176
12 Consequences
Julien (2010) provides a set of empirical equations to estimate τ y and μ m as a
function of material type and volumetric concentration. In the example of Figs. 12.1
and 12.2 the empirical equation for typical soils where the presence of clay minerals
is minimal, the particle distribution is composed of very fine sand, silt, and a minor
portion of clay-size particles were selected. The equations are:
τ y = 0.005 × 10
7.5Cv
(12.1)
μ m = 0.001 × 10
8.0Cv
(12.2)
Figure 12.3 shows the graph of τ y and μ m as a function of C v.
Using the equations above and the graph, it is easy to determine the following
Table 12.2 τ y and μ m as a function of C v .
As stated earlier, ρ m is the total density of the fluid: it is a function of C v , W w
and the density for the tailings solids which is 2.82 t/m
3 in the considered TSF. With
50% of volume of water and 50% of solids we have for 1 m
3 : 0.5 * 1 + 0.5 * 2.82
= 1.91 t/m
3 with 45% of solids we have 0.55 * 1 + 0.45 * 2.82 = 1.82 t/m
3 .
The resulting rheological parameters for the Bingham module to simulate the
“normal” (C v = 45) and “high” (C v = 50) tailings volumetric concentration scenarios
are listed in Table 12.3.
In the example above, the selection of C v = 45–50% to characterize “normal”
and “high” tailings volumetric concentrations is key to the discussion.
The histograms in Figs. 12.2 and 12.3 must be considered with attention and the
greatest care. Indeed, they present “gaps”; the medians and mean values seem too
similar to correspond to some significantly different populations, etc.
In particular, the graph in Fig. 12.1, with mean at 45.14, standard deviation at 1.63
and max at 46.94 denotes either a sampling problem or some other ill-conditioned
35.0
40.0
45.0
50.0
55.0
60.0
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
180.0
Cv % v/v
Tau, Mu
τ(Pa)
μ(Pa* s)
Fig. 12.3 Graph of τ y and μ m as a function of C v
12 Consequences
Julien (2010) provides a set of empirical equations to estimate τ y and μ m as a
function of material type and volumetric concentration. In the example of Figs. 12.1
and 12.2 the empirical equation for typical soils where the presence of clay minerals
is minimal, the particle distribution is composed of very fine sand, silt, and a minor
portion of clay-size particles were selected. The equations are:
τ y = 0.005 × 10
7.5Cv
(12.1)
μ m = 0.001 × 10
8.0Cv
(12.2)
Figure 12.3 shows the graph of τ y and μ m as a function of C v.
Using the equations above and the graph, it is easy to determine the following
Table 12.2 τ y and μ m as a function of C v .
As stated earlier, ρ m is the total density of the fluid: it is a function of C v , W w
and the density for the tailings solids which is 2.82 t/m
3 in the considered TSF. With
50% of volume of water and 50% of solids we have for 1 m
3 : 0.5 * 1 + 0.5 * 2.82
= 1.91 t/m
3 with 45% of solids we have 0.55 * 1 + 0.45 * 2.82 = 1.82 t/m
3 .
The resulting rheological parameters for the Bingham module to simulate the
“normal” (C v = 45) and “high” (C v = 50) tailings volumetric concentration scenarios
are listed in Table 12.3.
In the example above, the selection of C v = 45–50% to characterize “normal”
and “high” tailings volumetric concentrations is key to the discussion.
The histograms in Figs. 12.2 and 12.3 must be considered with attention and the
greatest care. Indeed, they present “gaps”; the medians and mean values seem too
similar to correspond to some significantly different populations, etc.
In particular, the graph in Fig. 12.1, with mean at 45.14, standard deviation at 1.63
and max at 46.94 denotes either a sampling problem or some other ill-conditioned
35.0
40.0
45.0
50.0
55.0
60.0
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
180.0
Cv % v/v
Tau, Mu
τ(Pa)
μ(Pa* s)
Fig. 12.3 Graph of τ y and μ m as a function of C v