Geoscience Reference
In-Depth Information
arrangement, we obtain a square and four contact points. The porosity of this loosest
type of arrangement is 47.64 %, rounded to 48 %.
The tightest arrangement is hexagonal since the connecting of the centers of
spheres surrounding a central sphere forms a hexagon in a two-dimensional array
provided that the connections passing the central sphere are not allowed. Or, if the
centers of spheres are connected in one direction only, we obtain a rhombus, and the
model is sometimes called rhombic or rhombohedral. The angle of each rhombus is
45°, not 90° as in cubic packing. The porosity of this tightest packing is 25.95 %,
rounded to 26 %. This extremely low value has never been reached in soils.
The third arrangement is a combination of the two abovementioned schemes that
generate porosity values between 26 and 48 %.
However, we know that no soil is a conglomerate of particles having identically
the same size. In reality, smaller particles penetrate into voids between bigger par-
ticles (Fig.
7.2
). And instead of being arranged in a regular system of cubes or
rhombi, they form all sorts of different kinds of lumps and bridges fi lling gaps
between larger particles. Previously, we implied that isolated soil particles rarely
exist. Usually, particles have tendencies to lump together to form microaggregates
and, subsequently, coalesce into still larger clusters known as macroaggregates.
Although some models of spherical particles can yield commonly observed soil
porosity values of 40-60 %, their design and numerical calculation are extremely
complicated. Generalizing such models of pores to the space between spherical
particles does not help too much because they fail to refl ect the various shapes of
soil particles that dominate many important properties of soil pores. We initially
selected spherical particles merely to create a relatively simple demonstration of
porosity.
In order to overcome the diffi culties in applying spherical models to real soils,
the pores have been modeled as tubes of various radii. Such models have been found
Fig. 7.2
Two illustrations of packing different distributions of unequal-sized spherical soil parti-
cles in models that yield more realistic porosities of natural soils
