• 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.

• Journal of the Korean Geotechnical Society
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• v.36 no.12
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• pp.125-132
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• 2020

Embedded joints in the rock mass are a major constituent influencing its mechanical behavior. Numerical analysis requires a rigorous modeling methodology for the rock mass with detailed information regarding joint properties, orientation, spacing, and persistence. This paper provides a mechanical model for a jointed rock mass based on the implicit joint-continuum approach. Stiffness tensors for rock mass are evaluated for an assemblage of intact rock separated by sets of joint planes. It is a linear summation of compliance of each joint sets and intact rock in the serial stiffness system. In the application example, kinematic analysis for a planar failure of rock slope is comparable with empirical daylight envelope and its lateral limits. Since the developed implicit joint-continuity model is formulated on a continuum basis, it will be a major tool for the numerical simulations adopting published plenteous thermal-hydro-chemical experimental results.

• Economic and Environmental Geology
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• v.50 no.1
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• pp.61-71
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• 2017

The effects of joint density and size distribution on the hydrogeologic characteristics of jointed rock masses are addressed through numerical experiments based on the 2-D DFN (discrete fracture network) fluid flow analysis. Using two joint sets, a total of 51 2-D joint network system were generated with various joint density and size distribution. Twelve fluid flow directions were chosen every $30^{\circ}$ starting at $0^{\circ}$, and total of 612 $20m{\times}20m$ DFN blocks were prepared to calculate the directional block conductivity. Also, the theoretical block conductivity, principal conductivity tensor and average block conductivity for each generated joint network system were determined. The directional block conductivity and chance for the equivalent continuum behavior of the 2-D DFN system were found to increase with the increase of joint density or size distribution. However, the anisotropy of block hydraulic conductivity increases with the increase of density discrepancy between the joint sets, and the chance for the equivalent continuum behavior were found to decrease. The smaller the intersection angle of the two joint sets, the more the equivalent continuum behavior were affected by the change of joint density and size distribution. Even though the intersection angle is small enough that it is difficult to have equivalent continuum behavior, the chance for anisotropic equivalent continuum behavior increases as joint density or size distribution increases.

• Economic and Environmental Geology
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• v.49 no.1
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• pp.31-41
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• 2016

A program code was developed to calculate block hydraulic conductivity of the 2-D DFN(discrete fracture network) system based on equivalent pipe network, and implemented to examine the effect of joint orientation distribution on the hydraulic characteristics of fractured rock masses through numerical experiments. A rock block of size $32m{\times}32m$ was used to generate the DFN systems using two joint sets with fixed input parameters of joint frequency and gamma distributed joint size, and various normal distributed joint trend. DFN blocks of size $20m{\times}20m$ were selected from center of the $32m{\times}32m$ blocks to avoid boundary effect. Twelve fluid flow directions were chosen every $30^{\circ}$ starting at $0^{\circ}$. The directional block conductivity including the theoretical block conductivity, principal conductivity tensor and average block conductivity were estimated for generated 180 2-D DFN blocks. The effect of joint orientation distribution on block hydraulic conductivity and chance for the equivalent continuum behavior of the 2-D DFN system were found to increase with the decrease of mean intersection angle of the two joint sets. The effect of variability of joint orientation on block hydraulic conductivity could not be ignored for the DFN having low intersection angle between two joint sets.

• Tunnel and Underground Space
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• v.23 no.6
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• pp.493-505
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• 2013

This numerical study investigates seismicity and fault slip induced by fluid injection in deep geothermal reservoir with pre-existing fractures and fault. Particle Flow Code 2D is used with additionally implemented hydro-mechanical coupled fluid flow algorithm and acoustic emission moment tensor inversion algorithm. The output of the model includes spatio-temporal evolution of induced seismicity (hypocenter locations and magnitudes) and fault deformation (failure and slip) in relation to fluid pressure distribution. The model is applied to a case of fluid injection with constant rates changing in three steps using different fluid characters, i.e. the viscosity, and different injection locations. In fractured reservoir, spatio-temporal distribution of the induced seismicity differs significantly depending on the viscosity of the fracturing fluid. In a fractured reservoir, injection of low viscosity fluid results in larger volume of induced seismicity cloud as the fluid can migrate easily to the reservoir and cause large number and magnitude of induced seismicity in the post-shut-in period. In a faulted reservoir, fault deformation (co-seismic failure and aseismic slip) can occur by a small perturbation of fracturing fluid (<0.1 MPa) can be induced when the injection location is set close to the fault. The presented numerical model technique can practically be used in geothermal industry to predict the induced seismicity pattern and magnitude distribution resulting from hydraulic stimulation of geothermal reservoirs prior to actual injection operation.

• 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.