The paper presents a rigorous thermodynamic derivation of the augmented Biot equations for a general case of adsorbing fluid mixture confined to nanoporous solid. The proposed approach extends the Gibbs excess adsorption thermodynamics to poroelastic nanomaterials. The augmented Biot equations contain additional terms associated with the adsorption stress, which represents the derivative of the excess grand thermodynamic potential of the adsorbed phase. The adsorption stress depends on the geometrical specifics of the material under consideration (pore size, shape, etc.) and the potential of fluid-solid intermolecular interactions. It can be calculated by using the density functional theory and/or Monte Carlo simulations, as well as empirical or classical thermodynamics theories. Special attention is paid to the specifics of adsorption deformation in micropores of molecular dimensions and the interpretation of the strain measurements in situ XRD and dilatometry experiments. Examples include micro- and mesoporous carbons and metal-organic frameworks.