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Quantitative Characterization of Rock Material for Modelling Of 1 QUANTITATIVE CHARACTERIZATION OF ROCK MATERIAL, FOR MODELLING OF MICROSTRUCTURE M. Taborda Duarte, P.-A. Lindqvist, S.Q. Kou, K. Miskovsky Department of Civil and Rock Engineering Luleå University of Technology SE-97187 Luleå - Sweden ABSTRACT Quantitative characterization is performed to model rock microstructure, by means of statistical modelling. The microstructural modelling is new and consists in the selection of the appropriate descriptors to characterize the rock, to quantify them through analysis of images taken with the polarizing microscope and thereafter to find the appropriate model among twelve statistical distributions. This approach was successfully applied to a fine even grained granite using grain size, grain shape and grain orientation of the microstructure but other rocks can be characterized. Concerning the orientation of the microstructure only Normal and Logistic distributions are appropriate models. Between the two distributions, Logistic distribution with parameters a=-3.17 and b=24.7 lead to the best fitting with data histogram. Concerning grain size and grain shape of the microstructure, Exponential distribution, Laplace distribution, Poisson distribution and Geometric distribution are not appropriate models. Beta distribution requires a pre treatment of the data and therefore does not fit the data. Among the remaining six distributions, Weibull distribution is the best model with b=75.7, c=1.20 as the seed parameters. Shape is best modelled by Weibull distribution b=65.0 and c=3.40. Quantitative characterization of the rock is important for the modelling and therefore the understanding of the rock material. Key words: microstructure, statistical modelling, image analysis, microscope 1. Introduction Characterization of rock material by means of microstructural modelling presented in this paper is new, and was developed to model rock material. Liu et al. (2002b) have used the microscopic image directly to incorporate the rock microstructure. Results were very satisfactory; however a rock characterization approach is required. The major advantage of this modelling approach is that the rock material can be reproduced and specify by the seed parameters of the statistical distributions. This opens the way to investigate and deeper understand of intrinsic heterogeneity of the rock. The final goal is to incorporate it into a rock breakage code so that different rock types can be distinguished and their mechanical response under different processes may be simulated. As local variations of the microstructure are known to influence considerably rock mechanical response, microstructural modelling for rock characterization is an important step to understand rock mechanical response. In fact, several industries dealing with rock material, such as rock cutting, drilling, crushing and milling can 2 benefit from the approach presented here and the analysis of the micro heterogeneity presented in future work. Shortly, in this paper in series, the microstructure is simplified, quantified and modelled. In order to this, the microstructure of fine even grained granite is seen as matrix where mineral grains are the main constituents. Besides that mineral grains are responsible for rock hardness, the grain boundaries and microcracks that exist in the granite are discontinuities which determine the granite strength and lead the material to fail. Hard rock can be reproduced when the properties of the matrix are appropriately modelled. Among the several properties of this microstructure, main sources of weaknesses in the hard rock are in focus. Once the simplification is performed, quantified by means of image analysis of the grain size, grain shape and grain orientation. Thereafter, by means of statistical distributions and its seed parameters, the microstructure is modelled. Thus, it is possible to reproduce the network of the boundaries, the main source of weaknesses. In the future the microstructural modelling approach will be used with the goal of analysing the heterogeneity and deformation present in microscopic scale. 2. Micro structural Modelling Rock appears as a mosaic of tightly and interlocked grain profiles regardless of the scale of observation. Both in thin sections when observed in the microscope as well as in polished sections in hand specimen, it is possible to observe projections of the geometrical characteristics of the crystal sections, including their apparent shapes, orientation and distributions. In this paper we are concern with the arrangement of the mineral grains named microstructure, which is the structure of the rock material when observed in the microscope. The polarizing microscope is the only one, among microscopes in which it is possible to observe the network of mineral grains. This microscope differs from the microscope for the metallurgist or the biologist, in that the light is polarized in order to vibrate at two perpendicular directions (Jones, 1987). The optical properties of the minerals are explored in this microscope and a trained observer is able to identify them. Bard (1980) have summarized and classified the principal textures of igneous and metamorphic rocks. Similar classification of the rock microstructures and a specific methodology to analyse the rock microstructure does not exist. An to specify different rocks despite their similar mineralogical composition is to quantitatively characterize their microstructure, which is the goal of this paper. Modelling of microstructure is done by through image analysis observations of thin sections. This requires having appropriate descriptors of the microstructure, having quantified them by semi automatic analysis of microscopic images and thereafter to model them by probabilistic distributions. To use appropriate distributions and to determine their seed parameters is the main goal of the micro structural modelling. Twelve distributions will be tested to fit the distributions of measurements of the descriptors of the microstructure of a fine and even grained granite. Selected of descriptors to characterize the hard rock crystal matrix are grain size, grain shape, grain orientation. Micro cracks are going to be modelled in the future. The fine and even grained granite is, when observed in hand scale, an homogeneous rock. When observed under the polarizing microscope at twenty 3 five times amplification (Fig.1), a thin section of the granite shows an imbricate microstructure. Therefore one can say that rock is homogeneous in hand scale but its microstructure might also show some variability, which is going to be evaluated in future work. With the help of a digital camera installed in the polarizing microscope which is connected to the computer, four microscopic images from a thin section are taken, which do not match, nor do they overlap (Fig.1). 2.1 Simplification of the microstructure Several simplifications are necessary to reduce the complexity of the microstructure of the fine and even grained granite. They are the basis for consider the results of the microstructural modelling as representative of the analysed rock material. In the sequel, it is assumed that: (1) One thin section gives representative information about the rock. As the rock is homogeneous in the hand scale often one thin section is required to petrographic examination. The reasonability of this assumption is investigated in future work in progress; (2) Grain minerals are homogenous and heterogeneity within the grain is not considered; (3) Thin section of the rock is representative of the real 3D microstructure and no stereological considerations are made. Stereology deals with the interpretation of the three-dimensional structures by means of the two-dimensional sections or projections (Nemati, 2000). This assumption is meaningful as the rock considered is fine even grained. This means that planar thin sections are representative of 3D structure. These introduce errors which simplifications give rise to error in the future crystal matrix model, if compared with reality but the error is considered to be meaningless, and therefore the modelling approach acquires the most meaningful characteristics of the microstructure. 4 Figure 1- Four microscopic images of the fine and even grained granite. 2.2 Image Analysis of microstructure Microscopic images taken with polarizing light are used to study the distribution of grain boundaries while microscopic images taken with parallel light are appropriate to study the distribution of micro cracks and weak areas. Four characteristics emerge due to the optical properties of the mineral: a) different tones and patterns can be observed for the same mineral type, depending the orientation of the crystallographic axis relatively to the cutting plane of the thin section; (b) the boundaries of the small grains are seldom clearly observed because of grain intergrowth; (c) within the mineral bounds the mineral shows a non homogeneous surface, (d) dark minerals occur due to optical extinction and are not possible to be identified mineralogically. The stated characteristics of the microscopic image make the segmentation of the network of grains impossible with known segmentation algorithms. Important code development was done in the early eighties as shown in Fabri (1984) but was not turned into commercial software. 5 Figure 2 - Simplified microstructure of the fine and even grained granite, after image analysis. Digits (not legible) correspond to identified and analysed grains. There is correspondence between each one of images
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