ABSTRACT

To assess the dynamic stiffness of shallow foundations, as an alternative to the existing rigorous approaches, it is convenient to idealize the soil as some semifinite truncated cones representing the infinite nature of the supporting soil. The one-dimensional wave equation for cones which is usually defined in frequency domain has been extended to be solved directly in the time domain. The recently streamlined strength of materials using cones has been developed in the time domain to calculate the response of shallow foundations on a layered half-space for translational degrees of freedom, while the wave pattern in the time domain is not studied for a rocking degree of freedom. The concept of echoes which converts the response of the footing on homogenous half-space to that of the footing on layered site is still applicable when the layered system excited by rocking moments. The echo constants are derived in the current research for rotational degrees of freedom in either the flexibility or stiffness formulation. In this paper, using the theory of cones, equations for direct analysis of soil-structure interaction in the time domain are obtained for the rocking degrees of freedom. The results, calculated exclusively in the familiar time domain, are in remarkable agreement with the results obtained in the frequency domain.

摘要

为了评估浅地基的动态刚度，作为现有严格方法的替代方法，可以方便地将土理想化为一些代表支撑土的无限性质的半有限截锥。将通常在频域定义的一维圆锥波动方程扩展到可以直接在时域求解。最近在时域中开发了使用锥体的材料流线型强度，以计算浅基础在分层半空间上的平移自由度的响应，而时域中的波型未针对摇摆度进行研究自由。当分层系统受到摇摆力矩激发时，将均匀半空间上基础的响应转换为分层站点上基础的响应的回波概念仍然适用。回波常数是在当前的研究中推导出来的，用于灵活性或刚度公式中的旋转自由度。本文利用圆锥理论，得到了在时域直接分析土-结构相互作用的摇摆自由度方程。仅在熟悉的时域中计算的结果与在频域中获得的结果非常一致。利用锥体理论，得到了摇摆自由度的时域土-结构相互作用直接分析方程。仅在熟悉的时域中计算的结果与在频域中获得的结果非常一致。利用锥体理论，得到了摇摆自由度的时域土-结构相互作用直接分析方程。仅在熟悉的时域中计算的结果与在频域中获得的结果非常一致。