• Economic and Environmental Geology
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• v.52 no.1
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• pp.81-90
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• 2019

In this study, the effects of fracture tensor component and first invariant on block hydraulic behaviors are evaluated in the 2-D DFN(discrete fracture network) systems. A series of regression analysis is performed between connected fracture tensor components and block hydraulic conductivities estimated at every $30^{\circ}$ hydraulic gradient directions for a total of 36 DFN systems having various joint density and size distribution. The directional block hydraulic conductivity seems to have strong relation with the fracture tensor component estimated in direction perpendicular to it. It is found that an equivalent continuum approach could be acceptable for the 2-D DFN systems under condition that the first invariant of fracture tensor is more than 2.0~2.5. The first invariant of fracture tensor seems highly correlated with average block hydraulic conductivity and can be used to evaluate hydraulic characteristics of the 2-D DFN systems. Also, a possibility of upscaling using the first invariant of fracture tensor for the DFN system is addressed through this study.

• Tunnel and Underground Space
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• v.31 no.1
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• pp.66-81
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• 2021

The effects of directional fracture tensor components and first invariant of fracture tensor on deformation moduli and shear moduli of fractured rock masses is analyzed based on regression analysis performed between 3-D fracture tensor parameters and deformability of DFN blocks. Using one or two deterministic joint sets, a total of 224 3-D discrete fracture network (DFN) cube blocks were generated with various configurations of deterministic density and probabilistic size distribution. The fracture tensor parameters were calculated for each generated DFN systems. Also, deformability moduli with respect to three perpendicular direction of the DFN cube blocks were estimated based on distinct element method. The larger the first invariant of fracture tensor, the smaller the values for the deformability moduli of the DFN blocks. These deformability properties present an asymptotic pattern above the certain threshold. It is found that power-law function describes the relationship between the directional deformability moduli and the corresponding fracture tensor components estimated in same direction.

• Tunnel and Underground Space
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• v.27 no.2
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• pp.100-108
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• 2017

As a measure of the combined effect of fracture geometry, the fabric tensor parameters could quantify the status of the connected fluid flow paths in discrete fracture network (DFN). The correlation analysis between fabric tensor parameters and hydraulic properties of the 2-D DFN was performed in this study. It is found that there exists a strong nonlinear relationship between the directional conductivity and the fabric tensor component estimated in the direction normal to the direction of hydraulic conductivity. The circular radial plots without significant variation of the first invariant ($F_0$) of fabric tensor for different sized 2-D DFN block are a necessary condition for treating representative element volume (REV) of a fractured rock mass. The relative error (ER) between the numerically calculated directional hydraulic conductivity and the theoretical directional hydraulic conductivity decreases with the increase in $F_0$. A strong functional relation seems to exist between the $F_0$ and the average block hydraulic conductivity.

• The Journal of Engineering Geology
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• v.32 no.1
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• pp.41-57
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• 2022

A workflow is presented to estimate the size of a representative elementary volume and 3-D hydraulic conductivity tensor based on fluid flow analysis for a discrete fracture network (DFN). A case study is considered for a Cretaceous granitic rock mass at Gijang in Busan, Korea. The intensity and size of joints were calibrated using the first invariant of the fracture tensor for the 2-D DFN of the study area. Effective hydraulic apertures were obtained by analyzing the results of field packer tests. The representative elementary volume of the 2-D DFN was determined to be 20 m square by investigating the variations in the directional hydraulic conductivity for blocks of different sizes. The directional hydraulic conductivities calculated from the 2-D DFN exhibited strong anisotropy related to the hydraulic behavior of the study area. The 3-D hydraulic conductivity tensor for the fractured rock mass of the study area was estimated from the directional block conductivities of the 2-D DFN blocks generated for various directions in 3-D. The orientations of the principal components of the 3-D hydraulic conductivity tensor were found to be identical to those of delineated joint sets in the study area.

• 한국지구물리탐사학회:학술대회논문집
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• 2003.11a
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• pp.150-155
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• 2003

Fractures in the form of micro cracks are commonly found in natural rocks. A rock behaves in a complex way due to fracture; in particular, the anisotropic strength of a rock material is significantly influenced by the presence of these fractures. Therefore, it is essential to understand the failure mechanism of a fractured rock. In this study, a fractured rock is formulated in terms of fabric tensor based on geometric and mechanical simplifications. In this way, position, density and shape of fractures can be determined by the fabric tensor so that rocks containing multi-fractures can successfully be modeled. Also an index to evaluate the degree of anisotropy of a fractured rock is proposed. Hence, anisotropic strength of a rock containing fractures under uniaxial compression condition is estimated through a series of numerical analyses for the multi-fractured model. Numerical investigations are carried out by varying the fracture angle from $0^{\circ}\;to\;90^{\circ}$ and relationship between uniaxial compression strength and the degree of anisotropy is investigated. By comparing anisotropic strength of numerical analysis with analytic solution, this study attempts to understand the failure mechanism of rock containing fractures.

• Geomechanics and Engineering
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• v.9 no.6
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• pp.793-813
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• 2015

Characterization of discontinuous media is an endeavor that poses great challenge to engineers in practice. Since the inherent defects in cracked domains can substantially influence material resistance and govern its behavior, a lot of work is dedicated to efficiently model such effects. In order to overcome difficulties of material instability problems, one needs to comprehensively represent the geometry of cracks along with their impact on the mechanical properties of the intact material. In the present study, stress-strain results from laboratory experiments on Inada granite was used to derive crack tensor as a tool for the evaluation of fractured domain stability. It was found that the formulations proposed earlier could satisfactorily be employed to attain crack tensor via the invariants of which judgment on cracks population and induced anisotropy is possible. The earlier criteria based on crack tensor analyses were reviewed and compared to the results of the current study. It is concluded that the geometrical parameters calculated using mechanical properties could confidently be used to judge the anisotropy as well as strength of the cracked domain.

• The Journal of Engineering Geology
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• v.10 no.1
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• pp.13-25
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• 2000

A three-dimensional discrete fracture network model based on probabilistic characteristics of fracture geometry and transmissivity was designed to calculate the conductivity tensor and to estimate theanisotropy of conductivity. The conductivities, $K_p$, obtained from the numerical simulation of single-holepacker test corresponded well to those from the field tests. From this, it can be concluded that thefracture network model designed in this study can represent hydraulic characteristics of in-situ fractured rock mass. Block-scale conductivities, $K_b$, estimated from the modelling of steady-state flow through the REV-scale block were ranged between the arithmetic mean and harmonic mean of theconductivity estimates from packer tests. The conductivity along north-south direction was 1.4 timesgreater than that along the east-west direction. It was concluded that the anisotropy of conductivitywas insignificant. It was also found that there was a little correlation between $K_b$ and $K_p$. This would be to that the conductivities from the packer test simulation was strongly dependent on thetransmissivity and the number of fractures within the packer test intervals.

• Tunnel and Underground Space
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• v.25 no.5
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• pp.450-461
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• 2015

Extensive numerical experiments have been carried out to investigate effect of block size and fracture geometry on hydraulic characteristics of fractured rock masses based on connected pipe flow in DFN systems. Using two fracture sets, a total of 72 2-D fracture configurations were generated with different combinations of fracture size distribution and deterministic fracture density. The directional block conductivity including the theoretical block conductivity, principal conductivity tensor and average block conductivity for each generated fracture network system were calculated using the 2-D equivalent pipe network method. There exist significant effects of block size, orientation, density and size of fractures in a fractured rock mass on its hydraulic behavior. We have been further verified that it is more difficult to reach the REV size for the fluid flow network with decreasing intersection angle of two fracture sets, fracture plane density and fracture size distribution.

• International Journal of Aeronautical and Space Sciences
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• v.2 no.2
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• pp.65-72
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• 2001

This paper demonstrates an explicit-implicit, finite element analysis for linear as well as nonlinear hygrothermal stress problems. Additional features, such as moisture diffusion equation, crack element and virtual crack extension(VCE) method for evaluating J-integral are implemented in this program. The Linear Elastic Fracture Mechanics(LEFM) Theory is employed to estimate the crack driving force under the transient condition for an existing crack. Pores in materials are assumed to be saturated with moisture in the liquid form at the room temperature, which may vaporize as the temperature increases. The vaporization effects on the crack driving force are also studied. The ideal gas equation is employed to estimate the thermodynamic pressure due to vaporization at each time step after solving basic nodal values. A set of field equations governing the time dependent response of porous media are derived from balance laws based on the mixture theory. Darcy's law is assumed for the fluid flow through the porous media. Perzyna's viscoplastic model incorporating the Von-Mises yield criterion are implemented. The Green-Naghdi stress rate is used for the invariant of stress tensor under superposed rigid body motion. Isotropic elements are used for the spatial discretization and an iterative scheme based on the full Newton-Raphson method is used for solving the nonlinear governing equations.

• The Journal of Engineering Geology
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• v.21 no.4
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• pp.295-304
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• 2011

The first step in improving our understanding of uncertainties suclt as rock mass strength parameters and deformation modulus in rock masses around high-level radioactive waste disposal repositories, for improved safety, is to study the process of crack development in intact rock. Therefore, in this study, the fracture process and crack development were examined in samples of KURT granite taken from the KAERI Underground Research Tunnel (KURT), based on acoustic emission (AE) and moment tensor analysis. The results show that crack initiation, coalescence, and unstable crack occurred at rock uniaxial compressive strengths of 0.45, 0.73, and 0.84, respectively. In addition, moment tensor analysis indicated that during the early stage of loading, tensile cracks were predominant. With increasing applied stress, the number of shear cracks gradually increased. When the applied stress exceeded the stress level required for crack damage, unstable shear cracks which directly result in failure of the rock were generated along the failure plane.