地震液化灾害自适应步长计算方法及控制参数研究

Adaptive time stepping method for seismic liquefaction disasters and its control parameters

饱和砂土液化是岩土地震工程和土动力学研究领域的重要课题。在动力液化数值计算中,计算精度和计算效率一直是衡量数值方法的重要指标。在水土二相耦合弹塑性计算的数值平台上开发了自适应步长方法,通过位移误差、孔压误差和混合误差的评估体系建立了时间步长自动调整的策略及相关控制参数。通过控制参数的影响性分析,确定了主要控制参数为误差允许值和孔压误差比例系数,辅助控制参数为初始时间步长、步长调整的下限和上限。对处于液化场地的地铁车站模型进行了动力自适应步长数值计算,获得了上浮位移和超孔压比的发展过程,预测出液化上浮的灾害。同时也对比了固定步长法和自适应步长法的精度和效率,发现采用自适应步长法可极大的节约计算成本并不失计算精度。

Seismic liquefaction of saturated soil is a serious problem in the area of geotechnical earthquake engineering. In the numerical analysis of dynamic process, calculation accuracy and efficiency are the two important indexes to evaluate the numerical method. An adaptive time stepping method is proposed based on a solid-fluid coupled method and an elasto-plastic analysis platform. According to the estimation system of displacement errors, pore water pressure errors and mixed errors, the strategy of time step adjustment and the relevant control parameters are established. Through the sensitivity analysis of control parameters, the error tolerance and proportionality coefficient of pore water pressure errors are identified as the main control parameters, while the initial time step size, lower and upper limits of time step adjustment factor are identified as the assistant parameters. Then, the adaptive stepping method is applied in the numerical analysis of a subway station located in the liquefiable area. The time histories of the uplift displacement and the excess pore water pressure ratio are obtained, which indicates the hazards of underground structure uplift induced by seismic liquefaction. Besides, the fixed stepping and adaptive stepping methods are compared, and it is found that using the adaptive stepping method can save more computational cost without losing the accuracy.