analyzed by fractal dimension. This paper computes sample fractal dimensions from the graphs of some number-theoretic functions. It argues for the usefulness of empirical fractal dimension as a distinguishing characteristic of the graph. Also, it notes a remarkable similarity between two apparently unrelated sequences: the persistence of a number, and the memory of a prime. This similarity is quantified using fractal dimension.

scholarly journals Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks

Gels ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 46
Author(s):  
Pedram Nasr ◽  
Hannah Leung ◽  
France-Isabelle Auzanneau ◽  
Michael A. Rogers
Keyword(s):  
Fractal Dimension ◽  
Crystallization Temperature ◽  
Cayley Tree ◽  
Fractal Dimensions ◽  
Self Similarity ◽  
Avrami Model ◽  
Cluster Aggregation ◽  
Box Counting ◽  
Self Assembled ◽  
Limited Diffusion

Complex morphologies, as is the case in self-assembled fibrillar networks (SAFiNs) of 1,3:2,4-Dibenzylidene sorbitol (DBS), are often characterized by their Fractal dimension and not Euclidean. Self-similarity presents for DBS-polyethylene glycol (PEG) SAFiNs in the Cayley Tree branching pattern, similar box-counting fractal dimensions across length scales, and fractals derived from the Avrami model. Irrespective of the crystallization temperature, fractal values corresponded to limited diffusion aggregation and not ballistic particle–cluster aggregation. Additionally, the fractal dimension of the SAFiN was affected more by changes in solvent viscosity (e.g., PEG200 compared to PEG600) than crystallization temperature. Most surprising was the evidence of Cayley branching not only for the radial fibers within the spherulitic but also on the fiber surfaces.

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.

scholarly journals Energy Absorption Characteristics of PVC Coarse Aggregate Concrete under Impact Load

2021 ◽  
Vol 15 (1) ◽  
Author(s):  
Shi Hu ◽  
Huaming Tang ◽  
Shenyao Han
Keyword(s):  
Compressive Strength ◽  
Energy Absorption ◽  
High Speed ◽  
Coarse Aggregate ◽  
Specific Energy Absorption ◽  
Low Speed ◽  
High Speed Impact ◽  
Aggregate Content ◽  
Dynamic Compressive Strength ◽  
Absorption Characteristics

AbstractIn this paper, polyvinyl chloride (PVC) coarse aggregate with different mixing contents is used to solve the problems of plastic pollution, low energy absorption capacity and poor damage integrity, which provides an important reference for PVC plastic concrete used in the initial support structures of highway tunnels and coal mine roadway. At the same time, the energy absorption characteristics and their relationship under different impact loads are studied, which provides an important reference for predicting the energy absorption characteristics of concrete under other PVC aggregate content or higher impact speed. This study replaced natural coarse aggregate in concrete with different contents and equal volume of well-graded flaky PVC particles obtained by crushing PVC soft board. Also, slump, compression, and splitting strength tests, a free falling low-speed impact test of steel balls and a high-speed impact compression test of split Hopkinson pressure bar (SHPB) were carried out. Results demonstrate that the static and dynamic compressive strength decreases substantially, and the elastic modulus and slump decrease slowly with the increase of the mixing amount of PVC aggregate (0–30%). However, the energy absorption rate under low-speed impact and the specific energy absorption per MPa under high-speed impact increase obviously, indicating that the energy absorption capacity is significantly enhanced. Regardless of the mixing amount of PVC aggregate, greater strain rate can significantly enhance the dynamic compressive strength and the specific energy absorption per MPa. After the uniaxial compression test or the SHPB impact test, the relative integrity of the specimen is positively correlated with the mixing amount of PVC aggregate. In addition, the specimens are seriously damaged with the increase of the impact strain rate. When the PVC aggregate content is 20%, the compressive strength and splitting strength of concrete are 33.8 MPa and 3.26 MPa, respectively, the slump is 165 mm, the energy absorption rate under low-speed impact is 89.5%, the dynamic compressive strength under 0.65 Mpa impact air pressure is 58.77 mpa, and the specific energy absorption value per MPa is 13.33, which meets the requirements of shotcrete used in tunnel, roadway support and other impact loads. There is a linear relationship between the energy absorption characteristics under low-speed impact and high-speed impact. The greater the impact pressure, the larger the slope of the fitting straight line. The slope and intercept of the fitting line also show a good linear relationship with the increase of impact pressure. The conclusions can be used to predict the energy absorption characteristics under different PVC aggregate content or higher-speed impact pressure, which can provide important reference for safer, more economical, and environmental protection engineering structure design.

LATTICE DYNAMICS OF THE BINARY APERIODIC CHAINS OF ATOMS I: FRACTAL DIMENSION OF PHONON SPECTRA

1995 ◽  
Vol 09 (12) ◽  
pp. 1429-1451 ◽  
Author(s):  
WŁODZIMIERZ SALEJDA
Keyword(s):  
Fractal Dimension ◽  
Lattice Dynamics ◽  
Nearest Neighbor ◽  
Average Distance ◽  
Local Maximum ◽  
Fractal Dimensions ◽  
Dimension Formula ◽  
Phonon Spectra ◽  
Wide Range ◽  
Silver Mean

The microscopic harmonic model of lattice dynamics of the binary chains of atoms is formulated and studied numerically. The dependence of spring constants of the nearest-neighbor (NN) interactions on the average distance between atoms are taken into account. The covering fractal dimensions [Formula: see text] of the Cantor-set-like phonon spec-tra (PS) of generalized Fibonacci and non-Fibonaccian aperiodic chains containing of 16384≤N≤33461 atoms are determined numerically. The dependence of [Formula: see text] on the strength Q of NN interactions and on R=mH/mL, where mH and mL denotes the mass of heavy and light atoms, respectively, are calculated for a wide range of Q and R. In particular we found: (1) The fractal dimension [Formula: see text] of the PS for the so-called goldenmean, silver-mean, bronze-mean, dodecagonal and Severin chain shows a local maximum at increasing magnitude of Q and R>1; (2) At sufficiently large Q we observe power-like diminishing of [Formula: see text] i.e. [Formula: see text], where α=−0.14±0.02 and α=−0.10±0.02 for the above specified chains and so-called octagonal, copper-mean, nickel-mean, Thue-Morse, Rudin-Shapiro chain, respectively.

Fractal dimension based features are useful descriptors of leaf complexity and shape

1999 ◽  
Vol 29 (9) ◽  
pp. 1301-1310 ◽  
Author(s):  
Wojciech Borkowski
Keyword(s):  
Fractal Dimension ◽  
Tree Species ◽  
Fractal Dimensions ◽  
Plant Identification ◽  
Simple Method ◽  
Mass Dimension ◽  
Scale Range ◽  
Computer Identification

An application of fractal dimensions as measures of leaf complexity to morphometric studies and automated plant identification is presented. Detailed algorithms for the calculation of compass dimension and averaged mass dimension together with a simple method of grasping the scale range related variability are given. An analysis of complexity of more than 300 leaves from 10 tree species is reported. Several classical biometric descriptors as well as 16 fractal dimension features were computed on digitized leaf silhouettes. It is demonstrated that properly defined fractal dimension based features may be used to discriminate between species with more than 90% accuracy, especially when used together with other measures. It seems, therefore, that they can be utilized in computer identification systems and for purely taxonomical purposes.

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