Environmental Engineering Reference
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Figure 3.31.
Development of solution zones in (a) a joint and (b) soluble rock substance or aggregate of
carbonate particles (Based on James and Lupton 1978).
For anhydrite
dM
dt
2
(3.2)
KA(c
c)
s
where M is the mass dissolved in time t, A is the area exposed to solution, c s is the solu-
bility of the material, c is the concentration of material in solution at time t and K is the
solution rate constant.
The limestone used in their laboratory tests was Portland stone, a dense, old rock
(Jurassic Age), in which the carbonate mineral is calcite. For this rock they showed that K
values rose sharply at flow rates close to the onset of turbulence. They note that these
“transitional” velocities (around 0.75-0.8 m/s) would be reached by water flow in joints
with apertures of about 2.5 mm, with an hydraulic gradient of 0.2.
James and Kirkpatrick (1980) use mathematical modelling to provide predictions of the
way joints enlarge as water flows through them. Their Figure 3, reproduced here as Figure
3.32 , shows their predictions for the enlargement by pure water of limestone joints with
initial apertures ranging from 0.5 mm to 2 mm.
It can be seen that the solution occurs essentially by downstream migration of the solu-
tion zone, with no enlargement further downstream. After a period of 100 years, the solu-
tion zone of the 0.5 mm open joint has migrated only 13 m from the inlet face. The
0.7 mm joint shows a similar type of behaviour, but the enlarged portion migrates 30 m in
only 40 years. During very short periods the larger aperture joints show long tapered
enlargements indicating that in real dam situations (i.e. seepage paths often much less
than 100 m) seepage flows would accelerate.
James and Kirkpatrick (1980) conclude that the smallest aperture joint which will cause
dangerous progressive solution in limestone is 0.5 mm for pure water or 0.4 mm for water
 
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