Conversions

Description

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Model theory

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Geometric mean size

The geometric mean size of a particle, [math]\displaystyle{ \bar d_{i} }[/math] (mm), is defined as:

[math]\displaystyle{ \bar d_{i} = \begin{cases} \sqrt{2} d_1 & i=1\\ \\ \sqrt{d_{i} d_{i-1}} & 1\lt i\lt n\\ \\ 0.5 d_{n-1} & i=n\\ \end{cases} }[/math]

where:

• [math]\displaystyle{ i }[/math] is the index of the size interval, [math]\displaystyle{ i = \{1,2,\dots,n\} }[/math]
• [math]\displaystyle{ n }[/math] is the number of size intervals
• [math]\displaystyle{ d_i }[/math] is the diameter of particles retained in a mesh at size interval [math]\displaystyle{ i }[/math] (mm)
• the value of [math]\displaystyle{ d_i }[/math] decreases as [math]\displaystyle{ i }[/math] increases, i.e. [math]\displaystyle{ d_{i}\gt d_{i+1} }[/math], [math]\displaystyle{ d_1 }[/math] = top size, [math]\displaystyle{ d_n = 0 }[/math]

Excel

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