For unsaturated poroelasticity, the pore pressure is computed from the volume average of the liquid water and moist air pressures, pl and pm

here, sl is the liquid saturation, and sm = 1 − sl is the moist air saturation.

here, ρa stands for the dry air density, ρv is the vapor density, ρl is the liquid water density, ρw is the volume average water density (vapor and liquid), and   ϕw is the relative humidity.

where χi stands for the i-component of the compressibility.

For a formulation equivalent to Large Strain Poroelasticity, the continuity equations read

The moisture flux Γw and the dry air flux the Γa are described in details in the Theory for Moisture Transport in Solids chapter.