Edinburgh Napier University

  The measured grading curve is an empirical distribution function, a step function. This is considered here as a discrete distribution with fixed statistical cells. In the grading entropy theory it is characterized by the relative entropy resulting in two sets of entropy coordinates. These first and second grading entropy coordinates classify well the grading curves and are statistically more soundly based in terms of information content than the approximate quantile type parameters used at present. In the theoretical and experimental work on the grading entropy coordinates, the physical content of the parameters are analysed. The results can be summarized as follows. The first entropy parameter seems to be a continuous internal stability measure. The second one allows the definition of a unique, mean grading curve with finite fractal grain size distribution for fixed value of the first parameter. The first parameter is related to internal structure, proven here by DEM tools. It is shown by Math tools that the probability of a stable state of the grading entropy theory is very low. The generally occurring stable states in the nature are originated from the degradation which is deterministic. The internal stability of the engineering structures can be characterized by grading entropy.