Civil Engineering Reference
In-Depth Information
where there is a mantle of soil over rock in a hillside and the slip surface is close to the
interface between the soil and the rock.
(a) Undrained loading
Figure 21.9(a) shows an infinite slope where the angle is an upper bound
i
u
with a
mechanism of plastic collapse consisting of a slip surface through the soil at the rock
level; there is a block of soil length
l
measured down the slope. The corresponding
displacement diagram for an increment of displacement
w
is shown in Fig. 21.9(b). For
an infinitely long slope, the forces on any such block are the same as those on any other
similar block and so the forces
F
1
and
F
2
are equal and opposite. From the geometry
of Fig. 21.9(a) the weight of the block (for unit thickness normal to the page) is
δ
W
=
γ
Hl
cos
i
u
(21.6)
and from Fig. 21.9(b) the vertical component of displacement is
δ
v
=
δ
w
sin
i
u
(21.7)
Hence, noting that the increments of work done by the equal and opposite forces
F
1
and
F
2
sum to zero, we have
δ
W
=
s
u
l
δ
w
(21.8)
δ
E
=
γ
Hl
cos
i
u
δ
w
sin
i
u
(21.9)
and, equating
δ
W
=
δ
E
, an upper bound for the critical slope angle is given by
s
u
γ
=
sin
i
u
cos
i
u
(21.10)
H
Figure 21.9
Mechanism of plastic collapse for an infinitely long slope for undrained loading.
