• Tunnel and Underground Space
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• v.13 no.5
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• pp.389-396
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• 2003

It is shown that the cubic law can be modified regarding the steady-state Navier-Stokes equations by using perturbation approximation method for a sinusoidal aperture variation. In order to adopt the perturbation theory, the sinusoidal function needs to be non-dimensionalized for the amplitude and wavelength. Then, the steady-state Navier-Stokes equations can be solved by expanding the non-dimensionalized stream function with respect to the small value of the parameter (the ratio of the mean aperture to the wavelength), together with the continuity equation. From the approximate solution of the Navier-Stokes equations, the basic cubic law is successfully modified for the steady-state condition and a sinusoidal aperture variation. A finite difference method is adopted to calculate the pressure within a fracture model, and the results of numerical experiments show the accuracy and applicability of the modified cubic law. As a result, it is noted that the modified cubic law, suggested in this study, will be used for the analysis of fluid flow through aperture geometry of sinusoidal distributions.

• Economic and Environmental Geology
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• v.52 no.4
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• pp.291-297
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• 2019

Fluid flow through rock fractures has been quantified using equations such as Stokes equations, Reynolds equation (or local cubic law), cubic law, etc. derived from the Navier-Stokes equations under the assumption that linear flow prevails. Therefore, these simplified equations are limited to linear flow regime, and cause errors in nonlinear flow regime. In this study, causal mechanism of nonlinear flow and critical Reynolds number were presented by carrying out fluid flow modeling with both the Navier-Stokes equations and the Stokes equations for a three-dimensional rough-walled rock fracture. This study showed that flow regimes changed from linear to nonlinear at the Reynolds number greater than 10. This is because the inertial forces, proportional to the square of the fluid velocity, increased enough to overwhelm the viscous forces. This tendency was also shown for the unmated (slightly sheared) rock fracture. It was found that nonlinear flow was caused by the rapid increase in the inertial forces with increasing fluid velocity, not by the growing eddies that have been ascribed to nonlinear flow.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2004.09a
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• pp.159-163
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• 2004

This study was conducted to calculate the permeability coefficient in a single fracture while taking the true fracture geometry into consideration. The fracture geometry was measured using the confocal laser scanning microscope (CLSM). The CLSM geometry data were used to reconstruct a fracture model for numerical analysis using a homogenization analysis (HA) method. The HA is a new type of perturbation theory developed to characterize the behavior of a micro-inhomogeneous material that involves periodic microstructures. The HA permeability was calculated based on the local geometry and local material properties (water viscosity in this case). The results show that the permeability coefficients do not follow the theoretical relationship of the cubic law.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2005.10a
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• pp.191-192
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• 2005

• Journal of the Korean Vacuum Society
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• v.1 no.1
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• pp.88-95
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• 1992

Abstract-Using a high resolution low energy electron diffraction(HRLEED), we report an exponent study of 2d continuous phase transition from an ordered ~ ( 2 x 1 )ox ygen overlayer on a W(110) surface. Temperature dependence of a (% 0) superlattice diffraction spot, characteristic of the p(2X 1) structure, shows power-law like divergence of the susceptibility and the fluctuation correlation length at T,=708.765 K. By fitting the intensities as well as the line-shapes, we obtained exponents P=0.19* 0.05, y=1.48+ 0.34, v= 1.23i 0.27 and q=0.38+ 0.12. The non-universal character of the exponents are understood in terms of a 2d XY model with cubic anisotropy as suggested previously.

• Nuclear Engineering and Technology
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• v.42 no.1
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• pp.9-16
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• 2010

Experimental examinations for evaluating fracutres were conducted by using transparent replicas of a single fracture in order to obtain the fracture data to contribute to the methodlogy on how to improve the definitaion of representative parameter values used for a parallel plate fracture model. Quantitative aperture distribution and quantitative tracer concentration data at each point in time were obtained by measuring the attenuation of transmitted light through the fracture in high spatial resolution. the representative aperture values evaluated from the multiple different measurement methods, such as arithmetic mean of aperture distribution measured by the optical method, transport aperture evaluated from the tracer test, and average aperture evaluated from the fracture void volume measurement converged to a unique value that indicates the accuracy of this experimental study. The aperture data was employed for verifying the numerical simulation under the assuption of Local Cubic Law and showed that the calculated flow rate through the fracture is 10%-100% larger than hydraulic test results. The quantitative tracer concentration data is also very valuable for validating existing numerical code for advection dispersion transport in-plane heterogeneous fractures.

• Geomechanics and Engineering
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• v.22 no.5
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• pp.375-384
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• 2020

In this study, the application of conventional cubic law to a deep depth condition was experimentally evaluated. Moreover, a modified equation for estimating the rock permeability at a deep depth was suggested using precise hydraulic tests and an effect analysis according to the vertical stress, pore water pressure and fracture roughness. The experimental apparatus which enabled the generation of high pore water pressure (< 10 MPa) and vertical stress (< 20 MPa) was manufactured, and the surface roughness of a cylindrical rock sample was quantitatively analyzed by means of 3D (three-dimensional) laser scanning. Experimental data of the injected pore water pressure and outflow rate obtained through the hydraulic test were applied to the cubic law equation, which was used to estimate the permeability of rock fracture. The rock permeability was estimated under various pressure (vertical stress and pore water pressure) and geometry (roughness) conditions. Finally, an empirical formula was proposed by considering nonlinear flow behavior; the formula can be applied to evaluations of changes of rock permeability levels in deep underground facility such as nuclear waste disposal repository with high vertical stress and pore water pressure levels.

• The Korean Journal of Air & Space Law and Policy
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• v.21 no.1
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• pp.7-27
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• 2006

When cadastre system was first introduced in Korea, we only uses the surface of the land and thus its form was very simple. Nowadays on account of the development of architectural technology, the rapid expansion of population and urbanization, the cubic utilization of land including the land usage of underground and surface space is widely settled. This article studies the function of cadastre and public notice to encourage cubic utilization of the land, argues the necessity of 3D-cadastre system to protect property right, and suggests the GPS land measurement as a possible measure.

• Journal of the Korean Ceramic Society
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• v.22 no.3
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• pp.25-28
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• 1985

The new compound $(Ba_{0.5}La_{0.5}) (Mg_0.5}Mo_{0.5})O_3$ is synthesized under the $H_2$-atmosphere and reveals to have a cation ordering between Mg and Mo in cubic lattic of ordered perovskite (a0=8.009(2)$\AA$) and obeys Curie-Weiss law below the room temperature with the effective magnetic moment of 1.60(5) Bohr Magneton.

• Bulletin of the Korean Chemical Society
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• v.15 no.5
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• pp.390-393
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• 1994

Details on the electrochemical formation of lead dioxide from aqueous plumbous ion are studied by measuring current-time behavior with potential step method at a rotating platinum electrode. A cubic law without induction period can be applied to the crystallization of lead dioxide in both acetate and nitrate media. In the course of the mechanistic study, the presence of a soluble intermediate during the nucleation step is clearly observed with a rotating ring-disk electrode. Decrease in the anodic ring current due to the reduction of soluble species formed during the anodic crystallization of lead dioxide at disk is detected.