A novel finite element two-step solution scheme for fully coupled hydro-mechanical processes in poroelastic media

A novel two-step solution scheme (TSSS) is described for fully coupled hydro-mechanical (FCHM) analysis of saturated poroelastic media. The TSSS is based on the pressure formulation in two-step. In step one, the pressure field is obtained directly by solving the sub-problems with a reduced scale of displacement variables. This process is fully decoupled. In step two, the displacement field is calculated by staggered iteration of pressure variables. The finite element method (FEM) is used for discretization of the FCHM differential equations in the space domain. The precise time step integration method is performed for the time derivatives. The stability and convergence of the TSSS are proved using a matrix-based spectral analysis in the time domain. It is demonstrated that the TSSS is unconditionally stable, fully explicit and highly precise. The algorithmic error estimation results indicate that the numerical performance in the time domain can match the computer precision. Theoretically, the algorithmic error is caused only by mesh discretization. The stability and accuracy of the TSSS are verified and calibrated by numerical examples. By comparing with the analytical or reference solutions, it is shown that the TSSS result is highly precise, and it is remarkably better than the standard FEM in terms of precision. In addition, the numerical results are stable and independent of the time step size. The numerical experiments also demonstrate the stability, convergence and precision for the pressure formulation of TSSS. The proposed scheme has great potential in engineering applications for long timescale problems, especially the problems focusing on the evolution of pressure field.