  In this work, we propose a structure-preserving discretisation for the
recently studied Cahn-Hilliard-Biot system using conforming finite elements in
space and problem-adapted explicit-implicit Euler time integration. We prove
that the scheme preserves the thermodynamic structure, that is, the balance of
mass and volumetric fluid content and the energy dissipation balance. The
existence of discrete solutions is established under suitable growth
conditions. Furthermore, it is shown that the algorithm can be realised as a
splitting method, that is, decoupling the Cahn-Hilliard subsystem from the
poro-elasticity subsystem, while the first one is nonlinear and the second
subsystem is linear. The schemes are illustrated by numerical examples and a
convergence test.
