Civil Engineering Reference
In-Depth Information
and
P
=
pL
=
20
×
7.6
=
152 kN
δ
w
f
=
From the geometry of Fig. 19.29(b), taking
1,
tan(45
◦
+
1
2
φ
) exp(
φ
)
δ
w
p
=
θ
tan
tan 55
◦
exp(
/2 tan 20
◦
)
δ
w
p
=
π
=
2.53
For drained loading, from Eq. (19.12),
δ
W
=
0. The work done by the external
γ
=
γ
=
loads is given by Eq. (19.9) with
0 for weightless and dry soil:
w
δ
E
=
V
u
δ
w
f
−
P
δ
W
p
Equating
δ
E
=
δ
W
,
V
u
=
152
×
2.53
=
385 kN
(b) Lower bound. Figure 19.30(a) shows an equilibrium stress field consisting of a
region B where
σ
1
(
σ
3
(
p
=
20 kPa) is
vertical. These are separated by a fan zone with a fan angle of 90
◦
. There could
be a similar stress field at the left-hand edge of the foundation. Figure 19.30(b)
=
q
l
) is vertical and a region A where
=
Figure 19.30
Equilibrium stress field for the foundation in Figure 19.26.
