Civil Engineering Reference
In-Depth Information
Figure 19.11
Change of stress across a discontinuity for drained loading.
19.8 Simple lower bounds for a foundation
We can now obtain a simple lower bound solution for the foundation shown in
Fig. 19.6. Figure 19.13(a) shows a state of stress with two vertical stress disconti-
nuities where the state of stress is symmetric about the centre-line. Shear stresses on
horizontal and vertical planes are zero and hence, from Eq. (19.17), the vertical stresses
in elements A and C in regions I and III are
σ
=
γ
z
(19.25)
z
and the vertical stresses in elements B and D in regions II and IV are
σ
=
q
l
+
γ
z
(19.26)
z
Figure 19.13(b) shows the Mohr circles of total stress for the elements A and B and
Fig. 19.13(c) shows the circles for the elements C and D; the points a and b represent
