Novel adaptive time stepping method and its application to soil seismic liquefaction analysis

• We developed an adaptive time stepping method for soil liquefaction analysis.
• The error estimator combines the displacement error and the pore pressure error.
• Fixed stepping method and adaptive stepping method are compared.
• The proposed adaptive stepping method is efficient and robust.

In solid–fluid coupled and dynamic analysis, the temporal discretization error related to the time step size is unavoidable. To improve the calculation efficiency, a novel adaptive time stepping procedure based on a finite element and finite difference (FEM–FDM) coupled method is proposed for soil seismic liquefaction analysis. The core concept of this adaptive stepping method is the mixed displacement and pore water pressure error estimation, which is obtained by an embedded error estimator, and a time stepping strategy, which is operated according to the relation between the current mixed error and the prescribed error tolerance. Two numerical examples were performed to validate the proposed method. It is shown that under the same condition of mesh size and other numerical parameters, the time step size obviously affects the calculation results; using adaptive stepping method is economical, robust and has the same degree of accuracy as compared with the fixed stepping method in the soil earthquake liquefaction analysis.