## Year

2013

## Degree Name

Doctor of Philosophy

## Department

School of Civil, Mining and Environmental Engineering

## Recommended Citation

Zhang, Zhenyu, Hydromechanical behaviour and nonlinear flow characteristics of rock fractures, Doctor of Philosophy thesis, School of Civil, Mining and Environmental Engineering, University of Wollongong, 2013. https://ro.uow.edu.au/theses/3802

## Abstract

Fluid flow through fractured rock occurs in geotechnical, mining and petroleum engineering applications. Engineering concerns for the fields of geotechnical and mining engineering, long-term safety assessment in underground waste storage, et al. have promoted research interest in this discipline. Due to the phenomenon complexity caused by the fracture roughness and flow tortuosity, attempts are still ongoing to improve the understanding of this flow process for geoengineering guidance. In this study, hydraulic behaviour and the flow regime of rock fractures is investigated and a model is proposed to capture the role of fracture roughness and tortuosity in the process of water flow through rough rock fractures.

To fulfil the study of this thesis, the upgrading of the existing triaxial flow testing system was performed by the author at the University of Wollongong. A large triaxial cell was redesigned and fabricated for coupled water flow tests on rock fractures. The issue of air dissolving into the pressurised water inside the water vessel was solved by introducing a new water vessel with an in-built high-strength bladder. Optical laser sensors were introduced to capture the normal deformation of the rock fracture.

With this innovated triaxial flow testing system, the hydraulic behaviour of sandstone, granite and limestone fractures was experimentally investigated with the coupling of normal confining stress. The results show that, for both mated and nonmated fractures, the volumetric flow rate decreases with the increase in the normal stress, but the decreasing trends of the flow rate tend to be smaller under higher confining stress. Due to fracture roughness, the closure of the mechanical aperture is much larger than that of the hydraulic aperture.

Subsequently, the flow regime of water flow through rock fractures was extensively investigated in the laboratory. The results of macroscopic flow tests show that the linear Darcy’s flow occurs for mated rock fractures due to the small aperture, while the nonlinear deviation flow occurs at relatively high Reynolds number in non-mated rock fractures. The analyses show that Izbash’s law can provide an excellent description for this nonlinear flow process as well as the Forchheimer equation. For the first time, the nonlinear factor b of Forchheimer equation was quantified with the increase of normal stress. The nonlinear factor b increases with normal confining stress, indicating that appreciable nonlinear effect occurs at lower volumetric flow rates for rock fracture of smaller true transmissivity. A factor E, which is defined as the ratio of pressure loss dissipated by the nonlinear term of the Forchheimer equation to the total pressure loss, was introduced to determine the critical Reynolds number for the initiation of significant nonlinear flow. The experimental data of both mated and non-mated fracture flow show that the confining stress does not necessarily change the linear and nonlinear flow patterns, however, it has a significant effect on flow characteristics.

The nonlinear flow deviation source was identified by conducting microfluidic flow tests based on advanced microfluidic fabrication technology. With the fluorescence labelling approach, the trajectory of water flow when it passes over the cavity under different flow velocities was captured by the microscope digital camera. The results indicate that the gradual reduction of flow trajectory within the channel adjacent to the cavity and the growth of eddy inside the cavity reflect the evolution of microscopic viscous and inertial forces as flow velocity increases. The eddy formed inside the cavity does not contribute to the total flow flux, but the running of the eddy consumes the flow energy. This amount of pressure loss due to eddies could contribute to the nonlinear deviation of fracture fluid flow from linear Darcy’s law. To understand the flow process in rock fracture, the pressure head loss of water flow through rough rock fractures was studied using the friction factor. Water flow tests were conducted through rock fractures with JRC from 5.5 to 15.4 under changing normal stresses from 0.5 to 3.5 MPa. The friction factor was formulated as a function of two independent variables: Reynolds number and relative roughness. Relative roughness is defined as the ratio of average peak asperity height to the equivalent hydraulic aperture. Sensitivity analyses show that in general, the proposed friction factor increases with the relative roughness of confined fractures. The large difference of friction factor induced by relative roughness occurs when the Reynolds number is lower than unity, especially for Re < 0.2.

Based on the proposed friction factor, an explicit mathematical model was derived for water flow through rock fractures. The model can be regarded as a modified cubic law extended by taking the relative roughness as the correction variable. The comparison of the normalized flow rate predicted by the proposed model and cubic law shows that the error of the predicted value by the model of parallel planar plates can be up to 10% when the relative roughness approaches 63.5, and the normalized flow rate is approximately 64% of the predicted value by cubic law for tight rock fracture with relative roughness up to 300. In order to examine the general suitability of the proposed model, the verification of the proposed friction factor to water flow through granite and limestone fractures was carried out. The results show that the proposed friction factor can describe the experimental data well.

## FoR codes (2008)

0905 CIVIL ENGINEERING

**Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.**