The mechanics of vertically stratified porous media has some similarities to and
some differences from the more typical layered analysis for purely elastic media.
Assuming welded solid contact at the solid-solid interfaces implies the usual continuity conditions,
which are continuity of the horizontal strain components and the vertical
stress components. These conditions are valid for both elastic and poroelastic media.
Differences arise through the conditions for the pore pressure and the increment of fluid content
in the context of fluid-saturated porous media. The two distinct conditions most typically considered
between any pair of contiguous layers are: (1) an undrained fluid condition at the interface, meaning
that the increment of fluid content is zero (i.e.
(2) fluid pressure continuity at the interface, implying that the change in fluid
pressure is zero across the interface (i.e.
). Depending on the types
of measurements being made on the system and the pertinent boundary conditions for these measurements,
either (or neither) of these two conditions might be directly pertinent. But these conditions are sufficient
nevertheless to be used as thought experiments to determine the expected values of all the poroelastic coefficients.
For quasi-static mechanical changes over long time periods, drained conditions hold, so the pressure
must then be continuous. For high frequency wave propagation, the fluid typically acts essentially
as if it were undrained - or nearly so, with vanishing of the fluid increment at the boundaries being
appropriate. The poroelastic analysis of both these end-member cases is treated in detail.