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An in-situ thermo-hydraulic experiment at the URL
Senjuntichai, Teerapong (University of Minnesota) | Detournay, Emmanuel (University of Minnesota) | Berchenko, Ilya (University of Minnesota) | Chandler, Neil (Atomic Energy of Canada Limited, Whiteshell Laboratories) | Martino, Jason (Atomic Energy of Canada Limited, Whiteshell Laboratories) | Kozak, Ed (Atomic Energy of Canada Limited, Whiteshell Laboratories)
ABSTRACT: This paper is concerned with an in situ thermo-hydraulic experiment carried out at the Underground Research Laboratory of Atomic Energy of Canada Limited. The thermo-hydraulic experiment was designed to determine a hydro-thermal coupling parameter as well as the permeability and the thermal and hydraulic diffusivities of the Lac du Bonnet granite. Several water injection and heater tests were conducted during this experiment. In an injection test, a given volume of water is pumped quasi instantaneously in a sealed-off interval of the borehole, while in a heater test, heat is produced at a constant rate over a certain period (ranging from about one day to several weeks). The experimental set-up involves a heater installed in a sub-horizontal borehole drilled from an underground gallery, and piezometers and thermistors located at different distances from the heater, in auxiliary boreholes drilled from an adjacent gallery. Determination of the material parameters relies on matching the measured pore pressure and temperature responses with the theoretical predictions based on singular solutions of thermoporoelasticity. INTRODUCTION Various geological structures, including thick clay layers, salt domes and hard rock, are being con- sidered in various countries to host nuclear waste repositories. The research described in this paper is associated with the Canadian used fuel program, which is focusing on developing technical capa- bility for the siting, design and safety assessment of a repository in a saturated granitic rock mass. One facility developed in the Canadian Nuclear Fuel Waste Management Program is Atomic En- ergy of Canada Limited's (AECL's) Underground Research Laboratory (URL), in southeastern Man- itoba, Canada. The geological setting of the URL is unique compared to other underground labora- tories in the world because the rock mass of the Lac du Bonnet batholith is essentially ,manufactured below 250 to 300 m depth ?. The Thermal-Hydranlic Experiment (abbrevi- ated to TI?) conducted at the URL included a series of water injection and heater tests. The main objective of TI? is to determine the in situ value of a hydro-thermal coupling parameter (7), characterizing the magnitude of the pore pressure induced by thermal loading, as well as the perme- ability (n) and the thermal (c.) and hydraulic (c) diffusivities of the Lac du Bonnet granite. In this paper, the experimental set-up of THE as well as some results from a back-analysis of the experiments are presented. These results are ob- tained by matching the time and the amplitude of the peak of the pore pressure and tempera- ture responses with theoretical predictions based on the singular thermoporoelastic solutions of a fluid source and a heat source. The analysis pre- sented in this paper is a follow-up of the prelimi- nary results discussed by Berchenko et al. (1998).
- North America > Canada (0.75)
- North America > United States (0.46)
- Geology > Geological Subdiscipline > Geomechanics (0.79)
- Geology > Rock Type > Igneous Rock > Granite (0.45)
- Reservoir Description and Dynamics > Reservoir Characterization > Reservoir geomechanics (0.79)
- Reservoir Description and Dynamics > Reservoir Characterization > Exploration, development, structural geology (0.54)
- Production and Well Operations > Well & Reservoir Surveillance and Monitoring > Production logging (0.49)
Propagation of a penny-shape hydraulic fracture in an impermeable rock
Savitski, Alexei (University of Minnesota) | Detournay, Emmanuel (University of Minnesota)
ABSTRACT: This paper deals with the self-similar solution of a penny-shape hydraulic fracture propa- gating in an impermeable elastic rock. Growth of the fracture is driven by injection of an incompressible Newtonian fluid at the center of the fracture, at a flow rate varying according to a power law of time (which includes the practically important case of a constant injection rate). The solution is restricted to the so-called viscosity-dominated regime where it can be assumed that the rock has zero toughness. In this regime, the fracture tip is characterized by a singularity which is weaker than the classical square root singularity of linear elastic fracture mechanics. The paper describes the construction of a semi- analytical similarity solution, which incorporates the known singularity of the fluid pressure at the center of the fracture and at the tip and which is based on series expansions of the fracture opening and fluid pressure in terms of Jacobi polynomials. It is shown that very few terms in the expansions are needed to capture the solution accurately. INTRODUCTION Mathematical modeling of hydraulic fractures has attracted numerous contributions since the 1950's. While early efforts dealt mainly with (approxi- mate) analytical solutions (see e.g. Khristianovic and Zheltov, 1955; Barenblatt, 1962; Perkins and Kern, 1961; Nordgren, 1972; Geerstma and Haaf- kens, 1979), the focus of researchas shifted in re- cent years towards the development of numerical algorithms to model the three-dimensional propa- gation of hydraulic fractures in layered strata char- acterized by different mechanical properties and/or in-situ stresses (e.g. Clifton and Abou-Sayed, 1979; Advani et al., 1990, Sousa et al., 1993; Shah et al., Despite this trend towards the development of realistic models of hydraulic fractures, there is still interest in obtaining "exact" solutions for simpler models with rigorous consideration given to both the flow of fluid in the fracture (generally modeled according to the lubrication theory) and the elas- tic deformation and propagation of the fracture. Such solutions can be used not only to benchmark numerical codes but also to explore the depen- dance of the solution to various parameters and to establish the existence of different regimes of propagation. These solutions are notoriously dif- ficult to construct, however, because of the strong non-linear coupling between the lubrication and elasticity equations and the non-local character of the elastic response of the fracture. Within the realm of "simple" models for hy- draulic fracturing, the penny-shape fracture is guably the most relevant one. Yet it has been treated by an handful of authors only (e.g. Baren- blatt, 1959; Abe et al., 1976; Abe et al., 1979; Cleaxy and Wong, 1985; Nilson et al., 1985; Ad- vani et al., 1987; Barr, 1991; de Pater et al., 1996; Yuan, 1997). Furthermore, no rigorous analytical (or semi-analytical) solution of this problem ex- ists to our knowledge, as published analytical so- lutions are based on approximations involving ad hoc forms of the fluid pressure or the crac? aper- ture. This paper deals with the construction of a semi-analytical solution for the problem of a penny- shape crack propagating in an unbounded imper- meable elastic medium, see Fig. 1. The fracture is driven by an incompressible Newtonlan fluid in- jected at the center of the fracture. As discussed in the paper, the injection flow rate is restricted to a power law of time, which includes, however, the practically important case of a constant flow rate.
Size effects in fracture of rock
Labuz, Joseph F. (University of Minnesota) | Biolzi, Luigi (Politecnico di Milano)
INTRODUCTION ABSTRACT: The fracture of rock is influenced by the development of an intrinsic process zone in the form of a localized region of microcracking. This zone has a fundamental importance for defining the system behavior in terms of the post-peak instability and in terms of material strength such that size effects appear. This paper illustrates the change in the load-displacement response and presents evidence of the process- zone development with varying specimen size. It is demonstrated that fracture problems do not require geometric or material nonlineaddty to produce instability. The size of a structure that fails by fracture is an important factor. Further more, experiments suggest that an intrinsic zone develops in rock as a material characteristic. Because of this intrinsic length, two competing factors define the nominal strength---the positive contribution of the process zone and the depleting aspects of the undamaged volume, that is, the size. Experiments on rock may exhibit behavior quite different for specimens of various size. This leads to the problems of interpreting test results, generalizing their significance, and identifying materials properties. For example, in rock-like mateddais, the nominal strength and the global response of a given geometry and load configuration are dependent on size (Bazant 1993). Due to the existence of a localized zone of microcracking, a specimen composed of rock may fail at a stress quite differenthan that shown by another specimen size. Conversely, for elastic- brittle and elasto-plastic materials, experiments and stress analysis indicate no dependence on scale: specimens of different sizes fail at the same maximum stress and in the same manner. An explanation for size effect was first offered by Weibull 0939)using a statistical argument. He showed that the strength of a material is a function of the volume of the specimen through the application of the weakest link concept. As explained by Bazant & Xi 0990, however, the Weibull theory may be inadequate because it ignores the stress distributions due to localized damage (the intrinsic process zone) prior to maximum stress. Extensive evidence is available from direct or indirect tensile tests indicating that the apparent or nominal strength is size dependent (Gluckiich & Cohen 1967; Hardy et al. 1973; Swan 1980; Bazant & Kazemi 1990). For uniaxial compression, Millard et al. (1955) and Evans & Pommeroy (1958) experimentally observed a strong correlation between size and strength, and suggested a relation in the form [Equation available in full paper](1) where o? is the nominal strength, k and n are constants, and a is the length of the cubic specimen, a characteristic size of the structure. Millard et al. noted that n on the order of 0.5 is expected if existing crack lengths are proportional to the sides of the cubic specimens. It is evident from experimental observations of rock (Zietlow & Labuz 1998) that an analysis of the structural behavior and in particular, an evaluation of the nominal strength requires a knowledge of the evolution of microcracking as a function of applied loads. Among the methods used to examine development of microcracks within a test specimen is the acoustic emission (AE) technique (for instance, Shah & Labuz 1995), which is based on the recording of transient elastic waves resulting from the sudden release of energy due to microcracking. The locations of AE close to peak load can define the region of localized damage prior to a visible fracture.
Static and dynamic loads in ore and waste rock passes in underground mines
Beus, M. (National Institute for Occupational Safety and Health) | Iverson, S.R. (National Institute for Occupational Safety and Health) | Dreschler, A. (University of Minnesota) | Scott, V. (University of Minnesota)
ABSTRACT: This paper describes research to improve safety during transport of ore and waste in underground mines. Field tests are underway in mines in Idaho and Montana. Strains measured on structural support members in an ore pass provided information aboutotal forces acting on the structure as material was dumped into it. Results show that measured static loads were considerably less than actual total weight of the material dumped and that dynamic loads were subject to many factors, such as effects of blasting to remove hang-ups. Comparisons of measurements and computeresults using a particle flow code indicated that several difficulties remain before achieving realistic determinations and models of the dynamic effects of particle flow in ore passes and impact loads on the gates. Impact loads were overestimated in computer analyses as compared to loads measured in field tests. An alternative design approach based on softening the chute and control gate assembly is being proposed. INTRODUCTION Hazards related to the operation of ore and waste rock passes have been identified as a significant safety problem in underground metal mines in the United States. Such hazards include structural failures, blocked gates, and water flow. Specifically, ore or waste rock hang-ups can collapse spontaneously or during freeing operations; the sudden release of hangups is the single most important cause of serious accidents. The dynamic loads induced by large falling blocks of ore or waste rock can weaken the chute and gate structure. Blocked gates can result in spillage of large volumes of material. Damage can also be caused from an air blast as material is released. Water flowing into an ore pass can result in catastrophic muck flows and inundation. Existing design standards for ore passes are essentially rules-of-thumb based on simplified equilibrium analyses, model experiments, empirical observations and experience. This approach tends to assign high safety factors to the chute and gate structure so it can withstand excessive static and dynamic loads. Ore pass design has structural and functional components, with one affecting the other and vice versa. The structural components are ore pass walls, liners, timber lagging, and chutes and gates, which control the flow of material. The functional component is concerned with the flow, or lack thereof (hang-ups), of ore and waste. Important structural design factors are the static and dynamic loads that ore pass chutes and gates must withstand. Blight et al. (1994) conducted tests on model underground ore passes to determine factors associated with static gate pressure and dynamic loads. The effects of ore pass length, inclination, and the presence or absence of doglegs, which absorb impacts from the release of hang-ups, were determined. The results indicated minimal change in static load when the material column exceeded a depth about 1 m above the gate, and that total static load and dynamic load factors decreased significantly when the inclination was less than 70øi They also found thathe presence of a dogleg had little effect on the static gate, and that peak impact loads could exceed four times the static load in vertical or near-vertical ore passes. Their conclusions were that static loads on the gate of an ore pass could be predicted accurately using equations developed by Janssen (1895) for vertical or inclined silos.
- North America > United States > Montana (0.25)
- North America > United States > Idaho (0.25)
- Materials > Metals & Mining (1.00)
- Energy > Oil & Gas > Upstream (0.87)
Discrete element modelling of rock cutting
Huang, Haiying (University of Minnesota) | Detournay, Emmanuel (University of Minnesota) | Bellier, Benoit (University of Minnesota)
INTRODUCTION ABSTRACT: The paper deals with a numerical analysis of rock cutting experiments using the discrete element method. The main objective of this research is to establish if the occurence of the two failure modes observed in rock cutting experiments (ductile at small depth of cut, brittle at large depth) can be duplicated in numerical simulation. The numerical analysis is carried out with the discrete element code PFC ?v which modelsolids as a collection of bonded disks. Scaling laws are first established between the micro-properties at the particle scale (such as the mean particle radius, and bond strengths) and the apparent material properties at the macroscopic scale (such as the compressive strength ac and the toughness Kxc). Cutting tests are then performed with a particle assembly of rock-like properties. The paper deaJs with a numerical analysis of rock cutting experiments in which rock is scratched by a cutter at a constant velocity and at a prescribed depth of cut. The objective of this preliminary study is to establish whether or not results obtained in laboratory rock experiments can be duplicated in numerical simulations. Cutting experiments carried out with the Rock Strength Device developed at the University of Minnesota have shown that two failure modes can occur depending on the depth of cut: (i) a ductile mode associated with plastic flow of failed rock ahead of the cutting face at small depth of cut (larger than the grain size and typically less than i mm in sandstones) and (ii) a brittle mode associated with fracture propagation and chipping of the rock at the depth of cut above a certain threshold (Richard et al., 1998). The transition depth of cut between the two failure modes appears to be related to the length scale (KIC/óc) ?, where KIC is the rock toughness and ac the uniaxial compressive strength. Furthermore, there is a large body of evidence to suggest that the average cutting force in the duct fie mode is proportional to the crosssectional area of the cut (i.e. to the depth of cut for a rectangular cutter) and that the coefficient of proportionality (referred to as the specific energy e) is itself proportional to óc In this study, the rock cutting process is investigated using the discrete element method, based on the approach by Cundall & Strack (1979) and Cundall & Hart (1993). The discrete element code PFC 2D (Itasca Consulting Group, 1996), is employed in the analysis. This code models solids as a collection of distinct and arbitrarily sized circular particles. The particles are treated as rigid bodies and allowed to overlap one another at the contact points. The contacts between particles are characterized through the stiffness, slip condition, and bonding models. The constitutive behavior of the particles enables the simulation of both plasticity and fracture at the macroscale. As a prerequisite to realistically represent rock-like materials by a particle assembly, scaling laws are first established between the micro-properties at the particle scale and the apparent material properties at the macroscopic scale. Numerical simulations on rock cutting experiments with a sharp cutter (no wear fiat) are then carried out to establish the existence of two failure modes in relation to the depth of cut, and to investigate the influence of material parameters on the transition depth of cut and on the magnitude of the cutting force.