考虑横向惯性效应的非饱和土中单桩的竖向动力响应

发布时间：2018-05-14 11:34

本文选题：非饱和土 + 算子分解　；参考：《力学学报》2017年02期

【摘要】：基于非饱和土的动力控制方程,考虑横向惯性效应,建立了三相非饱和介质中嵌岩桩的竖向动力响应连续介质模型,对桩侧非饱和土的动力控制方程进行Laplace变换,在频域内,通过引入势函数、算子分解等手段对控制方程进行解析,得到了桩侧土体剪应力及竖向振动位移的表达式.结合桩基的竖向振动方程及桩土接触面的连续性条件,使桩土耦合振动系统得以解答,最终在频域内得到了桩顶复刚度、导纳、桩土系统振动位移及应力的解析解,借助Laplace逆变换得到了半正弦激励载荷下桩顶的速度时程曲线.最后,通过算例分析验证了计算结果的准确性,分析了横向惯性、泊松比、饱和度、长径比、桩土模量比等因素对桩基动力响应的影响.结果表明:(1)单桩动刚度、阻尼、导纳等变量随频率变化发生周期性振荡,在桩基各阶固有频率处发生共振;(2)泊松比、饱和度、长径比、桩土模量比等因素对桩基的动力响应有较大影响,且频率越大,影响越明显;(3)泊松比越大,单桩动刚度、阻尼、导纳的波动幅值及对应的频率越小,桩顶时程曲线中的桩底反射信号越弱;(4)饱和度越大,对应各动力响应的波动幅值越大,且桩底反射信号的波峰越大.
[Abstract]:Based on the dynamic control equation of unsaturated soil and considering the lateral inertia effect, the vertical dynamic response continuum model of rock-socketed pile in three-phase unsaturated medium is established. The dynamic control equation of unsaturated soil on the side of the pile is transformed by Laplace in the frequency domain. By introducing potential function and operator decomposition, the governing equations are analyzed, and the expressions of shear stress and vertical vibration displacement are obtained. Combined with the vertical vibration equation of pile foundation and the continuity condition of pile-soil contact surface, the pile-soil coupling vibration system can be solved. Finally, the analytical solutions of pile top complex stiffness, admittance, vibration displacement and stress of pile-soil system are obtained in frequency domain. The velocity history curve of the pile top under half sinusoidal excitation is obtained by using the inverse Laplace transform. Finally, the accuracy of the calculation results is verified by an example, and the effects of such factors as lateral inertia, Poisson's ratio, saturation, ratio of length to diameter, pile-soil modulus ratio on the dynamic response of pile foundation are analyzed. The results show that the dynamic stiffness, damping and admittance of single pile oscillate periodically with the change of frequency, and the resonance occurs at every natural frequency of the pile foundation, such as Poisson's ratio, saturation, aspect / diameter ratio, etc. Factors such as pile-soil modulus ratio have great influence on the dynamic response of pile foundation, and the larger the frequency, the more obvious the Poisson's ratio is, the smaller the dynamic stiffness, damping, admittance amplitude and corresponding frequency of single pile are. The more weak the pile bottom reflection signal is in the pile top time history curve, the bigger the fluctuation amplitude of the corresponding dynamic response is, and the bigger the peak value of the pile bottom reflection signal is.
【作者单位】：同济大学道路与交通工程教育部重点实验室;
【基金】：国家自然科学基金资助项目(51478353,41472247)
【分类号】：TU473.1

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