Geoscience Reference
In-Depth Information
[3.32]) gives an explicit expression of the second factor of the second term with the
material grain size distributions. The quasi-linear expression of the stability
coefficient,
Γ
, with
cot
β
, gives the third factor of the second term from the diagram
in Figure 3.15:
[3.38]
Γ b,β c +d .
≈
(b) (b) cot
β
Thus, starting from an existing reference embankment prototype, the safety
factor for an extrapolated project, which is higher with coarser granulometry and
steeper slopes, is now given by the following relation:
3(b-1)
m
F
b-1
[3.39]
H,D,β
H,D,β
H
D
c + d . c o t β
S
≈
F
H
D
c + d . c o t β
S
0
0
0
0
0
0
0
3.3.2.3.
Example of calculation
Let us consider a construction project involving an embankment 200 m high,
with a slope of 1.3 h/1v, made of rockfill with maximum grain size of
D
Max
= 100
cm, extrapolated from a reference prototype that is 100 m high and has a slope of 1.4
h/1v, being made of rockfill with a maximum grain size of
D
Max
= 40 cm, coming
from the same mineral stock and prepared at the same density. For the material
parameters for the shear strength and grain breakage, we can use our typical values
of
b
= 0.77,
m
= 6; and for the linearized slope, we can use the stability coefficient
diagram in Figure 3.15, with c = 0.69 and d = 1.28. Under these conditions, equation
[3.39] leads to:
1
1.37
[3.40]
F
F
200 m,D ,1.3 / 1
100 m,D ,1.4 / 1
S
h
V
)
≈
100cm
S
h
V
40cm
0
We can see that the safety factor of the extrapolated project is strongly reduced,
when compared to the one obtained for the prototype.
To go further in the analysis, some orders of magnitude may be determined
by using the central trend of the shear strengths measured for rockfills with
D
Max
= 150 mm (see section 3.2.2.2) together with the corrections in grain size
distribution given by the scale effect rule:
− for shear strength, the central trend for:
τ
≈
0.77
4.
σ
D
MAX
= 15cm:
(KPa)
[3.41a]
n
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