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This paper deals with three grading entropy-based rules that describe different soil structure stability phenomena: an internal stability rule, a filtering rule and a segregation rule. These rules are elaborated on the basis of a large amount of laboratory testing and from existing knowledge in the field. Use is made of the theory of grading entropy to derive parameters which incorporate all of the information of the grading curve into a pair of entropy-based parameters that allow soils with common behaviours to be grouped into domains on an entropy diagram. Applications of the derived entropy-based rules are presented by examining the reason of a dam failure, by testing against the existing filter rules from the literature, and by giving some examples for the design of non-segregating grading curves (discrete particle size distributions by dry weight). A physical basis for the internal stability rule is established, wherein the higher values of base OPEN ACCESSEntropy 2015, 17 2782 entropy required for granular stability are shown to reflect the closeness between the mean and maximum grain diameters, which explains how there are sufficient coarser grains to achieve a stable grain skeleton.

Abstract:The grading entropy concept can be adapted to the field of geotechnics, to establish criteria for phenomena such as particle packing, particle migration and filtering, through a quantified expression of the order/disorder in the grain size distribution, in terms of two entropy-based parameters. In this paper, the grading entropy theory is applied in some geotechnical case studies, which serve as benchmark examples to illustrate its application to the characterisation of piping, softening and dispersive soils, and to filtering problems in the context of a leachate collection system for a landfill site. Further, since unstable cohesive (dispersive) soils are generally improved by lime, the effect of lime addition is also considered, on the basis of some measurements and a further application of the grading entropy concept, which allows evolutions in the entropy of a soil to be considered as its grading is modified. The examples described support the hypothesis that the potential for soil erosion and particle migration can be reliably identified using grading entropy parameters derived from grading curve data, and applied through an established soil structure OPEN ACCESSEntropy 2012, 14 1080 stability criteria and a filtering rule. It is shown that lime modification is not necessarily helpful in stabilizing against particle migration.