When I started getting interested in biomechanics, I made this little test example (zip) to get familiar with poroelasticity features in ABAQUS. It represents cartilage on impermeable subchondral bone and a permeable rigid indenter. Details can be found in the JoBM paper by Wu, Herzog and Epstein from 1997 (doi).

The model uses symmetric boundary conditions and axisymmetric elements. It runs with the ABAQUS  Learning Edition :-)  You don't need much imagination to visualize the cylindrical specimen (the left side is the center line). At the upper and right side free draining is allowed.  The animation shows the pore pressure and the velocity of the pore fluid, and the diagram shows the indenter displacement input and the corresponding transient reaction force (and the steady state force as a reference) as a function of the test time.

PS: Beyond the little test example, you can think about what happens when the diameter of the indenter becomes smaller (and impermeable). In the last decade, nano-indentation became popular for testing tissue. In my view, two aspects need to be carefully considered: First, the dimension of the indenter (diameter) may be smaller than a representative elemental volume (REV) of the tissue.  The second point is, that the poroelastic relaxation time depends on the diameter of the indenter, i.e. the experimental setup, and poro- and visco-elasticity may interact....

Addendum: I have elaborated on this point in my recent article published by Springer Nature, Scientific Reports, Towards a reduced order model of the periodontal ligament (doi), in the discussion, 'A promising route are nanoindentation experiments, ...'.