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

# When the ground is consists of layered strata the

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Unformatted text preview: s are restricted to a homogeneous half space. When the ground is consists of layered strata, the waves transmitted from the building are reflected at the layer interfaces and are returned to the building. Therefore, the radiation damping becomes normally smaller and the entire phenomenon becomes more complicated. 1.3 Vibration of the Foundation on Ground The vibration of the foundation is considered for the case when the dynamic force is applied to the top of the foundation on the ground surface. For simplification, it is assumed that the foundation is not deformed locally and that there are no shape changes during the vibration. When the sine excitation is applied in horizontal direction, the horizontal displacement UO and the rotation φ occur at the foundation bottom. Contact earth pressure resisting this displacement UO and the rotation φ is generated at the interface between the bottom surface of the foundation and the ground surface, and the radiation waves are transmitted to the ground. When the ground is represented by a spring and a dashpot to resist the displacement UO and the rotation φ, the numerical modeling for the foundation can be expressed by: As this foundation has two degrees of freedom in the horizontal displacement and the rotation, this model is called “ Sway Rocking Model” , abbreviated to S-R model. KH denotes the spring value of the ground resistance regarding the horizontal displacement UO. CH denotes the coefficient viscous damping absorbing energy proportional to the velocity dUO/dt as the energy is dissipated into the ground by the radiation waves. KR and CR are the same quantities as mentioned above regarding the rotation. The figures show the calculation results for KH, CH, KR and CR under that the ground and the bottom of the foundation are in perfect contact with each other. The horizontal spring value KH and the dashpot coefficient CH are nearly constant with increase of the vibration frequency. But, KR and CR exhibit remarkable frequency dependency. The KR decreases gradually with increasing frequency, and the CR shows opposite characteristic. The figure shows the horizontal displacement Uf at the top of the rigid foundation. The displacements are normalized by the exciting force . γf in the figure indicates the unit volumetric weight of the foundation. When the γf becomes smaller, that is, when the foundation becomes lighter, it can be seen that the peak frequencies (“ Resonance frequencies”) of the resonance curve become higher, and that the vibration amplitude becomes smaller. Equation of One Degree of Freedom System & m&& + cx + kx = Peiω t x (1) Static (ω=0) Displacement： Xs = P / k (2) Natural Circu...
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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.

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