黏弹性人工边界地震动输入方法及实现

Method and realization of seismic motion input of viscous-spring boundary

本文对实现黏弹性边界的常用方法进行了总结,对相应于黏弹性边界的地震动输入公式进行了详细推导,把自由场应力的求解也转化为自由场速度的求解,简化了地震动输入公式,并给出了地震动输入的简化方法。基于ABAQUS软件,进行算例分析并和理论解进行对比,验证了各种黏弹性边界实现方式及本文地震动输入方法的合理性和正确性。最后,对大朝山重力坝典型挡水坝段进行地震响应分析,通过施加黏弹性边界并输入相应地震动,评价了无限地基辐射阻尼的影响,并与无质量地基模型的计算结果进行了比较。结果表明,考虑辐射阻尼效应后坝体地震响应明显降低,故在实际工程抗震分析时对其影响应予以适当考虑。

Radiation damping of infinite foundation must be considered in the analysis of structure-foundation dynamic interaction, and viscous-spring artificial boundary method is widely applied because of its advantages. However, for the dynamic response analysis of structure-foundation system under the action of the exogenous earthquake, it still needs to determine the seismic motion input corresponding to viscous-spring boundary. Currently, it is usually changed to be the equivalent nodal forces on the artificial boundary nodes, however, it is complicated due to the requirement of the free-field displacement, velocity and stress. Therefore, this paper firstly summarized the various methods of achieving the viscous-spring boundary. Secondly, a formula of seismic motion input relative to the viscous-spring boundary was deduced. The free-field stress was calculated by the free-field velocity, which simplify the formula of seismic motion input. In addition, the simply realization of seismic input was presented. Thirdly, based on the ABAQUS software, a numerical example was conducted and compared with the theoretical values to evaluate the rationality and validity of the approaches of the viscous-spring boundary and the seismic motion input. Finally, the seismic response was analyzed aiming at a typical retaining section of the Dachaoshan gravity dam. Through implementation of the viscous-spring boundary and input of corresponding seismic motion, the effect of radiation damping was evaluated. Compared with the massless foundation model, it was found that the seismic response decreased significantly. Therefore, the impact of radiation damping of foundation should be considered properly in the seismic analysis of actual projects.