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lines. No exact solutions including the soil weight are available. In practice, one
adds in (12.7) a weight term, after Terzaghi, according to (
B
is the width of the
footing)
q = N
q
q
0
+ N
c
c + N
B
(12.8)
For the bearing capacity factor
N
empirical expressions are in use, e.g.
N
=
1.8(
N
q
) (Meyerhof). In literature
one may find tables with bearing capacity factor values for different situations, e.g.
inclined loading, and various geometries of the loaded base.
A generalization of (12.8) for drained soils is
1)tan
(Brinch Hansen) or
N
= (N
q
1)tan(1.4
q = i
q
s
q
N
q
q
0
+ i
c
s
c
N
c
c + i
s
N
B
(12.9)
Here, the
i
-coefficients reflect inclined loading situations and the
s
-coefficients
the shape of the foundation. The latter reflect that the previous theory of slip lines
is applicable for two-dimensional situations only. The shear resistance in three-
dimensional cases is usually larger, because the ratio between slip surface and slip
volume is larger than in two dimensions. Table 12 shows the formulae of EC7.
TABLE 12.1a SHAPE FUNCTIONS, VERTICAL
shape
Square or circle
rectangular B*L (B<L)
s
q
1
+
sin
1 + (
B/L
)sin
s
c
(
s
q
N
q
- 1)(
N
q
1)
(
s
q
N
q
- 1)(
N
q
1)
s
0.7
1 - 0.3(
B/L
)
TABLE 12.1b SHAPE FUNCTIONS, INCLINED (COMPONENTS
F
H
AND
F
V
)
case
F
H
directed along B
F
H
directed along L
(1 - 0.7
F
H
/(
F
V
+
BLc
/tan))
3
(1 -
F
H
/(
F
V
+BLc
/tan
))
3
i
q
i
c
(
i
q
N
q
- 1)(
N
q
1)
(
i
q
N
q
- 1)(
N
q
1)
))
3
))
3
i
(1 -
F
H
/(
F
V
+
BLc
/tan
(1 -
F
H
/(
F
V
+BLc
/tan
For undrained soils (12.8) is generalised to
q = q
0
+ i
c
s
c
(2
+
)
c
u
(12.10a)
with
s
c
=
1 + 0.2(
B/L
)
and
i
c
=
½ (1 + (1 - (
F
H
/BLc
u
)
½
)
(12.10b)
Beside the ultimate bearing capacity the allowable loading also depends on the
deformation or stiffness, the serviceability limit state (SLS). Short-term and long-
term behaviour may involve different mechanisms and the stiffness of the structure
being supported may cause a redistribution of the loading on the separate
foundation elements, which sometimes makes the situation more critical. The
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