  Multiphase poromechanics describes the evolution of multiphase flow in
deformable porous media. Mathematical models for such multiphysics system are
inheritely nonlinear, potentially degenerate and fully coupled systems of
partial differential equations. In this work, we present a thermodynamically
consistent multiphase poromechanics model falling into the category of Biot
equations and obeying to a generalized gradient flow structure. It involves
capillarity effects, degenerate relative permeabilities, and gravity effects.
In addition to established models it introduces a Lagrange multiplier
associated to a bound constraint on the effective porosity in particular
ensuring its positivity. We establish existence of global weak solutions under
the assumption of a weak coupling strength, implicitly utilizing the gradient
flow structure, as well as regularization, a Faedo-Galerkin approach and
compactness arguments. This comprises the first global existence result for
multiphase poromechanics accounting for degeneracies that are consistent with
the multiphase nature of the flow.
