Abstract
In this paper, we propose a new mixed finite element method for a swelling clay model with secondary consolidation, which is a process of the volume of saturated clay decreasing with time after the completion of primary consolidation. To better describe the multi-physics processes underlying in the original model, we firstly reformulate the swelling clay model with secondary consolidation by introducing a new variable to transform the fluid-solid coupling problem to a fluid coupled problem. Then we give the PDE analysis to prove the existence and uniqueness of the weak solution. And we design a fully discrete time-stepping scheme to use mixed finite element method with P2−P1−P1 element pairs for the space variables and backward Euler method for the time variable, give the stability analysis and the optimal convergence order error estimates. Finally, we show some numerical examples to verify the theoretical results and significant effect on the displacement of the secondary consolidation term.
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