4.3 Compressible Packing Model (CPM

4.3 Compressible Packing Model (CPM)
The aim of developing the Compressible Packing Model (CPM) was to predict the
packing density of polydisperse mixtures of grains; De Larrard [1999] presents the
model in full detail. According to De Larrard, the error in absolute value is 0.77% for
rounded grains and 1.77% for crushed aggregates. The model was validated with data
from literature and results of experiments from different laboratories.

Based on the residual packing density (the virtual packing density of a single sized
fraction), the interaction of smaller and larger particles is accounted for. Virtual means a
degree of packing that is non-accessible in experiments; the grains have to be placed by
hand into the optimum position. The interaction of a grain with larger particles results in
a wall-effect, smaller particles exert a loosening-effect. The effect of the interactions
between grains is assumed to be additive; no interaction between both effects was taken
into account. For each fraction (i) a mixed residual packing density of this fraction can
be calculated by applying Equation 4.3. The lowest number of all fractions results in the
‘true’ virtual packing density of the polydisperse mixture. The geometrical diameter
(dg=(Mi·Mi-1)0.5) was applied as the equivalent diameter of each single size fraction [De
Larrard, 1999].