The second gradient model of poromechanics, introduced in Part I, is here linearized
in the neighborhood of a prestressed reference configuration to be applied to the
one-dimensional consolidation problem originally considered by Terzaghi
and Biot. Second gradient models allow for the description of boundary
layer effects both in the vicinity of the external surface and the impermeable
wall.
The formulated differential problem involves linear pencils of ordinary differential
operators on a finite interval, with boundary conditions depending on the
spectral parameter. Taking into account the dependence of the differential
problem on initial stresses a linear stability analysis is carried out. Finally,
numerical solutions are compared with the corresponding classical Terzaghi
solutions.
Keywords
poromechanics, second gradient materials, consolidation