Finite element analysis of Biot’s consolidation with non-Darcian flow

Based on the classic Biot’s consolidation theory, the consolidation equation considering non-Darcian flow is set up and then solved numerically with the aid of the finite element method. Firstly, the well-known Hansbo’s non-Darcian flow model is incorporated and the selection of the input parameters is analyzed correspondingly. Then, with a further simplification of the hydraulic gradient combining with the flow continuity condition and the force equilibrium condition, the governing equations for the Biot’s general consolidation theory with non-Darcian flow are formulated. Based on this, the finite element formulations for the spatial eight-node block element are deduced by means of the weighted residual method. A program considering the effect of the non-Darcian flow is developed based on an existing procedure correspondingly. With this modified program, the obtained governing equations can be solved numerically. Finally, the reliability of the numerical method is verified against the established theoretical solutions. The results show that (1) the difference of the calculated results for the two methods increases with the increase of the non-Darcian flow parameters, and the maximum difference is smaller than 10%; (2) the consolidation rate will slow down when considering the effect of non-Darcian flow, and this effect is significant when the property of the non-Darcian flow is apparent.