Adjustment coefficients for planimetric analysis of the granulometry of coarse-grained sediments

What is it about?

A method for determining the grain-size distribution of coarse sediments like debris flow deposits has never been standardised. It is usually assessed through analysis of the matrix (finer fraction) or by estimation (Casagli et al., 2003). Sieving coarse-grained sediments is labour-intensive and time-consuming, and it sometimes hard to perform, for instance in the case of consolidated material. The results tend to depend on the researcher’s experience and may therefore not necessarily be representative (i.e., other researchers may obtain different results). This problem was mentioned for the granulometric analysis of flvial gravels by Wolman (1954), Leopold (1970), Kellerhals & Bray (1971), Church et al. (1989), Wohl et al. (1996), Verdú et al. (2005), Haschenburger et al. (2007) and Dugdale et al. (2010). A literature search indicates that two main sampling methods are commonly combined: planimetric analysis and the traditional sieve analysis. The objective of the present contribution is to determine whether the percentage of the areas occupied in a cross-section by a specific grain-size fraction can be used for estimating its volume percentage, or whether an adjustment coeffiient is required. A similar microscopic method was used for fie-grained sediments by Merta (1991). The relationships between fie-grained grains and their images in thin section were investigated also by Krumbein (1935), Greenman (1951), Packham (1955) and Kellerhals et al. (1975). This planimetric method is also commonly used in petrology to determine the petrographical composition and grain-size of lithifid sediments (Ratajczak & Tumidajski, 1979). As far as we know, no analysis has, however, been published as yet regarding the relationship between the area covered by a coarse-grained framework on a photo and the volume percentage of the framework. The methods cited above are all based on comparison of a model to actual sieve results. In contrast, our method applies a purely mathematical simulation on the basis of exactly known volumes of each of size fractions. Advantages of our method are not only that any subjective interpretation is avoided, but also that the calculations are based on much larger (virtual) sediment samples than can actually be sampled in the field.

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Why is it important?

It appears possible to derive the actual volume of the framework constituents (pebbles, cobbles, boulders) in a coarse-grained sediment from pictures of the wall of an outcrop, but for boulders an adjustment coeffiient (a) is required. The adjustment coeffiients for cobbles and pebbles have a relatively small standard error and are close to a = 1, indicating that a straight relationship exists between the percentage of the surface area covered on a photo by grains belonging to a specifi size fraction and the volume percentage actually occupied by the grains of this size fraction. This implies that no adjustment coeffiient need be applied for deriving the volume percentage from the surface areas on the photos. The larger standard error for the adjustment coeffiient for boulders might be caused by a surface area on the photo that is too small. The relationship between the surface areas of single grains in the cross-sections and that of the whole cross-section area depends relatively strongly on variations in the random distribution of grains of a particular size. The adjustment coeffiient for boulders (0.83) differs substantially from 1, implying that the planimetric method without application of an adjustment coeffiient causes a signifiant error in the estimation of the volume percentage of the boulders The grain-size analysis of coarse-grained sediments should be performed in two phases. In the fist phase, a standard sieve analysis should be performed for grains smaller than pebbles. The minimum sample weight should be 500 g. In the second phase, photographic planimetry can be applied to calculate the proportions of pebbles, cobbles and boulders, which should sum up to 100%. For boulders, an adjustment coeffiient of 0.83 should be used.