In this paper, a novel method is developed to solve the free-field motion of the non-horizontally layered half-space subjected to seismic excitation in the time domain. The total wave motions are decomposed into a known and an unknown wave motion. Making use of the fact that the nodal forces at nodes in half-space resulted from the two motions will be zeros, the scattering problem resulted from the seismic excitation is transformed into a radiation problem. The radiation damping of the unbounded layered foundation in the time domain is expressed by the acceleration unit-impulse response matrix obtained using the scaling surface based Scaled Boundary Finite Element Method (SBFEM). In the numerical examples, firstly, the accuracy of the scaling surfaced based SBFEM in simulating the radiation damping is demonstrated by surface excitations in the layered half-space. Then, a time-domain analysis of the free-field motion of a horizontally layered half-space is studied to verify the accuracy and validity of the proposed method. Finally, a study of the free-field motion of non-horizontally layered half-space is investigated, and the results show that increasing the dimensions of the computational domain can significantly improve the accuracy.

中文翻译：

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求解非水平层状半空间地震响应的新方法


本文提出了一种新方法来求解时域地震激励下非水平层状半空间的自由场运动。总波动被分解为已知波动和未知波动。利用两次运动引起的半空间节点处的节点力为零的事实，将地震激励引起的散射问题转化为辐射问题。时域无界层状基础的辐射阻尼由使用基于尺度表面的尺度边界有限元法（SBFEM）获得的加速度单位脉冲响应矩阵来表示。在数值算例中，首先，通过分层半空间中的表面激励证明了基于缩放表面的SBFEM在模拟辐射阻尼方面的准确性。然后，研究了水平分层半空间自由场运动的时域分析，以验证所提方法的准确性和有效性。最后，对非水平分层半空间的自由场运动进行了研究，结果表明，增加计算域的维度可以显着提高精度。