Element differential method for poroelastic problems

A numerical model for solving the coupling problem of fluid flow and solid mechanics in porous media is established based on the Biot's consolidation theory, and the numerical analysis and calculation are carried out by using a new strong-form finite element method (element differential method, EDM). By comparing with the weak-form methods, the control equation for poroelastic problems can be discretized directly by the element differential method without any numerical integration calculation. Therefore, the method has a relatively simple discrete format when solving the multi-field coupling problem, and it shows high efficiency when calculating the coefficient matrix. The numerical method uses the Lagrange element in the finite element method, which can obtain relatively accurate and stable results compared with the strong-form meshless method. By introducing the element differential method and the implicit time iteration scheme, the displacement and pore pressure of each time step in the porous media can be calculated directly. Two classical numerical models are selected, one is the one-dimensional Terzaghi column model, and the other is the two-dimensional saturated soil zone model. For these two problems, the accuracy and stability of the proposed are verified by comparing with the results of analytical solution and finite element method.