Shao-a Hu

Estimating hydraulic conductivity of fractured rocks from high‐pressure packer tests with an Izbash's law‐based empirical model

High-pressure packer test (HPPT) is an enhanced constant head packer test for characterizing the permeability of fractured rocks under high-pressure groundwater flow conditions. The interpretation of the HPPT data, however, remains difficult due to the transition of flow conditions in the conducting structures and the hydraulic fracturing-induced permeability enhancement in the tested rocks. In this study, a number of HPPTs were performed in the sedimentary and intrusive rocks located at 450 m depth in central Hainan Island. The obtained Q-P curves were divided into a laminar flow phase (I), a non-Darcy flow phase (II), and a hydraulic fracturing phase (III). The critical Reynolds number for the deviation of flow from linearity into phase II was 25−66. The flow of phase III occurred in sparsely to moderately fractured rocks, and was absent at the test intervals of perfect or poor intactness. The threshold fluid pressure between phases II and III was correlated with RQD and the confining stress. An Izbashs law-based analytical model was employed to calculate the hydraulic conductivity of the tested rocks in different flow conditions. It was demonstrated that the estimated hydraulic conductivity values in phases I and II are basically the same, and are weakly dependent on the injection fluid pressure, but it becomes strongly pressure dependent as a result of hydraulic fracturing in phase III. The hydraulic conductivity at different test intervals of a borehole is remarkably enhanced at highly fractured zone or contact zone, but within a rock unit of weak heterogeneity, it decreases with the increase of depth.

Micromechanical Modeling of Anisotropic Damage-Induced Permeability Variation in Crystalline Rocks

This paper presents a study on the initiation and progress of anisotropic damage and its impact on the permeability variation of crystalline rocks of low porosity. This work was based on an existing micromechanical model considering the frictional sliding and dilatancy behaviors of microcracks and the recovery of degraded stiffness when the microcracks are closed. By virtue of an analytical ellipsoidal inclusion solution, lower bound estimates were formulated through a rigorous homogenization procedure for the damage-induced effective permeability of the microcracks-matrix system, and their predictive limitations were discussed with superconducting penny-shaped microcracks, in which the greatest lower bounds were obtained for each homogenization scheme. On this basis, an empirical upper bound estimation model was suggested to account for the influences of anisotropic damage growth, connectivity, frictional sliding, dilatancy, and normal stiffness recovery of closed microcracks, as well as tensile stress-induced microcrack opening on the permeability variation, with a small number of material parameters. The developed model was calibrated and validated by a series of existing laboratory triaxial compression tests with permeability measurements on crystalline rocks, and applied for characterizing the excavation-induced damage zone and permeability variation in the surrounding granitic rock of the TSX tunnel at the Atomic Energy of Canada Limited’s (AECL) Underground Research Laboratory (URL) in Canada, with an acceptable agreement between the predicted and measured data.

The Friction Factor in the Forchheimer Equation for Rock Fractures

The friction factor is an important dimensionless parameter for fluid flow through rock fractures that relates pressure head loss to average flow velocity; it can be affected by both fracture geometry and flow regime. In this study, a theoretical formula form of the friction factor containing both viscous and inertial terms is formulated by incorporating the Forchheimer equation, and a new friction factor model is proposed based on a recent phenomenological relation for the Forchheimer coefficient. The viscous term in the proposed formula is inversely proportional to Reynolds number and represents the limiting case in Darcy flow regime when the inertial effects diminish, whereas the inertial term is a power function of the relative roughness and represents a limiting case in fully turbulent flow regime when the fracture roughness plays a dominant role. The proposed model is compared with existing friction factor models for fractures through parametric sensitivity analyses and using experimental data on granite fractures, showing that the proposed model has not only clearer physical significance, but also better predictive performance. By accepting proper percentages of nonlinear pressure drop to quantify the onset of Forchheimer flow and fully turbulent flow, a Moody-type diagram with explicitly defined flow regimes is created for rock fractures of varying roughness, indicating that rougher fractures have a large friction factor and are more prone to the Forchheimer flow and fully turbulent flow. These findings may prove useful in better understanding of the flow behaviors in rock fractures and improving the numerical modeling of non-Darcy flow in fractured aquifers.

Effect of seepage control on stability of a tailings dam during its staged construction with a stepwise-coupled hydro-mechanical model

Seepage flow renders tailings dams vulnerable to failure during their staged construction. Draining is one of the most effective measures in improving dam stability. In this study, a stepwise-coupled hydro-mechanical model is employed to examine the effect of seepage control on the stability of a tailings dam during its staged construction. The settlement and deformation of the tailings under gravity load are modelled using the Duncan–Chang non-linear elastic E–B model, and the seepage flow through the tailings with drains is characterised by a variational inequality formulation of Signorini’s condition. The Kozeny–Carman equation is calibrated to illustrate the dependence of hydraulic conductivity on the porosity and volumetric deformation of the tailings. The proposed model was applied to assess the performance of the drains designed for the Luogou tailings disposal in Luanchuan County, Henan Province, China. Numerical results show that the stress-induced variation in tailings permeability could be of 1–2 orders of magnitude, and a proper design of the drainage system is of great importance in lowering the phreatic surface and protecting the tailings from seepage erosion.