Substituting vse into in eq3 1 the natural

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Unformatted text preview: ituting Vse into in Eq.(3-1), 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: (3-3) where ρi is mass density. When the surface stratum has no damping, M.F at the first natural frequency is obtained as: (3-4) In this soil condition, the impedance ratio is: (3-5) so, M.F is: (3-6) As you can see, M.F= 4.5 obtained by Eq.(3-6) 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.(3-6) 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.(3-6). 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 spring-viscous 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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