  In this paper, we propose a new multiphysics finite element method for a Biot
model with secondary consolidation in soil dynamics. To better describe the
processes of deformation and diffusion underlying in the original model, we
reformulate Biot model by a new multiphysics approach, which transforms the
fluid-solid coupled problem to a fluid coupled problem--a generalized Stokes
problem and a diffusion problem. Then, we give the energy law and prior error
estimate of the weak solution. And we design a fully discrete time-stepping
scheme to use mixed finite element method for $P_2-P_1-P_1$ element pairs to
approximate the space variables and backward Euler method for the time
variable, and we prove the discrete energy laws and the optimal convergence
order error estimates. Also, we show some numerical examples to verify the
theoretical results. Finally, we draw a conclusion to summarize the main
results of this paper.
