Yi-Feng Chen

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.

Kinetic Energy Dissipation and Convergence Criterion of Discontinuous Deformations Analysis (DDA) for Geotechnical Engineering

The discontinuous deformation analysis (DDA) is a numerical method for modeling discontinuous deformation behaviour of jointed rocks. In this paper, two basic problems are discussed related to kinetic energy dissipation and the convergence criterion for the DDA method when it is applied to geotechnical engineering. In view of the fact that the deformation and progressive failure can be treated as a quasi-static process with low kinetic energy dissipation rates, this paper introduces a viscous damping component to absorb discrete blocks’ kinetic energy, establishes the global equations of motion of the discrete block system that take damping effects into account, investigates the energy dissipation mechanism when solving a static or quasi-static problem, and defines the convergence criteria of displacement, kinetic energy and unbalanced force for DDA solutions when the system arrives at a stable state.

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.

A new classification of seepage control mechanisms in geotechnical engineering

Abstract Seepage flow through soils, rocks and geotechnical structures has a great influence on their stabilities and performances, and seepage control is a critical technological issue in engineering practices. The physical mechanisms associated with various engineering measures for seepage control are investigated from a new perspective within the framework of continuum mechanics; and an equation-based classification of seepage control mechanisms is proposed according to their roles in the mathematical models for seepage flow, including control mechanisms by coupled processes, initial states, boundary conditions and hydraulic properties. The effects of each mechanism on seepage control are illustrated with examples in hydroelectric engineering and radioactive waste disposal, and hence the reasonability of classification is demonstrated. Advice on performance assessment and optimization design of the seepage control systems in geotechnical engineering is provided, and the suggested procedure would serve as a useful guidance for cost-effective control of seepage flow in various engineering practices.

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.

Impact of translation approach for modelling correlated non-normal variables on parallel system reliability

The adequacy of two approximate methods based on incomplete information, namely method P and method S, for constructing multivariate distributions with given marginal distributions and covariance has not been studied systematically. This article aims to study the errors of the method P and method S. First, the method P and method S as well as the exact method are presented. Second, the performance of the two approximate methods is evaluated based on their abilities to match exact solutions for system probabilities of failure. Finally, an illustrative example of a parallel system is investigated to demonstrate the errors associated with the two methods. The results indicate that the errors in system probabilities of failure for the two methods highly depend on the level of system probability of failure, the performance function underlying the system, and the degree of correlation. Such errors increase greatly with decreasing system probabilities of failure. When the target system probability of failure is larger than 1.0E−03, the system probabilities of failure obtained from the two methods and the exact method are of the same order of magnitude. The maximum error in the system probability of failure may not be associated with a large correlation. It can happen at an intermediate correlation.

A generalized multi-field coupling approach and its application to stability and deformation control of a high slope

Human activities, such as blasting excavation, bolting, grouting and impounding of reservoirs, will lead to disturbances to rock masses and variations in their structural features and material properties. These engineering disturbances are important factors that would alter the natural evolutionary processes or change the multi-field interactions in the rock masses from their initial equilibrium states. The concept of generalized multi-field couplings was proposed by placing particular emphasis on the role of engineering disturbances in traditional multi-field couplings in rock masses. A mathematical model was then developed, in which the effects of engineering disturbances on the coupling-processes were described with changes in boundary conditions and evolutions in thermo-hydro-mechanical (THM) properties of the rocks. A parameter, d, which is similar to damage variables but has a broader physical meaning, was conceptually introduced to represent the degree of engineering disturbances and the couplings among the material properties. The effects of blasting excavation, bolting and grouting in rock engineering were illustrated with various field observations or theoretical results, on which the degree of disturbances and the variations in elastic moduli and permeabilities were particularly focused. The influences of excavation and groundwater drainage on the seepage flow and stability of the slopes were demonstrated with numerical simulations. The proposed approach was further employed to investigate the coupled hydro-mechanical responses of a high rock slope to excavation, bolting and impounding of the reservoir in the dam left abutment of Jinping I hydropower station. The impacts of engineering disturbances on the deformation and stability of the slope during construction and operation were demonstrated.

Safety monitoring and stability analysis of left bank high slope at Jinping-I hydropower station

At the Jinping-I hydropower station the excavation height on the slope of the left bank is about 530 m. The stability of the excavated slope is very important because of the complicated geological conditions. To analyse the process of deformation evolution of the left abutment slope during construction, a comprehensive monitoring system was employed, which combined surface deformation observations, multi-point extensometers and graphite rod extensometers. This paper describes this monitoring system and analyses the deformation development with slope excavation. We also established a 3D numerical model of the slope and simulated the whole process of excavation using the finite-difference method. Results from both monitoring and numerical simulation show that the deformation depth in the left bank slope of the Jingping-I hydropower station is over 150 m owing to large-scale excavation unloading, far greater than that of general engineering slopes. The 3D limit equilibrium method and the strength reduction method are applied to evaluate the stability of the excavated slope. The calculated factors of safety indicate that the left abutment slope is stable and safe as a whole, which is in agreement with the deformation monitoring results.

Coupled hydro-mechanical analysis of a dam foundation with thick fluvial deposits: a case study of the Danba Hydropower Project, Southwestern China

The Danba Hydropower Project, located in Danba County, Sichuan Province, China, was planned to be constructed on a thick fluvial deposit foundation, with a maximum depth of the deposits up to 133 m. The loose deposits are characteristic of complex origin, composition, distribution, and mechanical and hydraulic properties. The controls of seepage flow and settlement in the foundation become two key technological issues for construction of the dam. In this study, the coupled processes between groundwater flow and deformation were modelled with the finite element method for performance assessment of the seepage control system and the foundation treatments. The saturated flow process was formulated with an adaptive variational inequality formulation of Signorini’s condition, which eliminates the singularity of the seepage points and the resultant mesh dependency. The deformation response of the loose deposits was described using the Duncan–Chang non-linear elastic E–B model, together with the Goodman interfacial elements for simulation of the soil–structure interactions. The stress-dependent variations in the permeability of the loose deposits were considered on the basis of the Kozeny–Carman’s model. The numerical results indicate that the designed seepage-control structures are effective and the settlement is limited within 20 cm using proper foundation treatments.

Visualizing and quantifying the crossover from capillary fingering to viscous fingering in a rough fracture

Immiscible fluid-fluid displacement in permeable media is important in many subsurface processes, including enhanced oil recovery and geological CO2 sequestration. Controlled by capillary and viscous forces, displacement patterns of one fluid displacing another more viscous one exhibit capillary and viscous fingering, and crossover between the two. Although extensive studies investigated viscous and capillary fingering in porous media, a few studies focused on the crossover in rough fractures, and how viscous and capillary forces affect the crossover remains unclear. Using a transparent fracture-visualization system, we studied how the two forces impact the crossover in a horizontal rough fracture. Drainage experiments of water displacing oil were conducted at seven flow rates (capillary number log10Ca ranging from −7.07 to −3.07) and four viscosity ratios (M=1/1000,1/500,1/100 and 1/50). We consistently observed lower invading fluid saturations in the crossover zone. We also proposed a phase diagram for the displacement patterns in a rough fracture that is consistent with similar studies in porous media. Based on real-time imaging and statistical analysis of the invasion morphology, we showed that the competition between capillary and viscous forces is responsible for the saturation reduction in the crossover zone. In this zone, finger propagation toward the outlet (characteristic of viscous fingering) as well as void-filling in the transverse/backward directions (characteristic of capillary fingering), are both suppressed. Therefore, the invading fluid tends to occupy larger apertures with higher characteristic front velocity, promoting void-filling toward the outlet with thinner finger growth and resulting in a larger volume of defending fluid left behind.