ABSTRACT: Numerical simulations of hydraulic micro-fractures are used to provide insight into techniques commonly used for stress measurement at depth. These simulations encompass initiation and propagation of hydraulic fractures from a borehole in poroelastic rock. It is shown that poroelastic effects may have a significant influence on the determination of the principal stresses in permeable rock. Specifically, it is found that (1) the breakdown pressure is not necessarily associated with the fracture initiation at a borehole, (2) the time of fracture closure can be identified from borehole pressure logs and (3) poroelastic effects can cause the borehole pressure at the time of fracture closure to markedly exceed the minimum in-situ stress
There has been a considerable effort directed towards practical development of techniques for in-situ stress measurement using hydraulic fracturing. However, there have been relatively few detailed simulations of these processes [2 ,3]. A series of simulations of hydraulic fracturing tests is presented. Here it is assumed that the rock mass is a poroelastic material. This assumption requires that the following phenomena be treated as fully coupled: (1) the fluid flow in the fracture,( 2) the deformation of the rock mass, and (3) the fluid flow in the rock. Treatment of the rock in this manner is a unique feature of the simulations presented herein.
A detailed description of the numerical procedure used in these simulations can be found in Ref. 4. Its salient characteristics are as follows: (1) the finite element method is used to approximate the fully coupled poroelastic solution for deformation and fluid flow in the rock mass, (2) a finite-difference approximation is used to model the fluid flow in the fractures, and (3) a generalized Dugdale-Barenblatt fracture model is incorporated as a natural product of the solution procedure. This fracture model allows the crack length to increase or decrease through the course of the simulation so that events related to shut-in and fracture closure can be investigated.
The results of these simulations are presented in the next section. In the third section, their significance is described and discussed with reference to published experimental and field data.
2. A SIMULATION OF FRACTURE INITIATION, PROPAGATION, AND CLOSURE IN POROELASTIC ROCK.
Hydraulic fracturing for the purpose of stress measurement involves the following: (1) pressurization of a borehole until a fracture is initiated; (2) controlled flow of fluid into the borehole to propagate the fracture a short distance; and (3) shut-in or cessation of the flow into the borehole, followed by monitoring of the pressure decline.
Figure1 . The finite element mesh used in the simulation of a series of hydraulically driven fractures in poroelastic rock. The fracture is constrained to propagate along the x-axis. (available in full paper)
The crack-mouth-pressure (CMP) versus time curve is then used to deduce the in-situ stress state. In this section, results are presented for detailed simulations of initiation and propagation of a hydraulic fracture from a borehole in a poroelastic material.
Khair, A.W. (Department of Mining Engineering, College of Mineral and Energy Resources, West Virginia University) | Ro, Y.S. (Department of Mining Engineering, College of Mineral and Energy Resources, West Virginia University)
ABSTRACT: This paper presents an analysis of fracture depth and intensity due to subsidence over the longwall panel. Sonic reflection techniques were utilized to determine fracture depth, and a variation of p-wave velocity was used as an indication of the fracture intensity. Instrumentation has been tested for consistency and accuracy first in the laboratory using small scale models, then applied in the field in two mine sites with different mining geometry and geologic conditions. A new sonic viewer was utilized for sonic velocity measurements. Regular hammering method was an acoustic source. The results were concurrent with monitored horizontal strain profiles and measured open fractures over the longwall panels.
Techniques involving the propagation of acoustic or seismic waves are becoming of increasing importance in the characterization of rock masses in mineral exploration, mining operations, site investigations and other engineering application. McCann et (1975) described the use of cross-hole acoustic measurements to delineate interfaces between homogeneous media, to detect localized, irregular features, and to estimate the degree of fracture in rock asses. Palmer et al., (1981) discussed the fracture detection in crystalline rocks using ultrasonic reflection techniques. Meister (1974) used ultrasonic pulse attenuation to determine the depth of fracturing behind excavation tunnel walls. In the area above longwall mining, discontinuous ground disturbances (i.e., open cracks, steps, cave-in pits), will occur along the surface of the subsidence trough, when mining thick seams or groups of seams which are under soft rock strata. The source of these disturbances are either static or dynamic loading of the overburden strata due to undermining. Static fractures are produced when ground movements cease and ground stresses reach their final equilibrium state, and are usually developed at the edge or border lines of excavations (see Fig. 1). Dynamic fractures develop during excavation, parallel to the longwall face at some distance ahead of the face in tension zone (see Fig. 2) and often close as the face passes by the fracture zone and leave fracture zones in the gob area, compression zone. The length, width, depth, and intensity of these disturbances, fractures, are dependent on mining geometry, depth of overburden, geology, topography of the area, rate of mining and direction of mining with respect to the topographic slope (Khair et al., 1988). Using the principal of sonic wave propagation and utilizing wave travel time and velocity attenuation, disturbance in terms of fracture depth and intensity can be quantified. The travel time of energy between two points in a medium is governed by Format's "minimum time" principle which suggests that the wave which reaches the target point first has followed the path of the minimum travel time. That wave path may not necessarily correspond to the minimum distance between the two points. In a perfectly elastic medium, energy would be fully transmitted between two points. However, since no such perfect medium exists, part of the transmitted energy is absorbed and the wave amplitude is attenuated. Furthermore, higher frequency components of pulse will attenuate more rapidly than the lower frequency components, leading to a decrease in the sharpness of the pulse with increased distance of propagation, thus resulting in pulse broadening.
ABSTRACT: Two methods for computing fractal dimension are applied to profiles of eleven fracture surfaces at or adjacent to Yucca Mountain, Nevada. In addition, a method for estimating joint roughness coefficient (JRC) is also applied for comparison to the fractal dimension results. One fractal dimension calculation technique involves the computation of the power spectrum of rock surface profiles. The second calculation method involves the use of dividers to measure the length of these profiles. The divider method yields results which have a correlation coefficient of 0.91 with JRC, whereas the spectral results have a correlation coefficient with JRC of 0.05. The divider method is preferred for the Yucca Mountain fracture surfaces when correlation with JRC is desired.
Previous research conducted on rock surfaces adjacent to Libby Dam, Montana demonstrated that rock surface roughness represented as joint roughness coefficient (JRC; Barton and Choubey, 1977) could be estimated using a parameter known as the fractal dimension (Cart and Warfiner, 1987; 1989). Concurrent research showed how roughness can be described using the spectral characteristics of the roughness; moreover, these spectral characteristics can be used to calculate fractal dimensions (Brown and Scholz, 1985). Fractal dimensions determined for rock surfaces by Carr and Warfiner (1987; 1989), however, differed substantially in magnitude from those determined by Brown and Scholz (1985), primarily attributable to differing research approaches.
Rock mass characterization is an integral portion of the scientific and engineering investigation into the suitability of the Yucca Mountain, Nevada site for underground storage of high level radioactive waste. One part of this site characterization involves the investigation of rock strength attributes, including shear strength. A key element of shear strength is surface roughness. Research was initiated to attempt the description of roughness using the fractal dimension concept. Because two fundamental approaches are available for fractal dimension calculation, each is used to describe roughness of fractures at Yucca Mountain.
Eleven fracture surfaces are used for this study. The rock unit targeted for the waste repository is a moderately to densely welded, rhyolitic tuff. This fine grained rock unit is associated with numerous ltthophysae and gas escape tubules. Discussion follows on the measurement and analysis of these surfaces.
2 MEASUREMENT TECHNIQUES
Rock surface roughness is quantified by digitizing elevation along a transect across a fracture surface. Two techniques are used for this. One relys on the use of a stringline stretched parallel to the rock surface. Elevations (distances from string to surface) are sampled at regular intervals along the string. The second technique, developed by Franklin (1987), uses photographs of a surface to quantify roughness. Each of these techniques is described.
2.1 Stringline measurements
This technique is described in Figure 1. Some of the fracture surfaces found at Yucca Mountain, Nevada are vertical, hence Figure 1 shows a stringline stretched parallel to a fracture where "elevation" is a horizontal distance from string to rock surface. One to two meter long strings were used at Yucca Mountain and elevation was sampled every two centimeters.
Mine gases cause major hazards to underground coal mining in many parts of the world. Among them, instantaneous outbursts of coal and gas as well as gas explosions are the most severe. During the formation of coal from vegetation, water, carbon dioxide and methane are produced in varying quantity. At the later stages of coalification, methane is produced in larger quantities and trapped within the coal.
It is commonly accepted that most of the amount of gases up till 80% - 90% of total quantity are deposited in coal or rocks as adsorbed ones, while the remaining 10% - 15% of the gas is recognized as the free gas. In theory, up to 200 m3 (Roberts 1983) or even up to 465 m3 (Kozlowski 1986) could be formed from 1 tonne of coal during coalification. The sorptive capacity depends on the internal area which in turnes is related to rank, to the nature of gas and to the pressure (Jackson 1984).
Gas hazard is a serious problem in Polish mining. Out of 70 coal mines operating in that country 44 are gasous mines giving 53% of total national production of coal. Accordingly, proper knowledge of gas content and its space structure in the deposit is of greate importance.
Very little has been done till now on study of space structure of gas content in deposits. Classifications of seams bases mainly on gas content hand produced maps with the use of simple algorithms of interpolation between data points (Kozlowski 1986). It has also been recognized as not creating truly reproducible results, i.e. results which are free from personal bias. Accordingly, to increase safety, high, single, occasional readings of gas content are considered decisive in the process of classification of gas hazard areas. Since the gas content data are very scattered, statistical methods to study the data should be employed. Among many of such methods (Agterberg 1974) geostatistics originating from the Matheron's concept of regionalized variable (Matheron 1903) has been successfully applied in many engineering areas (Journel and Huijbregts 1978). Structural analysis is one of the most important steps of geostatistical procedure.
2 GAS CONTENT AS A REGIONALIZED VARIABLE
There are many methods employed in determination of gas content in the deposit (Kozlowski 1986, Lama and Bartosiewicz 1983). The common future of the methods is their local character. Resulting from each method a numerical value of gas content is prescribed to a point in the deposit. The nature of gas distribution in the deposit as seen in Fig. 1 is typical to many geological values, for example : mineral grade, thickness of the seam, density etc. Regionalized variable theory as proposed by Matheron (Matheron 1963) is the basis for the ensuring geostatistical analysis.
Figure 1. Sample record of the gas content in the Lenin mine in E-W direction. (available in full paper)
A regionalized variable is any numerical function with a spatial distribution that varies from one place to another with apparent continuity whose changes cannot be represented by any workable function (Matheron 1970).
An analysis of data of borehole breakouts as an indication of orientation of in-situ stresses is presented. Wellbores drilled in Alaska and Colorado provided data for this investigation.
Two field cases illustrating borehole breakouts at opposing failure directions are discussed. The first case refers to an offshore well drilled in the Gulf of Alaska. The failure zone is predicted to take place centered on the diameter in the direction of the least horizontal principal stress. The second case refers to the failure in a coal seam in a wellbore drilled in the Piceance Basin (Colorado). The failure mode was located normal to the direction of the least horizontal principal stress. Both failures can be explained by the von Mises failure criteria.
Since the beginning of this decade breakouts have been used as indicators of the orientation of the principal stresses. Breakout (also referred as borehole ellipticity and borehole spalling) are zones of failure lying on opposite diameters of the wellbore. Failure leading to spalling results when the stresses at the borehole wall exceed or are equivalent to the local rock strength. Measurements of the spalled cross-sections, in vertical wells, with an ultrasonic televiewer disclosed broad depressions aligned in the direction of the minimum principal stress. Other observations [4,6,7,10] also indicate that breakout azimuth is in the direction of the minimum principal stress. Breakouts aligned in the direction of the maximum principal stress were first reported by Jones, et. al.. Breakouts in the direction of the maximum horizontal principal stress have been observed in friable rocks (e.g., coal seams) only.
This paper describes an analysis of wellbore breakouts for boreholes drilled in Alaska and Colorado. The first well is an example of breakouts aligned with the direction of the minimum principal stress, while the spalled zones for the other well are aligned with the direction of the maximum principal stress.
2. FIELD SPALLING OBSERVATIONS
Maintaining stable wellbore is of primary importance during drilling of oil and gas wells. Wellbore stability requires a proper balance between the in situ stresses, wellbore fluid pressure and mud chemical composition. Most oil field stability studies have used the von Mises failure criterion. This is based on the second invariant of deviatoric stress and differs from the shear stress by 0 to 15 percent. In the von Mises criteria the second invariant of the deviatoric stress (vJ2) at the wellbore is obtained from:
(available in full paper)
and the mean effective stress, (Pc - Po), where
(available in full paper)
and Po is the pore pressure. In equations 1 and 2, sr, s¿ and sz are the radial, tangential, and vertical stresses at the borehole wall, respectively. These parameters are obtained by superposition of the Kirsch  solution for biaxial far-field stresses and the solution for the stress distribution due to the application of a pressure (p) in the cylindrical cavity:
(available in full paper)
The modulus of deformation of a rock mass is one of the critical parameters in the safe and cost effective design of underground structures. Traditional methods used to determine this property often involve laboratory testing of a group of core samples and "correcting" the laboratory results by using empirical factors related to joint spacing and other conditions. It is well known that core samples are representative of only a limited region in the formation and not necessarily of all the rock surrounding a tunnel. In addition, empirical correction factors have been developed from data having a substantial amount of scatter (Deere et. al., 1967). Other traditional methods such as plate bearing tests and the Goodman jack test provide only localized data and are subject to similar empirical correction factors (Bieniawski, 1978). As a result, traditional methods predict modulus values which are questionable and which err, in most cases, in a non-conservative way. Recently, under DEFENSE NUCLEAR AGENCY (DNA) sponsorship, UTD has developed a methodology for the measurement of the modulus of deformation through monitoring of convergence. This method recognizes that convergence of tunnel walls is the result of the elastic strain, and movement along joints and other anomalies, in thousands of cubic yards of rock surrounding the underground opening. Analytical solutions were derived which relate radial convergence to the elastic modulus (after the theory of elasticity [Timoshenko and Goodier, 1951]) of this large sample of rock, under conditions where induced stresses are not large enough to create a plastic zone around the tunnel. Since the method includes radial convergence which is a composite measurement of elastic strain of the rock, and other strain due to geologic anomalies, the term modulus of deformation is used (Bieniawski, 1978). The calculation of the modulus in this manner is analogous to calculating the modulus of elasticity of a complex composite material from strain and loading conditions. The advantages of using tunnel convergence over other methods is that this method is representative of a substantial "test specimen" complete with fractures, joint fillings, and other anomalies. It is, in fact, the modulus which exists where the rock formation interacts with the tunnel support system.
This paper presents the theoretical basis for the convergence method, and provides equations and charts that can be used to directly calculate the modulus of deformation from field measurements. Case histories are presented and emphasize the differences in magnitude between modulus values obtained from laboratory specimens, empirical methods, and the convergence method described in this paper. In one program UTD utilized the radial convergence measurement technique to obtain the elastic modulus of material at the Nevada Test Site. When the values obtained were used in design equations, they predicted tunnel behavior which agreed very well with experimental observations.
2 TUNNEL CONVERGENCE
Tunnel convergence is deformation caused by stress redistribution around the periphery of an opening during excavation. Considering the state of stress in an element on the boundary of an opening to be excavated, the state of stress prior to excavation is equal to the free field stress; i.e., the stress state of the element is equal to the undisturbed ground pressure.
ABSTRACT: The applicability of the beam theory in analysis of roof- pillar-weak floor interaction in partial extraction room-and-pillar mining is presented. The mine structure is modeled as an equivalent multi-indeterminate overburden elastic beam supported by elasto-plastic pillars resting on a viscoelastic layer of immediate weak floor strata underlain by a competent rock mass. The developed analytical model was initially utilized to conduct sensitivity analyses of different variables affecting the mining system, such as the deformability of coal and weak floor strata, thickness of weak floor strata, number of pillars in a panel, width of pillars, width of panel etc. These analyses were then extended to three overburden strata - coal pillar - floor strata lithologies typical of active coal mining areas in Illinois.
The rational design of any mining system requires knowledge of the actual load and displacement characteristics in a panel as well in its adjoining areas. This implies a fundamental understanding of roof- coal seam-floor strata interaction, and load transfer within the different parts of the mine due to the mining sequence and resultant surface and subsurface movements associated with mining. To study these interactions, the authors developed an approximate two- dimensional time-dependent analysis technique based on the theory of beams on inelastic foundations (Pytel, et al., 1988). The model was developed with the specific objectives to predict: 1) pillar settlements and associated surface subsidence movements as a function of time due to mining of one or more panels, and 2) transfer of load as a function of time to adjoining pillars or adjoining areas due to pillar settlement of weak floor strata or yielding of pillars. The model can consider different size pillars in a panel, different rates of advance and time lag in mining in different parts of a panel, and up to 50 pillars across a panel. Based on model validation results to date, the authors think the model has significant potential in analyzing the relative magnitude of roof-pillar-floor interaction effects in different geologic settings.
2. MODEL DESCRIPTION
Figure 1 depicts the physical problem involving overburden strata, coal pillars, and floor strata and its idealization as a structural mechanics problem. The two dimensional plane strain model described here is based on the theory of beams on inelastic foundations. A summary of the theoretical background for the model was presented in an earlier paper (Pytel et al., 1988). A more detailed theoretical discussion of the model is currently under preparation by the authors. In the solution approach, the mine structure is modeled as an equivalent multi-indeterminate overburden elastic beam supported by elasto-plastic pillars resting on a viscoelastic layer of immediate weak floor strata underlain by a competent rock mass. Stratified overburden associated with a coal seam is transformed into a composite beam with stepwise varying flexural and shear stiffness. Overburden strata behavior depends on the degree of bonding between layers, and two extreme cases are considered: 1) the different layers are fully bonded and the overburden acts as a single thick beam, and 2) the overburden strata interfaces are smooth and act as a number of subbeams.
ABSTRACT: A new approach to the direct inclusion of the effects of joints and geologic structure in 'rock mechanics analyses is applied to an elastic analysis of stability of a Lucky Friday undercut and fill longwall stope (LFUFL) using the finite element method (FEM). The approach is based on the concept of equivalent properties of a heterogeneous test volume, but does not depend on the assumption that a test volume is a representative volume element. Comparison with conventional FEM results show greater variability in fields of stress, strain, displacement, safety factor and energy densities. Stability requires a knowledge of rock mass strengths as well as elastic moduli.
This paper presents the results of a demonstration study of a new method for modeling the elastic properties of well-jointed rock masses. Joint is used here as a generic term and refers to the many structural discontinuities such as faults, bedding planes and so forth generally present in rock masses. Rock mass itself refers to field scale volumes of rock that are large relative to laboratory size test volumes. The latter are generally "intact" because they lack the discontinuities found in field. For this reason, rock properties determined from tests on laboratory sample volumes of intact rock and joints do not directly reflect the properties of the parent rock mass. As a consequence, the engineering analysis of stress and stability of rock masses remains highly subjective despite considerable advances in numerical analyses and computer hardware.
The demonstration study uses the UTAH2 finite element program and a method for estimating jointed rock mass properties recently developed at the University of Utah. The new technique, PM theory (Pariseau and Moon), is currently limited to modification of the elastic properties of rock masses. An outline of PM theory and several examples are given by Pariseau and Moon (1988); computational details for the elastic compliances can be found in the dissertation by Moon (1987). Extension to plasticity theory and strength estimation is described Pariseau (1988). Strength properties are used in the demonstration study but are not modified. The demonstration is two dimensional, although the overall approach is also applicable to three dimensional analyses.
The primary objective of the study is to demonstrate the practical feasibility of implementing the PM method in an analysis of stress about an excavation in a jointed rock mass. PM theory and numerical analyses of small scale two and three dimensional models of sample volumes of well-jointed rock masses show excellent agreement over a wide range of conditions. This is the first attempt to apply the PM method to an actual excavation in rock. The 5100 Level of the Lucky Friday Mine undercut and fill longwall stope (LFUFL) was selected for the study.
The approach to the study is a comparative one between two finite element analyses. The first is a conventional analysis based on average values of laboratory rock properties.
Rao, M.V.M.S. (Geomechanics Section, Department of Mineral Engineering, Pennsylvania State University) | Sun, Xiaoqing (Geomechanics Section, Department of Mineral Engineering, Pennsylvania State University) | Hardy, H. Reginald (Geomechanics Section, Department of Mineral Engineering, Pennsylvania State University)
Huang, S.L. (Department of Mining and Geological Engineering, University of Alaxka Fairbanks) | Speck, R.C. (Department of Mining and Geological Engineering, University of Alaxka) | Yamasaki, K. (Department of Mining and Geological Engineering, University of Alaxka Fairbanks)