The Delft Sand, Clay & Rock Cutting Model, 2019a

Basic Soil Mechanics.
2.4.3.4. Porosity.
Porosity is the ratio of the volume of openings (voids) to the total volume of material. Porosity represents the
storage capacity of the geologic material. The primary porosity of a sediment or rock consists of the spaces between
the grains that make up that material. The more tightly packed the grains are, the lower the porosity. Using a box
of marbles as an example, the internal dimensions of the box would represent the volume of the sample. The space
surrounding each of the spherical marbles represents the void space. The porosity of the box of marbles would be
determined by dividing the total void space by the total volume of the sample and expressed as a percentage.
The primary porosity of unconsolidated sediments is determined by the shape of the grains and the range of grain
sizes present. In poorly sorted sediments, those with a larger range of grain sizes, the finer grains tend to fill the
spaces between the larger grains, resulting in lower porosity. Primary porosity can range from less than one percent
in crystalline rocks like granite to over 55% in some soils. The porosity of some rock is increased through fractures
or solution of the material itself. This is known as secondary porosity.
Vv
Vv
e
n
V V V 1
e
t s v
(2-8)
2.4.3.5. Void ratio.
The ratio of the volume of void space to the volume of solid substance in any material consisting of void space
and solid material, such as a soil sample, a sediment, or a powder.
Vv
Vv
n
e
V V V 1
n
s t v
(2-9)
The relations between void ratio e and porosity n are:
n
e
e and n=
(2-10)
1 n 1 e
2.4.3.6. Dilatation.
Dilation (or dilatation) refers to an enlargement or expansion in bulk or extent, the opposite of contraction. It
derives from the Latin dilatare, "to spread wide". It is the increase in volume of a granular substance when its shape
is changed, because of greater distance between its component particles. Suppose we have a volume V before the
enlargement and a volume V+dV after the enlargement. Before the enlargement we name the porosity ni (i from
initial) and after the enlargement ncv (the constant volume situation after large deformations). For the volume
before the deformation we can write:
i
V 1n V n V
(2-11)
i
The first term on the right hand side is the sand volume, the second term the pore volume. After the enlargement
we get:
V dV 1n V dV n V dV
(2-12)
cv
cv
Again the first term on the right hand side is the sand volume. Since the sand volume did not change during the
enlargement (we assume the quarts grains are incompressible), the volume of sand in both equations should be the
same, thus:
1 n V 1 n V dV
(2-13)
i
cv
From this we can deduce that the dilatation ε is:
dV ncv
ni
dn
V 1
n 1
n
cv
cv
(2-14)
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