Geoscience Reference
In-Depth Information
A value for the bearing capacity can be found by using Kötter's equation for
drained soil along the
s
-directions, according to equation (11.4a), which from point
1 to point 4 yields
04
= e
2 (
4
1
)tan
= e
2 tan
01
/
(12.11)
With
q
1
+ c/
tan
=
*
1
(1+sin
) and
q
4
+
c/
tan
=
*
4
(1+sin
), see the Mohr
circles in Fig 12.3, keeping in mind that
01
/
04
=
*
1
/
*
4
, the ultimate end-
bearing capacity
Q
becomes
BLe
2 tan
(
H - B e
tan
/
2tan(¼
))
+ BLc
(
e
2 tan
-
1)/tan
Q
e
=
- ½
(12.12)
=
30
o
and
c =
0
this
For a slender wall, e.g.
B/H
0.05, and soil conditions
becomes
Q
e
=
37.6
BLH
(1 - 5.3
B/H
)
27.5
BLH
(12.13)
=
0, a slightly different approach is to be used, similar to obtaining
equation (12.3), and the result is, with
c = c
u
and
c
u
/
For
L
0.08
Q
e
=
BLH
(1 - ½
B/H
)
+
2
BL
c
u
BLH
(1+2
c
u
/
H
)
1.50
BLH
(12.14)
For obtaining a reasonable ultimate end-bearing capacity of a pile, equations
(12.13) and (12.14) show that friction is essential. The low value (12.14) explains
why pile driving in soft cohesive soils is so easy. Moreover, the point resistance is
only obtained when the pile toe penetrates into the bearing layer 5 to 8 times the
pile width. For that reason end-bearing piles are driven firmly into a bearing layer.
Although the background of equations (12.13) is based on a kinematical approach
and hence the result is to be considered as an upper bound value, it is noted that the
adopted deformation and stress field is not complete, and therefore the real pile
bearing capacity could be higher.
Many studies have been executed to establish a reliable approach for
determining the ultimate static bearing capacity of a single pile. In general, the end-
bearing capacity of a pile can be expressed, similar to (12.8), by
Q
e
/BL = q
e
= N
q
q
0
+ N
c
c + N
B
(12.15)
There are several practical sets of values for the coefficients
N
q
,
N
c
and
N
,
i.e.
according to Terzaghi, Meyerhof, Vesi, or Janbu, and when applying these for a
specific case it appears that results may vary up to 50%. A proper safety factor is
obviously required.
The total bearing capacity
Q
c
(incorporating the weight of the pile itself) is found
by adding the end bearing
Q
e
and the adhesion (friction) along the shaft
Q
s
. When a
pile is (partly) supported by a shaft adhesion, this contribution is referred to as
positive skin resistance. Thus,
Q
c
= Q
e
+ Q
s
. However, local soil compaction and
settling after installation of a pile may reverse the adhesion to negative skin
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