Keywords: dynamic soil structure-interaction, Fourier amplitudes, Lax-Wendroff numerical scheme, flexible foundation, rigid foundation.

The dynamic soil-structure interaction problem is of much interest to engineers. It takes place during the passage of seismic waves through soil. The interaction has a bearing on the stresses in the structure and varies in the time history of the incident earthquake waves [1]. It is well known that dynamic soil-structure interaction (SSI) is a critical factor influencing the response and damage in structures during earthquakes. The main effects of SSI on the response are that the SSI decreases the dominant frequency of the structure's vibrations, filters the high frequencies in the excitation, and increases damping. The common approach to calculating the seismic response of tall buildings has been to formulate the response as a vibration problem in terms of the mass, damping and stiffness matrices of the building [2]. The amount of seismic energy transmitted from the ground to a structure and its propagation in the structure provide critical insight into how the structure will respond during an earthquake. Few studies of wave-propagation methods have been used frequently to analyze continuous structures, such as beams and walls [3].

In this study, a Lax-Wendroff numerical scheme is performed for the solutions. The solution of the interaction of an infinitely long shear wall supported by a rigid semi-circular foundation embedded in linear homogeneous half space and excited by plane SH waves with arbitrary incidence are derived using a wave propagation approach. Fourier amplitudes of the foundation motion connected with the soil-structure interaction are obtained for the numerical examples

The numerical results show that the response of the flexible foundation changes depending on the incident angle of the wave and characteristics of the structure, soil and foundation respectively. In this study, the foundation, structure and soil are all deformed with respect to frequency of the waves during the excitation. This case might indicate which cases of the rigidity of the foundation will be accepted as totally rigid. In the approach for a rigid foundation, the foundation is not deformed and responses are the same in whole foundation, hence the responses are independent of the incident angles.

1

M.D. Trifunac, "Interaction of a shear wall with the soil for incident plane SH waves", Bull. Seism. Soc. of America, 62(1), 63-83, 1972.

2

E. Safak, "Propagation of seismic waves in tall buildings", Struct. Design Tall Build., 7, 295-306, 1998. doi:10.1002/(SICI)1099-1794(199812)7:4<295::AID-TAL117>3.0.CO;2-5

3

M.D. Trifunac, M.I. Todorovska, "Antiplane earthquake waves in long structures", J. Engrg. Mech., ASCE, 115(12), 2687-2708, 1989.

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