Civil Engineering Reference
In-Depth Information
shows the two Mohr circles of effective stress for the two regions of uniform
stress.
From Eq. (18.39),
s
b
=
s
a
exp(2
φ
)
s
a
exp(
tan 20
◦
)
3.14
s
a
θ
f
tan
=
π
=
From the geometry of the Mohr circles,
p
20
1
1
20
0.66
s
a
=
=
=
−
φ
−
sin 20
◦
1
sin
1
q
l
q
l
1
1
1
1.34
s
b
=
q
l
=
=
φ
sin 20
◦
1
+
sin
1
+
Hence,
20
0.66
=
q
l
=
3.14
s
a
=
1.34
×
1.34
×
3.14
×
128 kPa
and
q
l
A
V
l
=
=
128
×
3
=
384 kN
Notice that these last upper and lower bound solutions are the same; this is
because the mechanism in Fig. 19.29 corresponds to the stress field in Fig. 19.30.
Further reading
Atkinson, J. H. (1981)
Foundations and Slopes
, McGraw-Hill, London.
Calladine, C. R. (1969)
Engineering Plasticity
, Pergamon Press, London.
Chen, W. F. (1975)
Limit Analysis and Soil Plasticity
, Elsevier, New York.
Sokolovskii, V. V. (1965)
Statics of Granular Media
, Pergamon Press, Oxford.
