An efficient finite element procedure for analyzing three-phase porous media based on the relaxed Picard method. Effective simulation of the solid-liquid-gas coupling effect in unsaturated porous media is of great significance in many diverse areas. Because of the strongly nonlinear characteristics of the fully coupled formulations for the three-phase porous media, an effective numerical solution scheme, such as the finite element method with an efficient iterative algorithm, has to be employed. In this paper, an efficient finite element procedure based on the adaptive relaxed Picard method is developed for analyzing the coupled solid-liquid-gas interactions in porous media. The coupled model and the finite element analysis procedure are implemented into a computer code PorousH2M, and the proposed procedure is validated through comparing the numerical simulations with the experimental benchmarks. It is shown that the adaptive relaxed Picard method has salient advantage over the traditional one with respect to both the efficiency and the robustness, especially for the case of relatively large time step sizes. Compared with the Newton-Raphson scheme, the Picard method successfully avoids the unphysical `spurious unloading’ phenomenon under the plastic deformation condition, although the latter shows a better convergence rate. The proposed procedure provides an important reference for analyzing the fully coupled problems related to the multi-phase, multi-field coupling in porous media.

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