Civil Engineering Reference
In-Depth Information
20
◦
. The bearing pressure
(i.e. the total stress on the underside of the foundation) is
q
φ
=
the ground surface in dry soil, which has a friction angle
=
V
/
B
. For simplicity
the soil is assumed to be weightless (
γ
=
0) except above foundation level, where
20 kN/m
3
, so that the 1 m deep layer applies a uniform surcharge
γ
=
20 kPa
at foundation level. The idealized loads and stresses are shown in Fig. 19.26(b).
γ
D
=
(a) Upper bound. Figure 19.27(a) shows a mechanism consisting of two wedges and
Fig. 19.27(b) is the corresponding displacement diagram. For
φ
=
20
◦
suitable
angles for the slip surfaces are 45
◦
±
10
◦
and all displacements are at angles
ψ
=
φ
=
20
◦
φ
>
30
◦
to the slip surfaces. (Notice that if
the directions ob and
ab diverge and the mechanism is not compatible.)
From the geometry of Fig. 19.27(a),
B
tan
2
(45
◦
+
1
2
φ
)
3 tan
2
55
◦
=
L
=
=
6.1 m
Figure 19.27
Mechanism of collapse for the foundation in Figure 19.26.
