Environmental Engineering Reference
In-Depth Information
Taking the above assumptions, the (dynamic or static) rotational spring stiffness c
w
at
the soil/structure interface can be calculated as follows:
c
w
¼
@
M
found
@w
E
s
I
found
t
found
¼
4
E
s
I
found
A
found
p
¼
c
s
I
found
¼
This equation is evaluated below for the customary foundation forms:
a) Square pad foundation (side length a
found
):
t
found
¼
0
a
found
:
25
a
found
;
c
w
¼
0
:
333
E
s
b) Circular foundation (diameter d
found
):
t
found
¼
0
0
:
5
125
p
0
:
5
:
25
ð
A
found
Þ
¼
0
:
d
found
¼
0
:
222
d
found
E
s
I
found
t
found
¼ 0
p
0:5
d
found
¼ 0
d
found
c
w
¼
:
125
E
s
:
222
E
s
c) Annular foundation (outside dia. d
a
, inside dia. d
i
):
An upper estimate of the effective depth t
found
is as follows:
t
found
<
222
d
a
From this we get a lower estimate for c
w
:
0
:
d
a
d
i
d
a
E
s
I
found
t
found
>
c
w
¼
0
:
222
E
s
4.2.2 Stability of towers on soft subsoils
A flexible spread foundation beneath a tower can lead to instability but not necessarily
to a heave failure (just like an excessively high centre of gravity can cause a floating
body to capsize).
The following description is based on [54]. A horizontal load H applied to the top of the
tower causes the tower to tilt as a consequence of its elastic support (Figure 4.3).
The deformed structure (second-order theory!) therefore experiences an additional
destabilising moment:
M
1
¼
G
h
s
sin
q
G
h
s
q
This together with the moment from the horizontal load
M
2
¼
H
h
causes the following reaction beneath the tower foundation:
Ds ¼ð
M
1
þ
M
2
Þ
x
=
I
found
¼
k
s
x
tan
q
k
s
x
q
where
A
found
area of foundation
I
found
second moment of area
k
s
modulus of subgrade reaction