• Computers and Concrete
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• 제9권1호
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• pp.1-19
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• 2012

The size-effect study of various fracture parameters obtained from two parameter fracture model, effective crack model, double-K fracture model and double-G fracture model is presented in the paper. Fictitious crack model (FCM) for three-point bend test geometry for cracked concrete beam of laboratory size range 100-400 mm is developed and the different fracture parameters from size effect model, effective crack model, double-K fracture model and double-G fracture model are evaluated using the input data obtained from FCM. In addition, the fracture parameters of two parameter fracture model are obtained using the mathematical coefficients available in literature. From the study it is concluded that the fracture parameters obtained from various nonlinear fracture models including the double-K and double-G fracture models are influenced by the specimen size. These fracture parameters maintain some definite interrelationship depending upon the specimen size and relative size of initial notch length.

• Advances in concrete construction
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• 제2권3호
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• pp.229-247
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• 2014

A numerical study of the influence of shear-span/depth ratio on the cohesive crack fracture parameters and double - K fracture parameters of concrete is carried out in this paper. For the study the standard bending specimen geometry loaded with four point bending test is used. For four point loading, the shear - span/depth ratio is varied as 0.4, 1 and 1.75 and the ao/D ratio is varied from 0.2, 0.3 and 0.4 for laboratory specimens having size range from 100 - 500 mm. The input parameters for determining the double - K fracture parameters are taken from the developed fictitious crack model. It is found that the cohesive crack fracture parameters are independent of shear-span/depth ratio. Further, the unstable fracture toughness of double-K fracture model is independent of shear-span/depth ratio whereas, the initial cracking toughness of the material is dependent on the shear-span/depth ratio.

• Computers and Concrete
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• 제9권2호
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• pp.81-97
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• 2012

This paper presents development of double-K fracture model for the split-tension cube specimen for determining the unstable fracture toughness and initial cracking toughness of concrete. There are some advantages of using of split-tension cube test like compactness and lightness over the existing specimen geometries in practice such as three-point bend test, wedge splitting test and compact tension specimen. The cohesive toughness of the material is determined using weight function having four terms for the split-tension cube specimen. Some empirical relations are also suggested for determining geometrical factors in order to calculate stress intensity factor and crack mouth opening displacement for the same specimen. The results of double-K fracture parameters of split-tension cube specimen are compared with those obtained for compact tension specimen. Finally, the influence of the width of the load-distribution of split-tension cube specimen on the double-K fracture parameters for laboratory size specimens is investigated. The input data required for determining double-K fracture parameters for both the specimen geometries are obtained using well known version of the Fictitious Crack Model.

• Advances in concrete construction
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• 제5권6호
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• pp.613-624
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• 2017

In this paper, an experimental investigation was carried out to study the effect of volume fraction of fiber and maximum aggregate size on mode-I fracture parameters of high strength concrete. Total of 108 beams were tested on loading frame with three point loading, the variables in the high strength concrete beams are aggregate size (20 mm, 16 mm and 10 mm) and volume fraction of fibers (0%, 0.5%, 1% and 1.5%). The fracture parameters like fracture energy, brittleness number and fracture process zone were analyzed by the size effect method (SEM). It was found that fracture energy (Gf) increases with increasing the Maximum aggregate size and also increasing the volume of fibers, brittleness number (${\beta}$) decreases and fracture process zone (CF) increases.

• Advances in concrete construction
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• 제1권4호
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• pp.319-340
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• 2013

This paper presents a comparative study on the double-K fracture parameters of concrete obtained using four existing analytical methods such as Gauss-Chebyshev integral method, simplified Green's function method, weight function method and simplified equivalent cohesive force method. Two specimen geometries: three point bend test and compact tension specimen for sizes 100-500 mm at initial notch length to depth ratios 0.25 and 0.4 are used for the comparative study. The required input parameters for determining the double-K fracture parameters are derived from the developed fictitious crack model. It is found that the cohesive toughness and initial cracking toughness determined using weight function method and simplified equivalent cohesive force method agree well with those obtained using Gauss-Chebyshev integral method whereas these fracture parameters determined using simplified Green's function method deviates more than by 11% and 20% respectively as compared with those obtained using Gauss-Chebyshev integral method. It is also shown that all the fracture parameters related with double-K model are size dependent.

• International Journal of Concrete Structures and Materials
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• 제18권3E호
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• pp.183-189
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• 2006

Many researchers have recently proposed various parameters, variables of models and experimental methods to evaluate fracture properties of concrete, and their developments allow us to analyze the non-linear and quasi-brittle fracture mechanisms. This paper presents a brief treatment of the fracture parameters. Additionally, three-point bending tests were conducted to compare J-integral($J_{Ic}$) with other parameters($K_{Ic},\;G_{Ic},\;and\;G_F$). The change in parameter values with respect to the width and notch length of concrete beam specimens was also considered. The load-displacement curves were used to measure the concrete fracture toughness experimentally. From the results of experiment, it was found that the value of $G_F\;and\;J_{Ic}$ decreased as the notch depth increased and that $G_F$ was less sensitive than $J_{Ic}$. Therefore, the former, $G_F$, is more appropriate in using it as the concrete fracture toughness parameter. The values of $G_F\;and\;J_{Ic}$ increased when the width of concrete specimens increasing from 75 mm to 150 mm. Thus, the effects of the specimen width should be considered in determining the fracture toughness of concrete.

• International Journal of Concrete Structures and Materials
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• 제10권2호
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• pp.163-175
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• 2016

This paper presents a revised procedure for computation of double-K fracture parameters of concrete split-tension cube specimen using weight function of the centrally cracked plate of finite strip with a finite width. This is an improvement over the previous work of the authors in which the determination of double-K fracture parameters of concrete for split-tension cube test using weight function of the centrally cracked plate of infinite strip with a finite width was presented. In a recent research, it was pointed out that there are great differences between a finite strip and an infinite strip regarding their weight function and the solution of infinite strip can be utilized in the split-tension specimens when the notch size is very small. In the present work, improved version of LEFM formulas for stress intensity factor, crack mouth opening displacement and crack opening displacement profile presented in the recent research work are incorporated. The results of the double-K fracture parameters obtained using revised procedure and the previous work of the authors is compared. The double-K fracture parameters of split-tension cube specimen are also compared with those obtained for standard three point bend test specimen. The input data required for determining double-K fracture parameters for both the specimen geometries for laboratory size specimens are obtained using well known version of the Fictitious Crack Model.

• 한국세라믹학회지
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• 제49권4호
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• pp.385-396
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• 2012

Thermal shock test methods and thermal shock parameters for ceramics were reviewed from the following viewpoints: (1) The test methods should be based on the precise estimation of both temperature and thermal stress distributions in a specimen taking into account the temperature-dependent thermo-mechanical properties; (2) The thermal shock parameters must be defined as a physical property of the materials and described as a function of temperature at the fracture point of the specimen; (3) The relation between the strength and fracture toughness of brittle ceramics under a thermal shock load must be the same as the relation under a mechanical load. In addition, appropriate thermal shock parameters should be defined by the thermal shock strength and thermal shock fracture toughness based on stress and energy criteria, respectively. A constant heat flux method is introduced as a testing technique suitable for estimating these thermal shock parameters directly from the electric power charged.

• 자원환경지질
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• 제28권5호
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• pp.503-512
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• 1995

2차원 불연속 절리 모델 (Discrete Fracture Model)을 사용하여 절리망 내에서 지하수 흐름을 시뮬레이션하였다. 불연속 절리 모델에서는 지하수가 오직 절리망을 통해서 흐른다고 가정한다. 이와 같은 분석은 결정질암 같이 지질 매체의 투수율이 매우 낮은 경우에 유용하다. 하지만 불연속 절리망을 완벽하게 구현하는 것이 불가능하므로, 이에 접근하는 방법으로 확률 통계적 모델이 제안되었다. 확률-통계적 모텔은 특성인자(밀도, 방향, 길이, 틈새두께 등)가 특별한 분포 유형을 갖는다고 가정한다. 확률-통계적 모델은 가정된 분포를 따르도록 특성인자를 생성한다. 이 후 본 모델을 통해 분석된 몇몇 특성인자를 가지고 절리망을 생성한다. 절리망을 생성한 이 후 지하수의 유통을 계산하기 위해 유한요소법을 적용하였다. 이 때 일차원 선요소가 유한요소망의 주요 요소이다. 시뮬레이션 결과는 절리망 내의 주요 흐름 경로를 통해 보여진다. 절리망 내의 지하수 속도를 비교하여 주요 흐름 경로를 찾아낸다. 본 연구에서 개발된 모델은 절리망 내의 지하수 흐름에 특성인자들이 미치는 영향을 평가할 수 있는 방법을 제공한다. 이를 위하여 30번의 생성을 하는 몬테카를로 시뮬레이션을 통해서 여러 특성 인자들이 지하수 흐름에 미치는 영향을 평가하였다.

• 한국지반환경공학회 논문집
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• 제10권6호
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• pp.125-133
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• 2009

유체를 주입하여 암반을 파쇄하는 기술은 지열이나 석유 및 가스 등을 추출하는데 널리 사용되고 있는 방법이다. 본 기술을 적용 시 단일균열이 형성되면 이러한 에너지를 추출하는데 가장 이상적이다. 그러나 이러한 단일균열의 형성은 매우 드문 현상이며 분할된 형태의 균열생성이 흔한 현상이다. 이에 균열간 기계적 상호작용의 영향으로 설계변수에서도 단일균열을 가정하고 적용되었던 값과 차이를 보일 것으로 예상된다. 본 연구에서는 균열이 분할 생성되었을 경우 기계적인 상호작용을 고려할 수 있는 수치해석기법을 기존의 개발된 모델과 연계하여 설계변수인 길이, 균열폭, 그리고 압력을 계산하였다. 그 결과 균열의 형성은 이렇게 유체를 주입하여 암반을 파쇄 시 사용되는 설계변수에 상당한 영향을 끼치는 것으로 나타났다.