Civil Engineering Reference
In-Depth Information
Figure 19.7
Mechanism of collapse for a foundation.
Table 19.1
Work done by internal stresses for mechanism in Figure 19.7
Slip plane
Shear stress
Length
Displacement
δ
W
=
s
u
L
δ
w
√
2
1
oa
s
u
√
2
B
δ
w
f
s
u
B
δ
w
f
ob
s
u
B
2
δ
w
f
2
s
u
B
δ
w
f
√
2
1
oc
s
u
√
2
B
δ
w
f
s
u
B
δ
w
f
√
2
δ
w
f
1
ab
s
u
√
2
B
s
u
B
δ
w
f
√
2
δ
w
f
1
√
2
B
bc
s
u
s
u
B
δ
w
f
fa
0
B
δ
w
f
0
Total
6
s
u
B
δ
w
f
19.7 Discontinuous equilibrium stress states
To calculate a lower bound it is necessary to analyse an equilibrium state of stress and
to show that it does not exceed one of the failure criteria given by Eqs. (19.1) and
(19.2). The equilibrium states of stress may vary smoothly from place to place or there
can be sudden changes of stress across stress discontinuities, provided, of course, that
the conditions of equilibrium are met across the discontinuities.
