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Why fractal distribution is so frequent? It is true that fractal dimension is always less than 3? Why fractal dimension of 2.5 to 2.9 seems to be steady-state or stable? Why the fractal distributions are the limit distributions of the degradation path? Is there an ultimate distribution? It is shown that the finite fractal grain size distributions occurring in the nature are identical to the optimal grading curves of the grading entropy theory and, the fractal dimension n varies between –¥ and ¥. It is shown that the fractal dimensions 2.2–2.9 may be situated in the transitional stability zone, verifying the internal stability criterion of the grading entropy theory. Micro computed tomography (μCT) images and DEM (distinct element method) studies are presented to show the link between stable microstructure and internal stability. On the other hand, it is shown that the optimal grading curves are mean position grading curves that can be used to represent all possible grading curves.

Grain breakage affects a number of geotechnical engineering problems. In this research study, the breakage of an artificial, porous granular material (light-expanded clay aggregate (LECA)) has been studied in one-dimensional compression with both standard laboratory techniques and in situ X-ray tomography during loading. X-ray tomography has revealed that there is a wide distribution of internal porosity among LECA particles, and particle tracking has been used, for the first time, to give an objective measurement of each particle's life expectancy. Links between micro-and macro-scale quantities are discussed.

The increasing understanding of the connection between particle morphology and mechanical behaviour of granular materials has generated significant research on the quantitative characterisation of particle shape. This work proposes a simple and effective method, based on the fractal analysis of their contour, to characterise the morphology of soil particles over the range of experimentally accessible scales. In this paper, three new non-dimensional quantitative morphological descriptors are introduced to describe (i) overall particle shape at the macro-scale, (ii) particle regularity at the meso-scale, and (iii) particle texture at the micro-scale. The characteristic size separating structural features and textural features emerges directly from the results of the fractal analysis of the contour of the particle, and is a decreasing fraction of particle dimension. To explore the meaning of the descriptors, the method is applied first to a variety of Euclidean smooth and artificially roughened regular shapes and then to four natural and artificial sands with different levels of irregularity. Relationships are established between the new morphological descriptors and other quantities commonly adopted in the technical literature.

This work presents a study on the evolution of the Grain Size Distribution (GSD) of an artificial granular material with crushable grains and its relation with the observed mechanical behaviour. The main aim of the work is to find a relationship between the initial GSD, its evolution and the mechanical behaviour. The artificial material used is a Light Expanded Clay Aggregate (LECA) subject to one-dimensional compression at various stress levels with eight initial GSDs characterised by four coefficients of uniformity and two mean diameters. The evolution of the GSD is characterised by a double mechanism depending on the initial GSD and on the applied stress level. A link between the evolution of the GSD, breakage and the compressibility curves is observed. A bimodal Weibull distribution function is proposed to describe the GSD before and after testing. The long term objective of the work is to link the evolution of breakage, from moderate to high stress, with the mechanical behaviour and to formulate a constitutive model able to describe the observed behaviour