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ABSTRACT: Most of the papers designated as being within the topic of underground storage at this Symposium are concerned with aspects of radioactive waste isolation. Although this is, unquestionably, an important international application of underground storage, and one involving a considerable number of research investigations, the subject of underground storage is indeed much broader. Several major international conferences have been devoted exclusively to it. Applications include storage, under a range of temperatures and pressures, of oil and liquefied petroleum products, compressed air, heat, foodstuffs of various kinds, hazardous and 'nuisance' industrial by-products, and a variety of special applications, both civilian and military - some in use, others proposed.

Storage may be in caverns excavated specifically for the purpose, exhausted mines may be adapted for storage or, in some cases, the material to be stored may be injected under pressure into the pore spaces of porous-permeable formations at depth. A variety of rock types and geological environments are used, e.g. excavations in salted or domal salt, where long-term creep closure of the openings is a concern; massive granite, where fluid loss through fissures may be important. Cavities may have spans of several tens of meters, and there is interest in achieving still larger excavations.

As would be expected, this breadth of underground storage applications introduces a similarly broad range of questions in rock mechanics and rock engineering. The report will review these questions and recent developments in rock mechanics research, computational procedures, and design applications - and will also discuss the opportunities for a still greater range of applications of underground storage to current industrial and social problems.

ARMA-89-0019

The 30th U.S. Symposium on Rock Mechanics (USRMS)

Hyett, Andrew J. (Rock Mechanics Research Group, Department of Mineral Resources Engineering, Imperial College of Science, Technology and Medicine) | Hudson, John A. (Rock Mechanics Research Group, Department of Mineral Resources Engineering, Imperial College of Science, Technology and Medicine)

1 INTRODUCTION

The ISRM commission on testing methods has recently presented Suggested Methods for rock stress determination (Him & Franklin, 1987). This proposes that even if the magnitude of *in situ* stress is not sufficient to cause significant ground problems, the optimum shape, orientation, and layout of underground structures can be significantly affected by it. In the design of underground excavations, the engineer often requires a knowledge of the average *in situ* stress tensor in the rock mass. However, attempts to measure a stress state applicable to design have proved frustrating, and a high degree of uncertainty is introduced by the variability in results. In the belief that deduced fluctuations are random in nature, many separate measurements are often made, so that a more reliable stress tensor average, and some indication of the associated variance (see Dyke ½t al., 1986) can be calculated. Unfortunately, this approach is limited by economic considerations and, as with any sampling procedure, it is imperative to understand the sources of measured variability, in order to design an optimum measurement programme.

Cundall(1987) itemised the main causes of stress variability as

- Instrument and measurement errors, and
- Natural fluctuations of stress from point to point, induced by the action of a boundary stress on the internal rock structure. At least four categories exist:
- inhomogeneous rock, bedding, intrusions etc.;
- differential contraction, creep, or changes in rock properties with time;
- proximity to faults or discontinuities;
- cycles of tectonic activity that cause movement on joints.

The latter was successfully investigated using the distinct element programme UDEC. In this paper, the contribution of items (iii) and (iv) (i.e. the items related to discontinuities) to the total stress variability will be discussed, for the kind of rock mass shown in Figure 1.

Although many authors have concluded that rock joints have an influence on the stress in their vicinity, a more analytical approach is required if the stress distribution associated with different jointed rock masses is to be (i) compared, and (ii) related to routinely measured joint parameters. If this can be achieved then, prior to any attempt to measure stress in a jointed rock mass, a consideration of joint geometry, joint deformability, and the geological kinematics of joints (e.g. the magnitude and direction of previous movements), can place valuable 'common sense' constraints on the expected stress system for minimal extra cost.

2 IN SITUSTRESS MEASUREMENTS IN DISCONTINUOUS ROCK MASSES

Two field measurement programmes specifically designed to measure the state of stress in a discontinuous rock mass will serve to introduce the nature of the problem.

Figure 1. Excavation in a moderately fractured rock mass of the kind addressed in this paper.(available in full paper)

Figure 2.

ARMA-89-0293

The 30th U.S. Symposium on Rock Mechanics (USRMS)

ABSTRACT: Finite element method was employed to assess the performance of a two-cavern system over 20-year period of operation. Of primary importance was evaluation of the stability of the pillar separating two caverns. Results of these analyses are discussed along with practical implications relevanto cavern operation.

INTRODUCTION

Utilization of solution-mined underground caverns created within natural salt formations for storage purposes has been increasing steadily in the U.S. over the last several decades. Numerous underground storage sites have been developed and millions of tons of crude oil and other fluid products are stored in solution-mined caverns or abandoned salt mines. After decades of seemingly smooth operation some storage fields exhibit surface subsidence occurring at a rate that concerns the operators with respect to the long-term stability of the cavern systems. It is natural to suspect that high subsidence rates are the primary indicators of potential problems which may arise within an underground structure. Efficient utilization of the salt volume available (i.e. the size of a salt dome) requires that caverns be located at some optimum distance away from each other, such that the operation of one cavern has a negligibleffect on performance of the adjacent cavern. Adjacent caverns are separated by an unexcavated portion of the salt strata, referred to as a pillar. For obvious reasons, this pillar as well as the entire cavern system "should" remain stable over the cavern life. Numerical modeling provides a convenient means by which the performance of underground excavations can be studied. The ever-increasing power of microcomputers permits the numerical modeling of relatively complex systems that in the past were possible only on mainframe computers. The advantage of numerical modeling techniques, such as finite element method, is that the analysis can be performed on the entire system, rather than its components. The purpose of the study discussed in this paper was to evaluate the performance of a simple two-cavern system with particular interest focused on the behavior of the pillar separating two caverns. A finite element method implemented on a microcomputer was used to perform the analysis.

SYSTEM GEOMETRY

The cavern geometry and location was selected to represent a general case of two caverns of similar shape, located at different depths. A situation often encountered in storage operations in domal salt. The model representing the shape, dimensions, and the relative orientation of the caverns analyzed here is shown in Figure 1. The size of the pillar separating the two caverns was assumed equal to 100 feet. An elastic overburden was assumed to overlay the salt dome to a depth of 1000 feet. A two-dimensional, plane strain finite element model representing a section through the cavern centers was used in the analysis. To limit the time necessary to complete calculations two models were employed: model (a), comprised of 207 4-node isoparametric elements and 167 nodes, and a simplified model (b) comprised of 62 elements and 44 nodes. As indicated earlier, the focus of the analysis was on the stability of the pillar. In the more complex model (a) the pillar is denoted by the following nodes: 54, 55, 56, 57, 58 (top of the pillar), 49, 50, 51, 52, 53 (horizontal mid-section), and 44, 45, 46, 47, 48 (bottom of the pillar).

ARMA-89-0689

The 30th U.S. Symposium on Rock Mechanics (USRMS)

SPE Disciplines:

ABSTRACT: Recent improvements are described in several techniques for ground control in underground mining. Promising methods for analysis and mitigation of rockbursts are discussed. Methods of assessing damage to underground excavations from repetitive seismic loading are reviewed. Analysis of mining-induced surface subsidence is discussed.

INTRODUCTION

The purpose of this paper is to assess the current status of rock mechanics practice in mining and excavation engineering, and to identify those topics which need further attention to improve the reliability of particular aspects of engineering design in rock. The review is by no means comprehensive. It is intended instead to indicate some areas where substantial progress has been made recently, in both engineering principles and field practice, and to consider issues of topical significance in both mining practice and engineering construction in rock.

Mining practice involves maintenance or deliberate modification of the properties of the host rock mass. In this regard, research in techniques to preserve rock mass integrity has improved the technology of large-scale rock reinforcement and engineered backfills. Improved practices for design of grout curtains are developing for reduction of fissure permeability around shafts and similar facilities where groundwater flow must be restricted. For mine settings prone to induced seismicity and rockbursts, there has been considerable improvement in understanding of rockburst mechanics, with the prospect that control and mitigation measures may be developed.

There are several matters for which the state of theory and practice needs to improved to satisfy demands for a more reliable capacity to predict rock mass response to engineering activity. These include surface subsidence over longwall mines in areas with faulted cover and irregular surface topography, the dynamic performance of underground excavations subject to repetitive seismic loading and joint-controlled creep around excavations in hard rock.

1 GROUND CONTROL TECHNIQUES

Recent developments in ground control practice have been concerned with improvement of rock mass capacity to sustain induced loads and to maintain integrity while resisting displacements. Techniques which have improved substantially, in either operational function or design principles, include large-scale rock reinforcement, backfill design and grouting.

1.1 Rock reinforcement

Several recent well-executed investigations demonstrate the performance and benefit of cable reinforcement of stope boundaries. These include test stopes at the Cart Forks Mine (Pariseau et al., 1984), and the Mount Isa Mine, Australia (Greenelsh, 1985). The evaluation of several cable bolt reinforcement patterns in stopes at the Pyhasalmi Mine, Finland, is reported by Lappalainen and Antikainen (1987).

Field investigations of rock reinforcement show that the grouted steel tendons are effective when loads are mobilized in the reinforcement elements by inelastic strains in the host rock. This indicates that appropriate methods of design analysis for cable bolt reinforcement must provide for large strain in the constitutive model of the rock mass. A finite difference scheme simulating the interaction of deforming rock with grouted tendons has been described by Cundall and Board (1988), based on the conceptual model of reinforcement presented by St.John and Van Dillen (1983).

ARMA-89-0005

The 30th U.S. Symposium on Rock Mechanics (USRMS)

analysis, control, deformation, design, displacement, excavation, fault, fill, ground, loading, mechanics, mine, mining, performance, pillar, reinforcement, rock, rockburst, stope, stress

Industry:

- Materials > Metals & Mining (1.00)
- Energy > Oil & Gas > Upstream (1.00)

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Exploration, development, structural geology (1.00)

ABSTRACT: The interpretation of coal seismic data requires a certain precision and accuracy to make the results more reliable. The signature of the seismic wavelet provides a host of valuable geologic information. Subtle features and anomalies, not easily observed in conventional black and white seismic sections, are enhanced through color attribute displays in terms of frequency, amplitude and phase. Coal seam anomalies like sandstone washouts produce a distinct pattern in frequency and amplitude displays due to the change in the net acoustic impedance contrast. Faults produce frequency and amplitude variations due to interference within the Fresnel zone that straddles the fault. The magnitude of displacement is estimated by studying the effects of faults on reflection amplitudes and frequency from computer-generated models.

1 INTRODUCTION

Consolidation Coal Company (Consol) and Conoco Inc. initiated a seismic program for coal mining applications in the mid-1970s. During its developmental stages, there were some successes and failures of seismic reflection techniques to detect anomalies at the coal seam horizon. However, the mining industry cannot afford to have an average success rate, especially when safety and productivity are important factors for operating a coal mine. Each seismic survey has to fulfill its objectives. The success of any seismic project depend largely on the three most important processes; namely, field acquisition, data processing and interpretation. In 1987, Consol R&D acquired and developed its own Seismic Inter- active Interpretation Workstation based on a microcomputer system in order to further enhance the seismic program. With some refinements from petroleum applications, the workstation is used to help design the field acquisition parameters and to evaluate the data processing sequence. This process ensures quality control. It is most useful in the interpretation of coal seismic data where computer-generated models are correlated with the processed seismic data. The work- station integrates various sets of geophysical and geological data to form a network of information which is stored in a database. Data sets are retrieved, processed and crosscorrelated to provide the best possible interpretation. The workstation can generate attribute displays of the seismic section to highlight the characteristics of the seismic reflection associated with the target coal seam horizon. The success rate of Consol's seismic program has increased dramatically in recent years due to the introduction and application of state-of-the-art technologies borrowed from the petroleum industry. Transformations of data from one form to another are common in signal analysis. Interpreting data from different points of view often results in new insight and the discovery of relationships not otherwise evident. The transformation of seismic data from the time domain to the frequency domain is the most common example of data rearrangement which is accomplished through Fourier transform. Complex trace analysis is a transform technique which separates the physical characteristics of the waveform that may have significant information about the local geology. It effects a natural separation of amplitude and phase information. The amplitude attribute is called "reflection strength." The phase information is also an attribute and is used to calculate the instantaneous frequency.

ARMA-89-0311

The 30th U.S. Symposium on Rock Mechanics (USRMS)

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

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.

1 INTRODUCTION

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.

ARMA-89-0723

The 30th U.S. Symposium on Rock Mechanics (USRMS)

SPE Disciplines:

ABSTRACT: The scope of this paper is to introduce a mathematical model based on matrix algebra in order to determine similitude quantities, which can be arranged in specific formats to simulate the field conditions and associated behavior. The formulation of a typical mathematical model applicable to Geomechanics is demonstrated here. The examples provided are intended to facilitate comprehension and application of the proposed model in practice.

1 INTRODUCTION

The methods of investigation of the engineering behavior of geologic media mainly include numerical techniques, analytical models, field and laboratory tests, physical models and empirical methods. Although many advances have been made in Geomechanics, current problems in the design of underground structures in rock have reflected the need for more appropriate simulation methods beyond the capabilities of current conventional modeling techniques. In this paper, the authors present a method of combining physical simulation techniques with aspects of mathematical modeling. This proposed model can incorporate many variable parameters, hence would provide a fundamental input base for analytical and numerical computations and also for experimental design.

2 DIMENSIONAL ANALYSIS

The original concept of dimensional analysis was proposed by Buckingham (1914) in the early twentieth century. This paper presents an extension of this valuable tool as relevant to Geomechanics utilizing matrix algebra. Buckingham's theorem states that if an equation is dimensionally homogeneous, it can be reduced to a relationship among a complete set of dimensionless products. The dimensionally homogeneous equation does not depend on the units of measurement. In most cases the governing equation is not precisely known, but it can be considered as homogeneous, provided that all the pertinent variables are included in the analysis. Therefore, the selection of variables is an important step which can be based upon theory or experiments or both. After selecting the appropriate variables, the dimensional matrix can be formed. The dimensions of any variable U_{j} can be written as a function of the basic terms, mass(M), length(L), and time(T) as given below:

(available in full paper)

Hence dimensions of a set of variables U_{1},U_{ 2} ..... U_{n} may be described by the exponents a_{ij}. The first subscript i, indicates the dimension and the second subscript j, indicates the variable. In this way an exponent a_{ij} specifies the dimension and the variable associated with it. A dimensional matrix can be represented by:

(available in full paper)

The number of independent dimensionless products which can be formed from the above matrix is equal to the total number of variables (i.e. columns,n) minus the rank of [a_{ij}].

3 SIMULATION OF STRESS-STRAIN BEHAVIOUR

3.1 Material similitude parameters

In the case of modeling stress-strain behavior, similitude of material properties is of paramount importance. The Soilowing matrix analysis (Table 1) demonstrates briefly the method of computing the relevant dimensionless terms to establish stress-strain similarity between two materials.

Table 1 : Dimensional matrix for material similitude(available in full paper)

Stress and Young's modulus have the same dimension ML-1T -2 and they are shown accordingly in the table. Poisson's ratio and friction angle are dimensionless, so they are represented by zeros.

ARMA-89-0301

The 30th U.S. Symposium on Rock Mechanics (USRMS)

ABSTRACT: Characteristics of rock fracture roughness profiles obtained by close-range photogrammetry and subsequent stereo digitizing are compared to those obtained by traditional mechanical profilometer methods. Statistical, geostatistical, and fractal dimension measures are used in the comparisons and indicate that fracture roughness can be anisotropic. Stereo digitizing appears to have more flexibility and wider applicability than mechanical profiling with a stylus, but has slightly poorer resolution at profile increments smaller than 0. 1 mm in a 100-mm field of view.

1 INTRODUCTION

A numerical description of the roughness of a rock fracture surface is essential to the estimation of shear strength, dilatancy, and stiffness of the fracture. In this context, the term "fracture" refers to any semiplanar discontinuity in a rock mass, such as a joint, bedding plane, or fault. In engineering practice the most commonly used measure of roughness is the joint roughness coefficient (JRC) proposed by Barton (1973) and adopted by the ISRM (1978). This coefficient ranges in value from 0 to 20 and can be estimated either by visual matching of surface profiles with "standard" profiles or by back calculation using the peak shear strength and the basic friction angle(obtained from direct shear tests) in conjunction with the joint-wall compressive strength. The first approach is highly subjective, while the second has little practical merit because roughness should be used to predict shear strength, not vice-versa.

In recent years, investigators have developed more objective, quantitative methods to measure rock fracture roughness. Fracture surfaces can be digitized with mechanical profilometer (see Weissbach, 1978; Swan, 1981) to provide detailed elevations along cross-sections (i. e., profiles or traces) that form the basis for various statistical and analytical measures of roughness. A comprehensive overview of fracture roughness measurement using profilometers and of subsequent analyses of roughness can be found in the works of Swan (1983), Reeves (1985), and Brown and Scholz (1985). Analytical schemes presented in the first two references rely on traditional statistical tools grounded on an assumption of Gaussian distributed elevations. The third source emphasizes the method of fractal dimensions. In all cases, original fracture roughness data were obtained by mechanical profilometers.

Advances in computer technology and photogrammetry during the last decade now make it possible to efficiently collect, reduce, and display detailed digital elevation data, even at sensing ranges from several centimeters to several meters. Such technology could provide a viable new approach to measuring rock fracture roughness, particularly in regard to field studies addressing a wide range of fracture sizes. Because this approach relies on photographic stereo pairs, it is portable, it provides a permanent record of the entire area of interest on the fracture surface (not just selected traces), and it avoids the typically cumbersome tasks of rock sample collection and/or instrument setup. Digitized elevations are obtained from a given pair of photographs by using a stereo analytic plotter in conjunction with a data acquisition system and a microcomputer. An initial study has been completed in which this type of close-range photogrammetry for measuring rock fracture roughness has been evaluated and compared to methods based on mechanical profilometers.

ARMA-89-0201

The 30th U.S. Symposium on Rock Mechanics (USRMS)

SPE Disciplines:

ABSTRACT: Much of the present knowledge about caving behavior of rock masses has been obtained from empirical observations. Additional notions about caving have been developed through inferences derived from two-dimensional finite element analyses. These analyses have indicated that a combination of one low-angle set of fractures and one nearly vertical set of fractures is the optimum fracturing configuration for ease of cavability of an orebody. This paper presents the results of two- and three-dimensional distinct element analyses which draw different conclusions than those reported from finite element studies. The distinct element method is selected for analysis of cavability because this method treats the rock mass as an assemblage of rock blocks which may interact individually. The results of the analyses are compared to a documented case history which involved a groundfall of 80,000 tons of ore in a 160-foot high pillar. The mechanics associated with these results are explained in terms of simple static stability analysis of wedges. The propensity for orebody caving is primarily a function of the number of joint sets or potential "release" surfaces in the orebody. This mechanism is influenced by the bounding weak discontinuities and intact strength of rock material.

1 INTRODUCTION

The cavability of orebodies is important to various mining methods in distinctly different ways. The block caving mining method relies on caving to extract massive ore economically, whereas other methods rely on the stability of the orebody and host rock to extract ore selectively. Cavability is a function of the geomechanical properties of the rock mass and the in-situ and mining-induced stresses. It has long been recognized that "the ability of a block to cave or fragment is a function of its strength in tension or shear and the value of applied forces" (Bucky, 1956). Numerous attempts have been made to develop classification systems for use in determining cavability. Much of the present knowledge about caving behavior has been obtained from empirical observations. For example, Mahtab and Dixon (1976) concluded from observations that the principal geomechanical features influencing cavability are in-situ stress field, rock strength, and the geometry and strengths of discontinuities in the rock mass. These authors also, by back-analysis of elastic calculations, postulated effective fracturing configurations. They concluded that "a combination of one low-angle (0° to 30° dip) set of fractures and another nearly vertical (75° to 90° dip) set of fractures is the most effective two- dimensional fracturing configuration for ease of cavability of an orebody. In an actual three-dimensional situation, one set of low angle fractures and two sets of nearly vertical fractures will be most effective in improving cavability."

These observations, concerning favorable joint orientations, may be valid for environments lacking lateral confinement (i.e., as a result of boundary slots or boundary weakening). However, results of two- and three-dimensional distinct element analysis, presented herein, suggest that caving in confined environments requires that additional release surfaces be present. Release surfaces may be either preexisting or form as a result of high horizontal stresses.

ARMA-89-0167

The 30th U.S. Symposium on Rock Mechanics (USRMS)

SPE Disciplines:

- Reservoir Description and Dynamics > Reservoir Characterization > Exploration, development, structural geology (0.49)
- Management and Information > Professionalism, Training, and Education > Communities of practice (0.36)
- Management and Information > Information Management and Systems > Knowledge management (0.36)
- (3 more...)

ABSTRACT: If all stratifications are horizontal, the computation of surface deformation induced by coal mining involves the prediction of roof and floor convergence and then the transfer of the effects of this relative displacement to the surface through the use of the appropriate influence functions. A laminated model, in the form of a quasi- continuum, provides a simple means of computing the approximate convergence distribution and leads to the Gaussian distribution as the influence function.

The ideas presented in this paper represent a subtle but fundamental generalization of the influence function method. It is postulated that the influence of a small area of extraction is proportional to the roof and floor convergence and not to the thickness extracted. This difference in definition removes many conceptual difficulties associated with the influence function method.

To demonstrate the utility of the model, the surface disturbances induced by the extraction of a parallel sided long panel are derived. Formulae giving subsidence, tilt, horizontal displacement and strain are given.

1 INTRODUCTION

Considerable research has been devoted in recent years to the development of methods for the prediction of ground surface distortion induced by coal mining in the U.S.A. The majority of the investigators appear to have come to the conclusion that the influence function method represents the most promising approach (see for example: Brunner et al 1983, Jeran et al 1986, Karmis et al 1986, Heasley et al 1986, Peng et al 1986, Karmis et al 1987). The acceptance of the principle of superposition or of the linearity of the underlying rock mass behaviour is inherent in this method. In view of this conclusion, it is somewhat surprising that only Karmis et al (1987) appear to make specific mention of the role of roof and floor convergence and that the applicability of linear elastic models has been left largely unexplored.

Since the early 1960's the prediction of rock mass behaviour on the basis of elastic models has gained wide acceptance in hard rock mining (Salamon 1963, 1964a, 1964b, 1974, Cook et al 1966). Of course, it is hardly likely that the elastic model which has proved to be effective in deep level hard rock mines would be suitable to describe the behaviour of stratified coal measures. It is tempting to suggest, however, that a simple elastic approach, based on the long-neglected 'frictionless laminated model' (Salamon 1961), may prove useful in these conditions. This expectation is supported, as it will be seen later, by several features of the model. This promise has recently prompted a comprehensive investigation of the basic theory of this model (Salamon 1989). In this paper the fundamental aspects of the derivations are not repeated, but attention is focused on a particular solution, involving a parallel sided long panel in the case of horizontal stratification.

2 THE MODEL

The model is pie e-wise homogeneous, consisting of a pile of homogeneous isotropic strata where the interfaces between beds are parallel and free of shear stresses and cohesion.

ARMA-89-0503

The 30th U.S. Symposium on Rock Mechanics (USRMS)

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Exploration, development, structural geology (0.71)