sgr ms thesis - University of Maine

where N (≥r) is the count of clasts with a radius greater than or equal to r, k is a
unit-dependent constant, and D s is the fractal dimension for clast distribution, and
it is considered to be a measure of fracture resistance relative to the mechanism
or process of fragmentation. D s is proportional to the magnitude and rate of
stress loading, the inherent strength properties of the rock, and the possibility of
repeated fracturing events, and therefore can be used to determine the
mechanisms involved in rock fragmentation (Figure 5.3). It is also sensitive to
any secondary mechanisms that may alter the original distribution. The negative
slope signifies the advance of clast population with decreased size.
When producing results for CSD, the clasts in breccias are not perfect
spheres, therefore one must correlate the volume of the clast with an equivalent
value for radius (equal area diameter of Brittain, 2001; Bjork et al., 2009)
calculated by defining a circle with an area identical to that of the clast of interest
(5.4)
The radius value is directly proportional to the area of the clast and is therefore
both suitable for CSD analysis and allows for coherent comparison of data to
other studies, as using an equivalent radius/diameter value is the most popular
method to display CSD data from 2 dimensional sources (Barnett, 2004; Farris
and Paterson, 2007; Bjork et al., 2009).
Sample bias from the inability to see the finest clast populations can
produce a non-fractal trend for finer-scale populations; therefore it is necessary
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