Strona 2_redak - Instytut Agrofizyki im. Bohdana Dobrzańskiego ...

77
ƒ for the active case (fig. 10.1c):
1−
sinϕ
cosα
k =
,
1+
sinϕ
cosα
(10.4)
where:
sinϕw
α = arcsin −ϕw,
sinϕ
(10.5)
ƒ and for the passive case (fig. 10.1d):
1+
sinϕ
cosα
k =
,
1−sinϕ
cosα
(10.6)
where:
sinϕw
α = arcsin + ϕw.
sinϕ
(10.7)
A plot of the pressure ratio for yielding at the silo wall and the active and the
passive stress cases for typical range of values of the angle of internal friction and
the angle of wall friction is shown in figure 10.2. The pressure ratio observed in
practice varies in a considerably smaller range [91]. A plot of the stress ratio
calculated from the angle of internal friction according to the simplified formula
recommended by Eurocode 1 [50]:
k
ϕ
= 1.1(1
− sinϕ),
(10.8)
is shown in figure 10.2. The angle of internal friction 3 used in this formula should be
determined experimentally in the direct shear test or in the triaxial compression test.
The plot of the pressure ratio obtained from formula (54) is located in the upper limit
of theoretical values obtained for the active stress case and yielding at the wall (i.e. for
the wall friction angle 3 w close to the internal friction angle 3).