3454
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
Theoretical solution for such foundation subjected to sliding
and rocking forced vibration is presented below. The vibration
amplitude and natural frequencies of the block can be derived
from displacement equation (see Eq. 1).
a)
txP 2hxnK
k
1 1hxK x xnK xK
..
xm
tуРуMx1hxK 2hxnK
1Qh 2
2hxnK
k
1 2
1hxK K
..
(1)
Ах, mkm
0
10
20
30
40
50
60
70
26
30
34
38
42
f, Hz
1
2
b)
Where: m – mass of block;
K
x
, K
xn
- sliding subgrade modulus of the block and
plate;
Ах
K
f
– rocking subgrade modulus of the block;
For vibration amplitude the solution to Eg.1 can be given as:
5h
5h
1
P
хA
(2)
Where:
;
2m хпК хК
;
2hxпK
k
1 1hхК
;
2
1Qh 2
2hxK
k
1 2
1hxK K
2hxпK1hxK
The solution to Eg.1 of natural frequencies (see Eq. 3) can be
written as
B4 2А А
2
1
2,1
(3)
Where
;
2
2hxnKk1 2
1hxK1Qh K
m
xnKxK
А
m
1Qh K xnK xK 2
1hxnKxKk12
B
.
Figure 10 shows the comparison of analytical solution (see
Eq. 2) to field test result. The amplitude-frequency responses of
the combined massive and plate foundation are shown. The
plates with area 2.13 m
2
and 4.15 m
2
were located on the soil at
the top of the foundation. This simple spring-mass system can
be used for definition vibration level of the combined massive
and plate foundation on the understanding that properties of
dynamically loaded soil mast be correctly evaluated.
, mkm
0
5
10
15
20
26
30
34
38
42
f, Hz
1
2
Figure 10. Comparison of analytical solution to field test result,
y with dynamic
loa
REFERENCES
mics of Bases and Foundations. MCGraw-Hill,
Kir
Verru
0. An introduction to soil dynamik. Springer. Delft.
25
amplitude-frequency responses of the combined massive and plate
foundation with the plates on the top of foundation: a – area of the plate
is equal 2.13 m
2
, b – area of the plate is equal 4.15 m
2
, 1 – analytical
solution , 2 – field test result.
4 CONCLUSION
The new type of foundation under machiner
ding was developed. It was named the combined massive and
plate foundation. The foundation consists of deepened massive
block and attached in soil one or more horizontal plates. Finite
element analysis and experimental investigation showed that
the combined massive and plate foundations have advantage
over block-type foundations in low-frequency range, as their
vibration level is considerably less. The slab brings positive
influence on vibration level of type-block foundations, their
vibration levels get two or three times reduced and their natural
frequency increases. For most problems the analytical
derivation of solution is given using asymptotic and
perturbation methods. The mathematical models for the
oscillation of the combined massive and plate foundation are a
lumped mass with beams or plates on the viscous-elastic basis.
Integral transformations, Fourier series, averaging methods are
applied for solution to such equations. The analytical and
numerical results are compared with large-scale modeling test
data.
5
Barkan D.D. 1962. Dyna
Inc., New York.
Brajama M.D. and Bamana G.V. 2011. Princeples of soil dynamics.
Cengaga Learning. 552p.
Kirichek Y. 2011. Analisys of the bechavior of massive plate
foundations on viscoelastic base. Proc. of the 15-th European
Conference on Soil Mechanic and geotechnical engineering.
Athens, 557 – 562.
ichek Y. 2000. Combined Massive and Plate Foundations for
Dynamic Loaded Machines,
Soil Mechanics and Foundations
5,
292-299.
ijt A. 201
433p.
