Conversions

Description

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Model theory

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Geometric mean size

The geometric mean size of a particle, ${\bar {d}}_{i}$ (mm), is defined as:

${\bar {d}}_{i}={\begin{cases}{\sqrt {2}}d_{1}&i=1\\\\{\sqrt {d_{i}d_{i-1}}}&1<i<n\\\\0.5d_{n-1}&i=n\\\end{cases}}$

where:

• $i$ is the index of the size interval, $i=\{1,2,\dots ,n\}$
• $n$ is the number of size intervals
• $d_{i}$ is the diameter of particles retained in a mesh at size interval $i$ (mm)
• the value of $d_{i}$ decreases as $i$ increases, i.e. $d_{i}>d_{i+1}$, $d_{1}$ = top size, $d_{n}=0$

Excel

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