  In this paper we investigate the limit behavior of the solution to
quasi-static Biot's equations in thin poroelastic plates as the thickness tends
to zero. We choose Terzaghi's time corresponding to the plate thickness and
obtain the strong convergence of the three-dimensional solid displacement,
fluid pressure and total poroelastic stress to the solution of the new class of
plate equations. In the new equations the in-plane stretching is described by
the 2D Navier's linear elasticity equations, with elastic moduli depending on
Gassmann's and Biot's coefficients. The bending equation is coupled with the
pressure equation and it contains the bending moment due to the variation in
pore pressure across the plate thickness. The pressure equation is parabolic
only in the vertical direction. As additional terms it contains the time
derivative of the in-plane Laplacean of the vertical deflection of the plate
and of the the elastic in-plane compression term.
