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. The energy-transmitting boundary, which is used in the well-known FEM program FLUSH, is a quite efficient technique for the earthquake response analysis of buildings considering soil-structure interaction. However, it is applicable only in the frequency domain. The author has studied and proposed methods for transforming frequency dependent soil impedance into the time domain. In the previous paper, the author proposed an earthquake response analysis method using the energy transmitting boundary in the time domain using the transform method, because the kernel of the boundary is the frequency dependent impedance full matrix. Then, an earthquake response analysis with a nonlinear building using the boundary was carried out, and the accuracy and the efficiency of the boundary were confirmed. In that analysis, the inner field (the region inside the boundary) could be treated as the nonlinear system, but the free field (the region outside the boundary) and the boundary were treated as the linear system. Contrary to this, in this paper, the nonlinear transmitting boundary is proposed. By using it, all of the inner field, the free field and the boundary itself can be treated as the nonlinear system. The boundary impedance matrix is calculated in the frequency domain corresponding to the condition of the free field at the specific times. Then, these impedance matrices are transformed to the impulse response matrices in the time domain. In the nonlinear response analysis of the total system, the transmitting boundary at each time step is obtained by interpolation of these impulse response matrices between the specific times. Then, example earthquake response analyses were performed using a practical soil and building model to evaluate the soil-structure interaction effect. The response accuracy was compared with the cases of viscous boundary, which is the most common and representative boundary in the time domain. It was shown that the area of the inner field can be greatly reduced by using the proposed method because the accuracy of the boundary is quite high. Therefore, it was confirmed that the proposed method is effective.

EARTHQUAKE RESPONSE ANALYSES OF SOIL-STRUCTURE INTERACTION SYSTEM USING NONLINEAR ENERGY TRANSMITTING BOUNDARY