Civil Engineering Reference
In-Depth Information
and
1
2
sin
−
1
2
s
u
=
i
u
(21.11)
γ
H
Figure 21.10(a) shows forces and stresses on an element in an infinite slope where
the angle is a lower bound
i
l
. The state of stress increases linearly with depth from zero
at the surface and the maximum shear stress
s
u
occurs on a surface parallel with
the slope. For an infinite slope, as before, the forces
F
1
and
F
2
are equal and opposite
and the weight of a block of soil of length
l
is
W
τ
=
=
γ
Hl
cos
i
l
. Hence, resolving normal
to and along the slope, we have
H
cos
2
i
l
σ
=
γ
τ
=
γ
H
sin
i
l
cos
i
l
(21.12)
s
s
σ
τ
where
s
are the normal and shear stresses in the soil on the surface par-
allel to the slope at a depth
H
. The Mohr circle of total stress for an element of
soil just above the rock is shown in Fig. 21.10(b). The pole is at P and points a
and b represent the states of stress on a horizontal plane and on a plane parallel
s
and
Figure 21.10
Equilibrium state of stress for an infinitely long slope for undrained loading.
