Layer | Fill | Outline |
---|
Map layers
Theme | Visible | Selectable | Appearance | Zoom Range (now: 0) |
---|
Fill | Stroke |
---|---|
Collaborating Authors
Results
ABSTRACT ABSTRACT: A probabilistic approach for key block analysis was introduced and compared with the current deterministic analysis in key block theory. A case study was made to demonstrate the capability of the probabilistic key block analysis, where three subway tunnels were studied. The probabilistic key block analysis incorporates probability distributions of rock joint orientations, trace lengths, spacings and friction angles to predict the size, shape, frequency of occurrence of key blocks as well as a positional probability of failure, which identifies the parts of the rock mass being most susceptible to key block failure. Deterministic procedures do not take into account these important variables and give a worst case analysis. 1 INTRODUCTION Rock joints or discontinuities in a rock mass play an important role in the design and stability analysis of geotechnical structures such as mines, storage chambers, power houses, or nuclear waste disposal sites. Generally a stereographic projection was applied to the kinematic analysis of rock joints for the structural stability (Hoek and Bray 1981). Also, a factor of safety could be obtained for potential failure blocks (John 1968). Recently, Goodman and Shi (1985) developed the key block theory which is a numerical algorithm of joint analysis for structural stability and support design. A common point among the above techniques of joint analysis is that a joint set was represented by a single joint plane whose orientation and geometry is known precisely. However, natural rock joints have significant dispersions and require a cluster analysis to group them into several joint sets. Various joint models were studied and their key parameters were inferred from the field data (Arnold 1941, Grossman 1985). McMahon (1971) realized the influence of joint orientation dispersion over the mean attitude on the slope stability and incorporated the probabilistic distribution of joint orientations into the kinematic slope analysis. Also, a non- parametric geostatistics was introduced to model the joint systems in a rock mass, which predicted not only the global probability distributions of joint parameters, but also their local probability distributions (Young 1987). By applying this model, the superiority of a localized probabilistic approach for kinematic rock slope stability analysis was demonstrated on an open pit mine (Young and Hoerger 1988). In this paper, the key block theorem (Goodman and Shi 1985) was incorporated with simulation techniques to obtain a probabilistic key block analysis, which takes into account the probabilistic distributions of whole joint parameters; orientations, spacings, and trace lengths. Then, metropolitan subway tunnels were studied to show the advantages of the probabilistic approach over the deterministic key block analysis. It was found that the probabilistic approach yields additional information about the key block failure, which is very important for designing an excavation and supporting systems to prevent key block failure. The probabilistic key block analysis does not require additional field sampling of joints and its whole input data is available from the joint mapping data used for the deterministic key block analysis. 2 KEY BLOCK ANALYSIS The principle of "block theory" (or key block theorems) is that the potential key blocks are found prior to their failures and their stability is secured, then no block failure will occur anywhere in the entire excavation area.
- Water & Waste Management > Solid Waste Management (1.00)
- Materials > Metals & Mining (0.67)
ABSTRACT ABSTRACT: A method is presented for the inclusion of expert opinion and off-site data into site characterization studies-which is intended to meet the requirements of regulatory agencies for auditability of design data. Experts must evaluate off-site data for both quality and applicability to the new site. Since a statistical distribution of a property is often needed in computations, the expert must provide his information in a form which arrows this distribution to be assessed. Bayesian reasoning is used to modify a prior distribution with new data. 1 INTRODUCTION: Rock mechanics studies, especially at the site investigation stage, are often hindered by a scarcity of site-specific data on the physical properties of the rock at the site. The use of "engineering judgment" to interpret and supplement inadequate data, while often both necessary and desirable, will not satisfy the requirements of regulatory agencies or other parties demanding more rigorous approaches to predicting the performance of structures in rock. Such expert opinion is generally based on experience and, at least implicitly, on data from other, similar sites. This paper presents the results of a pilot study of an alternative approach to the incorporation of this expert knowledge into rock mechanics analysis by using Bayesian analysis. The direct applicability of off-site data to rock mechanics projects is generally limited by the degree of similarity of the rock type and geo- Logic setting and by how critical a specific parameter is to the project in question. For example, properties of evaporites in bedded deposits would be much more likely to be similar than limestones. Density would vary less within a given rock type than would tensile strength. Host engineers would be more comfortable designing a shaft pillar from off- site data than a roof support system or a pit slope. Another factor which would complicate the situation is the reliability of the off-site data, especially from published sources. The interpretation and evaluation of these issues of similarity, criticality, and reliability in a given instance require expert judgment. Since rock is heterogeneous, performance prediction calculations using computer modeling often require that the distribution of the parameter be supplied; the average value will not be enough. Furthermore some statement regarding the confidence that can be placed in that distribution must be made so that the reliability of the prediction may be assessed. Bayesian reasoning is a format mathematical approach to providing both the distribution and the confidence measure. The expert's initial beliefs about the distribution function for a particular property at the site in question are expressed in a prior probability distribution. These data are derived from the expert's analysis of a set of off-site data, supplied by him or others, and are adjusted by him for accuracy as welt as similarity of the sites and rock types. Bayesian analysis then compares this prior distribution to data from the site, assesses the likelihood of observing this data given the prior distribution, and expresses revised beliefs in a posterior probability distribution.
Correlation Between Unconfined Compressive And Point Load Strengths For Appalachian Rocks
Vallejo, Luis E. (Department of Civil Engineering, University of Pittsburgh) | Welsh, Robert A. (Office of Surface Mining Reclamation and Enforcement, Department of the Interior) | Robinson, Michael K. (Office of Surface Mining Reclamation and Enforcement, Department of the Interior)
ABSTRACT ABSTRACT: The strength measured by the uniaxial compression test is a parameter that is widely used for the engineering classification of rocks. Sedimentary rocks such as shales, however, are difficult to evaluate by uniaxial compression testing because the rocks slake during the preparation of the standard samples required for the tests. Indirect methods such as the point load test have been proposed to determine the unconfined compressive strength of shales and other soft rocks. It is current practice to use 24 as the conversion factor between the point load strength, Is, and the unconfined compressive strength, sf (sf.= 24 Is). The present study investigated index-to-strength conversion factors for shales and sandstones obtained from surface coal mining sites in the Appalachian region. Regression analyses indicate that a conversion factor of 12.5 best correlated the strength obtained from the point load and unconfined compression tests in the case of shales. For the sandstones, a value of 17.4 best correlated the sty. The unconfined compressive strength is a parameter that is widely used for the engineering classification of rocks (Bieniawski, 1973, 1974; Olivier, 1979; and Welsh et al., 1987). Tne unconfined compressive strength of rocks is obtained from uniaxial compression tests that require the use of smooth samples with standardized dimensions (i.e., cylinders with a length-to-diameter ratio of two). Shales, however, are not completely suited for uniaxial compression tests (Bailey, 1976). Shales slake during sample preparation under the stresses of diamond drilling and the addition of water used to cool the tool face. Additional equipment used to prepare uniformly dimensioned, smooth samples required for the uniaxial compression test are not highly successful with shales. Such experience with shales has demonstrated the need for another type of test that can be used as an indirect way to obtain the uniaxial compressive strength. Broch and Franklin (1972) and Bieniawski (1975) have proposed the point load strength test as an indirect way to obtain the uniaxial compressive strength of rocks. According to Broch and Franklin (1972), the advantages of using the point load strength test are: (a) specimens in the form of irregular lumps are used and require no machining, (b) smaller forces are needed, so that a small, portable testing machine can be used, (c) fragile and broken materials can be tested, and (d) it is inexpensive. The above advantages of the point load strength test make it suitable for shales in obtaining their unconfined compression strength. The point load apparatus compresses a piece of rock between two points using two cone-shaped platens. A rock core of diameter (D) is compressed diametrically to failure under a point load (P). From the test, a point load index (Is) is calculated using the following relationship (Broch and Franklin, 1972)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Mudrock > Shale (1.00)
- Geology > Structural Geology > Tectonics > Compressional Tectonics > Fold and Thrust Belt (0.63)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Sandstone (0.51)
- Materials > Metals & Mining (1.00)
- Government > Regional Government > North America Government > United States Government (0.68)
ABSTRACT 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.
- Geology > Rock Type (1.00)
- Geology > Geological Subdiscipline > Geomechanics (1.00)