Unformatted text preview: ituting Vse into in Eq.(31), the natural
frequencies can be estimated approximately. M.F at the natural frequencies depend on both a damping
factor h of surface stratum and an impedance ratio α given
by:
(33)
where ρi is mass density.
When the surface stratum has no damping, M.F at the first
natural frequency is obtained as:
(34)
In this soil condition, the impedance ratio is:
(35)
so, M.F is:
(36) As you can see, M.F=
4.5 obtained by Eq.(36)
is larger than that of the
resonance curve.
This discrepancy comes
from the damping factor
0.05 of the surface
stratum.
Note that M.F estimated
from Eq.(36) gives the
maximum M.F.
When you want to know how larger the ground surface
will be amplified in a given soil condition, you can
estimate roughly it by Eq.(36). 3.3 Dynamic Impedance Function
and Foundation Input Motion
Dynamic impedance functions (D.I.F) for the raft(spread)
and the pile foundation are depicted in the figure. D.I.F indicates dynamic soil springs, and it can be
expressed by complex number. Real part of the function
denotes dynamic stiffness, while imaginary part
corresponds to damping capacities. It was already explained in previous chapters that the
damping came from both the radiation damping and the
hysterics damping of soil medium.
In order to understand physical meaning of complex
number of D.I.F, we consider a spring system shown in the
figure comprising of a spring K and a viscous damping
coefficient C. This springviscous damping system is called
“Voigt Model”. When a harmonic external forces
Peiωt is applied to the both sides
of the spring model and
displacements 0.5...
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This note was uploaded on 03/14/2014 for the course CE 5680 taught by Professor Drgrd during the Summer '14 term at Indian Institute of Technology, Chennai.
 Summer '14
 DrGRD

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