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− with correction of grain sizes, central trend for
D
MAX
= 40 cm:
0.77
τ≈
3.57. σ
[3.41b]
n
(KPa)
− with Charles and Soares' diagram for stability coefficient
Γ
, taking into
account common values of unit weight γ:
(
γ
Γ
0.77 ; 1.4 h/1v
≈
2.46
≈
22
3
KN/m
− the safety factors corresponding to the end of the construction without water
effect are determined for the considered embankment works:
[3.42]
A.Γ b,β
3.57x2.46
1.50
F 100m,D
,1.4 h / 1V
=
=
=
S
40cm
(1-b)
( 2 2x100)
0,23
γ.H
1.5
==
1.37
1.10
F 200m,D
,1.3 h / 1V
S
100cm
The safety factor found for the 100 m high prototype has exactly the usually
recommended value (1.5) for this kind of construction. Conversely, due to the
combined influences of scale and slope effects, the value of 1.1 found for the
extrapolated 200 m high embankment project appears to be far too small.
3.3.2.4.
Scale effect compensation
Used in a reverse way (see Figure 3.16), the above relations for the safety factors
may also be used to determine the constraints on grain size distributions and slopes
in the construction projects in order to maintain the value of the safety factor at a
given level.
As shown in Figure 3.16, the extrapolation to a 200 m high embankment project
starting from our reference prototype with a height of 100 m and a slope of 1.4 h/1v
built with rockfill with a maximum grain size equal to 400 mm leads to the
following results:
− the 1.3 h/1v slope is definitely too steep, unless the maximum grain size is
significantly reduced;
− if the initial maximum grain size equal to 400 mm is kept, the slope of the
200 m high embankment should be decreased to a value close to 1.73 h/1v in order
to keep a safety factor value equal to 1.5;
− should a coarser rockfill be chosen, for example with
D
max
= 1,000 mm, then
the slope should be flattened further.
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