自适应时间步长法及三维堤坝地震液化数值模拟

Three-Dimensional Numerical Simulation of Embankment Seismic Liquefaction Using Adaptive Time-Stepping Method

摘要:

三维大模型数值计算因巨大的单元和结点数目而非常耗时,在地震响应分析中受计算时间步长的限值则更加耗时。在饱和砂土动力液化计算平台上开发时域离散误差评估方法和时间步长自适应调整的计算程序,并成功应用于三维堤坝地震液化响应分析。时域离散误差包括土骨架的位移误差和单元孔压误差,通过定义孔压误差影响系数计算出混合误差,根据混合误差和设定的误差允许值进行计算步长的自适应调整。在三维堤坝地震液化数值模拟中,采用自适应时间步长法有效避免小步长精确但耗时、大步长省时而不精确的缺点。在大模型和超大模型计算中,最优调整每一步的计算时间步长,完美实现既节省时间又不失精度的时域离散策略。

Abstract:

Three-dimensional (3D) numerical simulation of a large model is a time-consuming process due to the huge number of elements and nodes. This is particularly true for seismic behavior analysis in which the accuracy is limited by the size of the time increment. In this study, the temporal discretization error estimator and time increment adaptive adjustment method is proposed on the basis of the numerical platform for seismic liquefaction analysis of saturated soil. The proposed method is successfully applied in 3D embankment seismic response analysis. The temporal discretization error estimation includes errors in soil skeleton displacement and pore water pressure. These two types of errors are combined to form a mixed error as an effect of pore water pressure error. The time increment is adaptively adjusted by the relationship of mixed error and the given error tolerance. Through a numerical example of 3D embankment, it is determined that the adaptive time-stepping method can be used to improve the accuracy of small time increments. The results of this method are comparable to those obtained using highly efficient but time-consuming large time increments.