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where V
W
, V
IR
and V
A
are the volumes of water, intact rock and anhydrite. In (8.5),
the water consumption of the swelling clay is neglected since, as mentioned above, the
volume increase due to the transformation of anhydrite into gypsum is large compared
with the volume increase due to the swelling of clay minerals.
For unleached Gypsum Keuper
corresponds to the degree of swelling consisting of
water uptake of the clay and the degree of transformation from anhydrite into gypsum.
For
ω
= 1 swelling of the corrensite is completed and the anhydrite fraction of the rock
is completely transformed into gypsum. However, it should be noted that a complete
transformation of anhydrite into gypsum is only possible if the anhydrite and clay frac-
tions are adequately distributed in the specimen.
ω
Figure 8.7 shows water uptake and swelling of a rock specimen as a function of time in
a one-dimensional swelling test. In three dimensions, water uptake can be described by
the following equation:
(8.6)
Figure 8.7
One-dimensional formulation of water uptake and swelling
Anisotropy of water uptake can be accounted for by a water uptake tensor [D
W
] (Wittke
2003).
According to the homogeneous model, water uptake in jointed rock can be described by
considering a representative elementary volume (REV) which consists of several rock
blocks. Thereby, for simplifi cation, instead of the spatial distribution of
ω
in individual
blocks
ω
B
(x,y,z,t) the average over each block B is considered (Fig. 8.8, upper):
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