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considering the fact that the angle between s- direction and r- direction (radial) is
constant, i.e. ½
+
.
$
c/ta n
q
s
q 0
c
A
s
@A
@$
* 3
* 1
Figure 12.2b Stress state
Kötter's equation for drained soil along the s -directions, according to equation
(11.4a), becomes (the soil weight of the plastic zone has been disregarded)
0 ,s + 2
0
,s tan
= 0 or (ln
0 + 2
tan
) ,s = 0
(12.4)
Integration yields
ln
0 + 2
tan
= C s in the s-direction
(12.5)
From zone 1 to zone 3 this gives
03 = e 2( 3 1 )tan
ln
01 + 2
1 tan
= ln
03 + 2
3 tan
or
01 /
(12.6)
With
3
1 =
/2, q + c /tan
=
* 1 (1+sin
) and q 0 + c/ tan
=
* 3 (1
sin
),
see Fig 12.2b, keeping in mind that
01 /
03 =
* 1 /
* 3 , this provides the ultimate
bearing capacity
q = N q q 0 + N c c
(12.7a)
1
sin
tan
with N q =
e
and N c = (N q - 1)/tan
(12.7b)
1
sin
= 30 o , the bearing capacity factors become N q =
18.4 and N c = 30.1. In reality, the specific soil weight
For the present case, with
affects the pattern of slip
 
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