• Computers and Concrete
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• v.9 no.1
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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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• v.2 no.3
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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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• v.9 no.2
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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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• v.5 no.6
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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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• v.1 no.4
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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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• v.18 no.3E
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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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• v.10 no.2
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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.

• Journal of the Korean Ceramic Society
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• v.49 no.4
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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.

• Economic and Environmental Geology
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• v.28 no.5
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• pp.503-512
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• 1995

Groundwater flow in fracture networks is simulated using a discrete fracture (DF) model which assume that groundwater flows only through the fracture network. This assumption is available if the permeability of rock matrix is very low. It is almost impossible to describe fracture networks perfectly, so a stochastic approach is used. The stochastic approach assumes that the characteristic parameters in fracture network have special distribution patterns. The stochastic model generates fracture networks with some characteristic parameters. The finite element method is used to compute fracture flows. One-dimensional line element is the element type of the finite elements. The simulation results are shown by dominant flow paths in the fracture network. The dominant flow path can be found from the simulated groundwater flow field. The model developed in this study provides the tool to estimate the influences of characteristic parameters on groundwater flow in fracture networks. The influences of some characteristic parameters on the frcture flow are estimated by the Monte Carlo simulation based on 30 realizations.

• Journal of the Korean GEO-environmental Society
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• v.10 no.6
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• pp.125-133
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• 2009

Rock fracturing technique through fluid injection into the wellbore has been widely used to extract geothermal heat and to enhance oil and gas production. Single fracture formation is ideal for the production. However, it is very difficult to form single fracture formation. Instead, the formation of segmented fracture is a common phenomenon. Therefore, design parameters are expected to be different from those of single fracture because of mechanical interaction between segmented fractures. In this paper, design parameters such as length, aperture, and net pressure are evaluated by using model of segmented fracture in which numerical technique is incorporated to consider mechanical interaction between segments. Results show that the existence of fracture segmentation affects design parameters in fracturing treatment in rock by fluid injection.