E0-190-2008_(2)Chapter_1.pdf

The damping caused by escape of the seismic waves

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Unformatted text preview: lding. The damping caused by escape of the seismic waves, which have been transmitted into the building, back into the ground is called “ Radiation Damping”. 1.2 Radiation Waves The seismic waves escaping back into the ground are called radiation waves, and these waves cause radiation damping. When the building foundation is forced to vibrate vertically, a stress called “ Contact Earth Pressure” is caused at the boundary between the bottom surface of the foundation and the ground. The distribution of this contact earth pressure over the bottom surface of the foundation is called “ the Contact Earth Pressure Distribution”. Three types of distribution (Rigid, Uniform, and Parabolic distribution as shown) are observed. The types of the distribution are altered depending on : (a) foundation rigidity (b) soil classification (c) soil nonlinearity. When a part of the vertical contact earth pressure is picked out and applied on the ground surface, the vertical displacements of the ground surface can be calculated. At a distance of 10 m from the point where the impulsive force is applied, the first peak denoted by P is appeared, and two peaks denoted by S and R are appeared following the P. With increasing distance from the force application point, these peaks appear at an increasingly later time, and it can be seen that these peaks are propagated at a certain velocity. Connecting the occurrence times of these peaks by straight lines and estimating the propagation velocity from the inclination of these lines. It can be found that the propagation velocity for the peak P is 2450m/sec, that for the S is 1000m/sec, and that for R is 920m/sec. The seismic waves consist of ;(a) P-waves , (b) S-waves and (c) Rayleigh’s waves called “ Surface Waves”. These peaks correspond to the P-waves, the S-waves, and the Rayleigh’s waves. In the case of a homogeneous half space, the relation of propagation velocity between these waves is decided only by the Poisson’s ratio of the ground as shown in the Figure. The Poisson’s ratio of the ground is normally in the range of 0.4 to 0.5. The propagation velocity of the Rayleigh’s waves is about 10 % lower than that of the Swaves. The vibration of energy to the ground is transmitted by Pwaves, S-waves, and Rayleigh’s waves, and in the case of a homogeneous half space, the contribution ratio of the energy transmission for the these waves are 7%, 26%, and 67% respectively for P, S, and Rayleigh’s waves. So, the calculation shows that more than one half of the energy is transmitted by the Rayleigh’s waves. The above explanations with regard to the radiation wave...
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