Study On The Adaptive Time Stepping Method In Seismic Liquefaction Analysis Of Saturated Sand

Numerical method is an effective and fast research way to represent the disasters caused by the saturated soil liquefaction. For the two phase mixture, solid-fluid coupled analysis is generally used in the dynamic calculation scheme. However, the partition of time increment is a serious problem to the calculation accuracy and efficiency, especially in the explicit solving scheme. Therefore, a complete adaptive time stepping stratagem is developed in this research and four applications are conducted in two dimension and three dimension seismic liquefaction simulations. The research ideas and process can be summarized as follows:(1) Against the characteristic of saturated soil dynamic analysis, an effective error estimation system is developed including displacement error estimation and pore water pressure error estimation, as well as the mixed error is proposed to investigate the node displacement variables and element pore water pressure variables during the solution of the solid-fluid governing equations. Through a typical two dimensional embankment model, the traditional uniform stepping method is investigated by setting different time step size and error analysis. The information of error time histories and error distributions are obtained, and the relation between mixed error and time step size is obviously expressed by error convergence.(2) According to the error estimation results and the error convergence, the formula of time step adjusting factor is defined as well as the load item updating formula, the adaptive stepping flowchart and five controlling parameters:initial time step, error tolerance, pore water pressure error proportionality coefficient, the maximum and minimum value of time step adjusting factor. Through the parameter sensitivity analysis, the main controlling parameters are determined as error tolerance and pore water pressure error proportionality coefficient, while the auxiliary parameters are determined as initial time step and the limitation of the step adjusting factor.(3) Four typical numerical examples are conducted to verify the calculation accuracy and the efficiency of adaptive time stepping method. Comparing the fixed time step and adaptive step, it is consistently found that using adaptive step and suitable parameters can make the displacement behaviors and pore water pressure behaviors be close to the results using small time step, meanwhile, it can immensely reduce the calculation time and save the calculation cost.(4) Excepting the robust and high efficiency of the adaptive time stepping method. Some soil liquefaction disasters are represented, such as vertical sink, lateral spreading, uplift behavior to the underground structure and damage to the port industry structure. According to this research, the characteristic of liquefied soil is further studied, which can provide some references to the design of ground and related structure located at the seismic belt and liquefiable soil layers.