考虑行波时序特征的地基无限域动力模型的时频域转换改进模型研究

Research on improved model of time-frequency domain conversion for infinitedomain dynamic model of foundations considering time series characteristics

复杂场地条件下地基的时域脉冲响应函数难以直接求解,建立地基频域动刚度曲线与时域模型间的高精度转换关系是当前关注的热点问题。基于行波叠加原理,考虑动刚度的奇异性,对一种从频域动刚度转换到时域脉冲响应函数的中村模型进行改进。经典中村模型中存在的重复相位角和奇异项往往会导致不稳定的数值结果。为了解决这些问题,分析了重复相位角出现原因,通过公式推导揭示了重复相位角的分布规律,并提出简便可行的微量调整方法避免重复相位角的出现,使该方法更具有鲁棒性;此外,由于频域动刚度中包含奇异项,无法采用数值傅里叶变换直接向时域转换,以剥离奇异项、只拟合常规项的策略使时域脉冲响应函数达到了较高的拟合精度。以弹性全空间中存在空洞、弹性半空间的半无限杆的解析解为例,验证了改进方法可获得高精度的时域脉冲响应函数,且提高了计算稳定性;以层状地基为例,求解了相互作用力,说明了改进方法在工程应用中的适用性。

It is difficult to directly solve the time-domain impulse response function of foundations in complex sites.Establishing the high-precision conversion relationship between the frequency domain dynamic stiffness curve and the time domain model of the foundations is a hot issue of current concerns.Based on the traveling wave superposition principle and considering the singularity of the dynamic stiffness,the Nakamura model that transforms the frequency domain dynamic stiffness to the time domain impulse response function is improved.The repeated phase angles and the singular terms in the classic Nakamura model often lead to unstable numerical results.In order to solve these problems,the reasons for the repeated phase angles are analyzed,the distribution law of the repeated phase angles is revealed through formula derivation,and a simple and feasible micro-adjustment method is proposed to avoid the occurrence of the repeated phase angles,making the improved method more robust.In addition,due to the singular terms contained in the frequency domain dynamic stiffness,it is impossible to use the numerical Fourier transform to directly convert to the time domain.The strategy of stripping the singular terms and fitting only the conventional terms enables the time domain impulse response function to achieve a higher fitting precision.Taking the analytical solutions of a cavity in an elastic full space and a semi-infinite rod in an elastic half space as examples,it is verified that the improved method can obtain a high-precision time-domain impulse response function and improve the calculation stability.A case study illustrates the applicability of the improved method in engineering application.