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
 
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