Selection criteria of mesh size and time step in FEM analysis of highly nonlinear unsaturated seepage process

The selection criteria of the mesh size and time step that ensures a convergent result in FEM analysis of highly nonlinear unsaturated seepage process is established. First, the concept of critical mesh size (Lc) and critical time step (Δtc) are theoretically deduced, and their framework is set up. Subsequently, formulas for the prediction of Lc and Δtc are proposed through a series of numerical experiments. Additionally, the reliability of the proposed criteria is verified by analytical solutions, model test results, and quasi-engineering problems, respectively. Finally, the ranges of Lc and Δtc under various conditions in engineering applications are recommended. The results show that the proposed criteria can predict the approximate range of Lc and Δtc, so as to obtain the convergent wetting front position and water content distribution. In addition, the criteria can be applied to the scale and dimensions of laboratory experiments and engineering cases. Moreover, the mesh size and time step were interdependent. Under limiting conditions, the appropriate mesh size should be selected prior to the time step. The research results can provide a reference for improving the accuracy of the FEM analysis of unsaturated seepage.