Dependencies between Grain Sizes Analyses Results Obtained by Various Methods

"Various methods are used to identify the grain composition of fine-grained materials because so far the best notion of the grain size has not found and there is no single method to define grain size. In practice the most important are the following grain sizes: sieve diameter dt, effective diameter de, substitute diameter d2 and statistical diameter dst. The mentioned sizes are connected with the methods of analyses. Methods are correct but measure of different diameters of grain and their results are different.The most important methods of granulometric composition analyses are the following: the sieve analysis, the sedimentation method and the conductometric (Coulter-Counter) methods. In each of these methods various physical features connected with the grain size are measured.Sizes of grains defined by different formulas or measurement methods are associated mutually by dependencies, which are results of differences in their determination or calculation ways.In order to determine principles of results comparison the classification analysis results on linearly or non-linearly connected was made. Analyses which results demonstrate the same type of grain size distribution are treated as linearly connected. It is based on the general formulae which determines the probability density function of random variable which is the function of another random variable having the known density function.In order to show the difference in the grain composition of the same material qualified by different methods, three methods of investigations were distinguished. They are: the sieve analysis performed on precise sieves, the sedimentation analysis performed by means of a sedimentation balance “Sartorius” and the microscopic analysis performed after preparing a microscopic slide where the grain size was measured by the Martin’s method.The materials selected for the analysis were quartzite and glass, which are the material of high purity.The obtained results of mentioned above three types of analyses were approximated by distribution function of four distributions: Weibull, log-normal, cut Weibull and Gaudin-Schuhman."