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

• Journal of the Korean Society of Groundwater Environment
• /
• v.4 no.3
• /
• pp.111-115
• /
• 1997

Discrete fracture model has become one of the alternatives for the classical continuum model to simulate the irregular aspects of the fluid flow and the solute transport in fractured rocks. It is based on the assumptions that the discharge in a single fracture is proportional to the cube of the aperture and the fractured rock can be represented by the statistical assemblage of such single fractures. This study is intended to evaluate the effect of the fracture junction on the cubic law. Numerical solution of flow in junction system was obtained by using the Boundary-Fitted Coordinate System (BFCS) method. Results with different intersection angles in crossing fractures show that the geometry of the junction affects the discharge pattern under the same simulation conditions. Therefore, strict numerical and experimental examinations on this subject are required.

• Tunnel and Underground Space
• /
• v.9 no.4
• /
• pp.328-336
• /
• 1999

To characterize the hydro-mechanical behavior of a rock joint, a rotary shear testing apparatus was devised in this study. Shear stress was driven by twisting the end of a sample in the rotary shear testing apparatus. The test results show that the rotary shear test underestimates the peak shear strength of a rock joint. The torque is known as a function of the radial distance from the axis of rotation, resulting in the radial variation of the shear stress. Fluid flow through rock joints is mainly dependent on the Joint roughness, contact area, initial aperture. To examine the dependency, the relationship between the hydraulic and the mechanical apertures for shear-flow was established by measuring the initial aperture. It shows that the mechanical aperture and the hydraulic aperture increase linearly with the dilatancy. The difference between the hydraulic and mechanical apertures describes the deviation from the behavior predicted by the parallel plate model.

• Tunnel and Underground Space
• /
• v.29 no.3
• /
• pp.197-213
• /
• 2019

We simulated the fault reactivation experiment conducted at 'Main Fault' intersecting the low permeability clay formations of Mont Terri Underground Research Laboratory in Switzerland using TOUGH-FLAC simulator. The fluid flow along a fault was modelled with solid elements and governed by Darcy's law with the cubic law in TOUGH2, whereas the mechanical behavior of a single fault was represented by creating interface elements between two separating rock blocks in FLAC3D. We formulate the hydro-mechanical coupling relation of hydraulic aperture to consider the elastic fracture opening and failure-induced dilation for reproducing the abrupt changes in injection flow rate and monitoring pressure at fracture opening pressure. A parametric study was conducted to examine the effects of in-situ stress condition and fault deformation and strength parameters and to find the optimal parameter set to reproduce the field observations. In the best matching simulation, the fracture opening pressure and variations of injection flow rate and monitoring pressure showed good agreement with field experiment results, which suggests the capability of the numerical model to reasonably capture the fracture opening and propagation process. The model overestimated the fault displacement in shear direction and the range of reactivated zone, which was attributed to the progressive shear failures along the fault at high injection pressure. In the field experiment results, however, fracture tensile opening seems the dominant mechanism affecting the hydraulic aperture increase.

• Journal of Soil and Groundwater Environment
• /
• v.8 no.4
• /
• pp.1-11
• /
• 2003

In order to measure aperture variation dependent on normal stress and to characterize on relationship between aperture variation and hydraulic conductivity this study measured apertures of rock fractures under a high resolution confocal laser scanning microscope (CLSM) with application of five stages of uniaxial normal stresses. From this method the response of aperture can be continuously characterized on one specimen by different loads of normal stress. The results of measurements showed a rough geometry of fracture bearing non-uniform aperture. They also revealed different values of aperture variations according to the load stages on each position along a fracture due to the fracture roughness. Laboratory permeability tests were also conducted to evaluate the changes of permeability coefficients related to the aperture variations by different loads. The results of permeability tests revealed that the hydraulic conductivity was not reduced at a fixed rate with increase of normal load. Moreover, the rates of aperture variations did not match to those of hydraulic conductivity. The hydraulic conductivity calculated in this study did not follow the cubic law, representing that the parallel plate model is not suitable to express the fracture geometry corresponding to the results of aperture measurements under the CLSM.

• Tunnel and Underground Space
• /
• v.28 no.5
• /
• pp.400-425
• /
• 2018

This study presents the research results and current status of the DECOVALEX-2019 project Task B. Task B named 'Fault slip modelling' is aiming at developing a numerical method to simulate the coupled hydro-mechanical behavior of fault, including slip or reactivation, induced by water injection. The first research step of Task B is a benchmark simulation which is designed for the modelling teams to familiarize themselves with the problem and to set up their own codes to reproduce the hydro-mechanical coupling between the fault hydraulic transmissivity and the mechanically-induced displacement. We reproduced the coupled hydro-mechanical process of fault slip using TOUGH-FLAC simulator. The fluid flow along a fault was modelled with solid elements and governed by Darcy's law with the cubic law in TOUGH2, whereas the mechanical behavior of a single fault was represented by creating interface elements between two separating rock blocks in FLAC3D. A methodology to formulate the hydro-mechanical coupling relations of two different hydraulic aperture models and link the solid element of TOUGH2 and the interface element of FLAC3D was suggested. In addition, we developed a coupling module to update the changes in geometric features (mesh) and hydrological properties of fault caused by water injection at every calculation step for TOUGH-FLAC simulator. Then, the transient responses of the fault, including elastic deformation, reactivation, progressive evolutions of pathway, pressure distribution and water injection rate, to stepwise pressurization were examined during the simulations. The results of the simulations suggest that the developed model can provide a reasonable prediction of the hydro-mechanical behavior related to fault reactivation. The numerical model will be enhanced by continuing collaboration and interaction with other research teams of DECOLVAEX-2019 Task B and validated using the field data from fault activation experiments in a further study.