# Research project: Grain Shape Analysis

A method for determining representative tracer shapes.

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A method for determining representative tracer shapes.

Bedload transport investigations using tracer grains require riverbed material to be accurately sampled so that representative tracer forms may be used. This is normally done on the basis of representative particle size; however, less attention has been given to selection by particle shape. We are investigating a new robust and reproducible method for the objective selection of tracer particle shapes.

The method, developed as part of a gravel tracing experiment, has been tested on eight gravel samples from a range of fluvial, beach and scree-slope environments. The method uses five representative shapes (an extreme blade, an extreme rod, an extreme spheroid, an extreme discoid and a median form) from three selected sieves that represent the 16th, 50th and 84th percentiles of the sample size distribution. These shapes have been selected to be extreme but within the realms of the observed shapes of the sampled population.

The best indices and form diagram to use, as a starting point for analysis, are the quantities S/I and I/L in the Cartesian co-ordinate Zingg (1935) diagram. In order for shape analysis to progress from this system, the data must form a joint probability density function that is the product of the marginal distributions of the shape indices and the axes of the diagram. This can be achieved by polar coordinate transformation of the data. Using and combining extreme percentiles of these distributions can identify the sought shapes. A reverse transformation returns these selected quantities back into Zingg indices and the positions of selected shapes can be plotted in the Zingg diagram.

Finally, using the intermediate axial dimensions of each of the sieve samples and scaling using the volume ratio finds the final tracer dimensions. In such a way, tracer dimensions are derived forming shapes with equal volume, thus ensuring the tracer's shape is the only transport variable. A further minor adjustment to the axial lengths ensures that the tracers' dimensions are such that they occur within the sieve boundary of the original sample. From this analysis, a set of tracers with equal weight, can be derived that characterise the shape of clasts present within the riverbed of a given size fraction.