Page 34 - The Combined Finite-Discrete Element Method

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A TYPICAL PROBLEM OF COMPUTATIONAL MECHANICS OF DISCONTINUA 17

Figure 1.24 Gravitational deposition sequence of a pack comprising spheres of three different
sizes: 319 spheres of diameter d = 29.988 mm, 1595 spheres of diameter d = 14.994 mm, 3506
3
spheres of diameter d = 9.996 mm; the total solid volume is V = 9.150e−03 m .

1
S3a
0.9 S3b
S3c
0.8 S3d
S3
0.7
Density 0.6

0.5
0.4
0.3
0.2
0.1
0 50 100 150 200 250 300 350
Distance from the bottom (mm)
Figure 1.25 Density proﬁle for gravitational deposition of a pack comprising spheres of three
different sizes: 319 spheres of diameter d = 29.988 mm, 1595 spheres of diameter d = 14.994 mm,
3506 spheres of diameter d = 9.996 mm; the total solid volume is V = 9.150e−03; S3a is initial
density proﬁle, S3 is the ﬁnal density proﬁle corresponding to the state of rest, and S3b, S3c and
S3d are transient density proﬁles.

Further increase in the fraction of smallest particles is obtained by using ﬁve different
particle sizes. The gravitational deposition of a pack comprising spheres of ﬁve different
sphere sizes is shown in Figure 1.28, while the packing density proﬁle for the same pack is
shown in Figure 1.29. It is observed that the packing density has increased in comparison
to the pack comprising spheres of four different sizes. However, it is still smaller than
the maximum theoretical density for packs comprising identical spheres.
None of the size distributions employed has produced a pack of a density that would
exceed the theoretical density of a pack comprising identical spheres. This is because the

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