• Structural Engineering and Mechanics
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• 제23권2호
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• pp.147-161
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• 2006

Recent developments in fractal theory suggest that fractal may provide a more realistic representation of characteristics of cementitious materials. In this paper, the roughness of fracture surfaces in cementitious material has been characterized by fractal theory. A systematic experimental investigation was carried out to examine the dependency of fracture parameters on the aggregate sizes as well as the loading rates. Three maximum aggregate sizes (4.76 mm, 12.7 mm, and 19.1 mm) and two loading rates (slow and fast loading rate) were used. A total of 25 compression tests and 25 tension tests were performed. All fracture parameters exhibited an increase, to varying degrees, when aggregates were added to the mortar matrix. The fracture surfaces of the specimens were digitized and analyzed. Results of the fractal analysis suggested that concrete fracture surfaces exhibit fractal characteristics, and the fractal geometry provide a useful tool for characterizing nonlinear fracture behavior of concrete. Fractal dimension D was monotonically increased as maximum aggregate sizes increase. A new fractal fracture model was developed which considers the size and shape of aggregate, and the crack paths in the constituent phases. Detailed analyses were given for four different types of fracture paths. The fractal fracture model can estimate fractal dimension for multiphase composites.

• Computers and Concrete
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• 제26권6호
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• pp.505-513
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• 2020

Grading of aggregate influences significantly almost all of the concrete performances. The purpose of this paper is to propose practicable equations that express the optimized total aggregate gradation, by weight or by number of particles in a concrete mix. The principle is based on the fractal feature of the grading of combined aggregate in a solid skeleton of concrete. Therefore, equations are derived based on the so-called fractal dimension of the grain size distribution of aggregates. Obtained model was then applied in such a way a correlation between some properties of the dry concrete mix and the fractal dimension of the aggregate gradation has been built. This demonstrates that the parameter fractal dimension is an efficacious tool to establish a unified model to study the solid phase of concrete in order to design aggregate gradation to meet certain requirements or even to predict some characteristics of the dry concrete mixture.

• Computers and Concrete
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• 제2권3호
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• pp.239-248
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• 2005

The article presents the results of examination of the fractal dimension D of concrete specimen fracture surfaces obtained in fracture toughness tests. The concretes were made from three different types of coarse aggregate: gravel, dolomite and basalt aggregate. Ordinary concretes (C40) and high-performance concretes (HPC) were subjected to testing after 7, 14, 28 and 90 days of curing, respectively. In fracture toughness and compressive tests, different behaviours of concretes were found, depending on the type of aggregate and class of concrete (C40, HPC). A significant increase in the strength parameters tested occurred also after a period of 28 days (up to the $90^{th}$ day of curing) and was particularly large for concretes C40. Fractal examinations performed on fracture replicas showed that the fractal dimension D was diverse, depending on the coarse aggregate type and concrete class being, however, statistically constant after 7 and 14 days for respective concretes during curing. The fractal dimension D was the greater, the worse strength properties were possessed by the concrete. A cross-grain crack propagation occurred in that case, due to weak cohesion forces at the coarse aggregate/mortar interface. A similar effect was observed for C40 and HPC made from the same aggregate. A greater dimension D was exhibited by concretes C40, in which case the fracture was easier to form compared with high-performance concretes, where, as a result of high aggregate/mortar cohesion forces, the crack propagation was of inter-granular type, and the resulted fracture was flatter.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집D
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• pp.605-611
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• 2001

A numerical technique for simulating the aggregation of charged particles was presented with a Brownian dynamic simulation in the free molecular regime. The Langevin equation was used for tracking each particle making up an aggregate. A periodic boundary condition was used for calculation of the aggregation process in each cell with 500 primary particles of 16 nm in diameter. We considered the thermal force and the electrostatic force for the calculation of the particle motion. The morphological shape of aggregates was described in terms of the fractal dimension. The fractal dimension for the uncharged aggregate was $D_{f}=1.761$. The fractal dimension changed slightly for the various amounts of bipolar charge. However, in case of unipolar charge, the fractal dimension decreased from 1.641 to 1.537 with the increase of the average number of charges on the particles from 0.2 to 0.3 in initial states.

• Korean Chemical Engineering Research
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• 제60권2호
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• pp.260-266
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• 2022

Average aggregate size in particulate suspensions is estimated with scaling theories based on fractal concept and elasticity of colloidal gel. The scaling theories are used to determine structure parameters of the aggregates, i.e., fractal dimension and power-law exponent for aggregate size reduction with shear stress using scaling behavior of elastic modulus and shear yield stress as a function of particle concentration. The structure parameters are utilized to predict aggregate size which varies with shear stress through rheological modeling. Experimentally rheological measurement is conducted for aqueous suspension of zinc oxide particles with average diameter of 110 nm. The predicted aggregate size is about 1135 nm at 1 s^-1 and 739 nm at 1000 s^-1 on the average over the particle concentrations. It has been found that the predicted aggregate size near 0.1 s^-1 agrees with that the measured one by a dynamic light scattering analyzer operated un-sheared.

• Advances in concrete construction
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• 제16권3호
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• pp.141-153
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• 2023

In order to develop and take full advantage of pasture fiber and waste concrete, this article studied how different amounts of pasture fiber influenced the toughness and pore structure of concrete with different replacement rates of recycled fine aggregate. Pasture fiber recycled concrete constitutive equations were established under idealized stiffness and toughness damage rate, based on fracture energy and damage mechanics theories. The relationship between pore structure and toughness was studied utilizing nuclear magnetic resonance and fractal theory. The toughness of text groups (0% (JZ), 10% (ZS10), 20% (ZS20)) first increased and then decreased with increasing amounts of pasture fiber, based on the damage rate of toughness. The toughness of concrete samples with recycled fine aggregate and pasture fiber is negatively correlated to the fractal dimension of small and medium-sized pores with a pore size of 0-500 nm. At a replacement rate of 10% of the recycled fine aggregate, the fractal dimension of the air voids (r: 500-9000 nm, i.e., Lg(r) ∈ [2.7, 3.9]) shows a gradual decrease with the increase of grass fiber dosage, indicating that with such a replacement rate of the recycled fine aggregate, the increase of pasture fiber can reduce the complexity of the pore structure of the air voids (500-9000 nm).

• 대한기계학회논문집B
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• 제26권2호
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• pp.227-237
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• 2002

A numerical technique for simulating the aggregation of charged particles was presented with a Brownian dynamic simulation in the free molecular regime. The Langevin equation was used for tracking each particle making up an aggregate. A periodic boundary condition was used for calculation of the aggregation process in each cell with 500 primary particles of 16 nm in diameter. We considered the thermal force and the electrostatic force for the calculation of the particle motion. The electrostatic force on a particle in the simulation cell was considered as a sum of electrostatic forces from other particles in the original cell and its replicate cells. We assumed that the electric charges accumulated on an aggregate were located on its center of mass, and aggregates were only charged with pre-charged primary particles. The morphological shape of aggregates was described in terms of the fractal dimension. In the simulation, the fractal dimension for the uncharged aggregate was D$\_$f/ = 1.761. The fractal dimension changed slightly for the various amounts of bipolar charge. However, in case of unipolar charge, the fractal dimension decreased from 1.641 to 1.537 with the increase of the average number of charges on the particles from 0.2 to 0.3 in initial states. In the bipolar charge state, the average sizes of aggregates were larger than that of the uncharged state in the early and middle stages of aggregation process, but were almost the same as the case of the uncharged state in the final stage. On the other hand, in the unipolar charge state, the average size of aggregates and the dispersion of particle volume decreased with the increasing of the charge quantities.

• 대한기계학회논문집B
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• 제23권9호
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• pp.1139-1150
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• 1999

The evolution of silica aggregate particles in coflow diffusion flames has been studied experimentally using light scattering and thermophoretic sampling techniques. The measurements of scattering cross section from $90^{\circ}$ light scattering have been utilized to calculate the aggregate number density and volume fraction using with combination of measuring the particle size and morphology through the localized sampling and a TEM image analysis. Aggregate or particle number densities and volume fractions were calculated using Rayleigh-Debye-Gans and Mie theory for fractal aggregates and spherical particles, respectively. Of particular interests are the effects of flame temperature on the evolution of silica aggregate particles. As the flow rate of $H_2$ increases, the primary particle diameters of silica aggregates have been first decreased, but, further increase of $H_2$ flow rate causes the diameter of primary particles to increase and for sufficiently larger flow rates, the fractal aggregates finally become spherical particles. The variation of primary particle size along the upward jet centerline and the effect of burner configuration have also been studied.

• 한국토양비료학회지
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• 제42권1호
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• pp.58-64
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• 2009

본 연구는 밭토양 내수성입단의 계절별 특성을 밝히고 파쇄프랙탈차원을 이용하여 대공극률과의 관계를 구명코자 수행하였다. 대상 토양은 토성이 다른 세 지점으로 고평통 (Fine, Typic Hapludalfs), 규암통 (Fine silty over coarse silty, Fluvaquentic Eutrudepts), 중동통(Coarse loamy, Typic Udifluvents)으로 경기도에 위치하였다. 봄, 여름, 가을에 불교란 시료를 채취하고 내수성입단과 대공극률, 토양이화학성을 측정하였다. 내수성입단은 파쇄프랙탈차원($D_f$), 기하평균지름(GMD), 중량평균지름(MWD)의 세 가지로 계수화하였다. $D_f$는 MWD보다 GMD와 상관이 높게 나타났고, 무차원의 입단파쇄과정에 근거하여서 실험에 사용한 입단크기와 전처리과정의 영향을 덜 받아 내수성입단의 계수화에 적절하다고 판단할 수 있었다. 계절적으로 내수성입단은 여름>봄>가을순으로 나타났고 생물활성과 토양수분의 영향으로 파악할 수 있었다. $D_f$ 3.1이하의 토양에서 $D_f$와 대공극률과역의 상관관계를 나타냈으며 특히 $99{\mu}m$ 이상의 공극률과 상관이 높았으며 $D_f$ 3.1이상의 토양에서는 상관이 나타나지 않았다. 또한 $D_f$ 3.1이하의 토양에서는 대공극률과 포화수리전도도의 누승함수 적합도가 높게 나타났다. 따라서 내수성입단의 파쇄프랙탈차원은 입단화에 의한 대공극형성과 해석에 유용하다고 판단할 수 있었다.

• Elastomers and Composites
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• 제54권2호
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• pp.156-160
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• 2019

The changes in the dispersion of carbon black in liquid polyisoprene under shear flow with time have been investigated by time-resolved ultra small-angle X-ray scattering (USAXS) method. The analyses of USAXS profile immediately after the start of shear flow clarified that the aggregates of carbon black with a mean radius of gyration of 14 nm and surface fractal dimension of 2.5 form the fractal network structure with mass-fractal dimension of 2.9. After the application of the shear flow, the scattering intensity increases with time at the observed whole entire q region, and then the a shoulder appears at $q=0.005nm^{-1}$, indicating that the agglomerate is broken and becomes smaller by shear flow. The analysis by the Unified Guinier/Power-law approach yielded several characteristic parameters, such as the sizes of aggregate and agglomerate, mass-fractal dimension of agglomerate, and surface fractal dimension of the primary particle. While the mean radius of gyration of the agglomerate decreases with time, the mean radius of gyration of the aggregate, mass fractal dimension, and surface fractal dimension don't change with time, indicating that the aggregates peel off the surface of the agglomerate.