3453
Technical Committee CFMS /
Comité technique CFMS
0
20
40
60
80
100
120
140
160
180
200
20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52
А,mkm
f,Hz
1
2
Figure 6. The amplitude-frequency responses of the block-type
foundations under horizontal periodic loading: 1 – the plate with area
12m
2
is on the top of foundation, 2 – no plate.
The vibration level of the plate extremely reduced with
increasing the distance from the block. Figure 7 shows
measuring on the large-scale model of block-type foundation
with attached thin plate lying on the soil. Similar effect we can
see on the slab around the block-type foundation of industrial
machinery (See Fig.8).
a)
1000
1000
1000
1000
2000
1 2
3
4
5
b)
0
10
20
30
40
50
60
70
0
0,2
1,2
2,4
3,6
4,2
l ,m
А,mkm
1
2
c)
0
40
80
120
160
0
0,2
1,2
2,4
3,6
4,2
l ,m
А,mkm
2
1
Figure 7. Decline of the vibration amplitude of the plate away the block:
a – the large-scale model, b - vertical vibration amplitude, c - horisontal
vibration amplitude, 1 – vibration frequency 40 Hz, 2 – vibration
frequency 20 Hz.
The large-scale test results and the finite element analysis
(Kirichek Y. 2000) present, that the combined massive and plate
foundations have advantage over type-block foundations in
frequency range 9 – 30 Hz, as their vibration level is
considerably less. The slabs bring positive influence on the
vibration level of block-type foundations in the low-frequency
range. The vibration level of type-block foundations reduced
two or three times as a result of increasing the natural frequency
of system “block – slab”.
0
4
8
12
16
20
0
5
10
15
20
А,mkm
l
,m
Figure 8. Decline of the horizontal vibration amplitude of the slab away
the block-type foundation.
3 ANALITICAL SOLUTION
The mathematical model of the combined massive and plate
foundations is a concentrated mass with either plates or beams
on a viscoelastic base. Integral transformations for vertical and
horizontal oscillations of the block and plates are considered as
a problem of beams or plates on a viscoelastic base using
asymptotic and transformation methods. The analytical
a)
b)
Figure 9. Design model of the combined massive and plate foundation
derivation of the complex problem is also given using a
elementary system (Barkan D.D. 1962. and Verruijt A. 2010).
Figure 9 shows the system consisted of a mass and some beams,
supported by a linear springs.
