Definitions of soil particle sphericity, roundness and roughness have existed since at least the 1930s. In the 1950s, charts of typical sphericity and roundness values were developed to alleviate tedious manual determination. They allowed users to classify particles by visual comparison to typical particles possessing ranges of sphericity and roundness. The original definitions and somewhat subjective chart methods are still widely used today. This paper describes robust numerical methods based on computational geometry to determine precisely the traditional values from two-dimensional images of particles. Statistical methods including locally weighted regression and K-fold cross-validation were used to discretise a mean particle surface and thereby quantify and remove roughness. The paper details the algorithms for identifying particle corners and fitting circles to them for computation of roundness. Conclusions are also drawn regarding the most appropriate definition for particle sphericity from among five that are commonly cited. Finally, recommendations are made for the minimum image resolutions and particle perimeter discretisation necessary to obtain accurate results.
SUMMARYA new finite element model based on a large strain formulation has been developed to study cone penetration in normally consolidated sand. An auto-adaptive remeshing technique was utilized for handling the very large distortion of sand surrounding the cone tip. A frictional contact interface utilizing Mohr-Coulomb's theory was chosen to represent interactions between the surface of the cone and sand. To model the sand behaviour, the non-associated Drucker-Prager constitutive model was selected. ABAQUS, a commercial finite element software package, was used to implement the model. The explicit solution algorithm was chosen due to its effectiveness for complicated contact problems. Analysis results proved that the model successfully captured the cone penetration behavior in sand. In addition, a chart to predict internal friction angles based on cone tip resistance for different vertical effective stresses was provided. This paper also shows a typical distribution of sleeve resistance, tip resistance}penetration relationship, and typical contours of vertical, horizontal, and shear stresses in normally consolidated sand. Finally, a non-uniform resistance was found along the length of the friction sleeve.
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