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The principle of virtual power is used to derive the equilibrium fieldequations of a porous solid saturated with a fluid, including seconddensity-gradient effects; the intention is the elucidation and extension of theeffective stress principle of Terzaghi and Fillunger. In the context of a firstdensity-gradient theory for a saturated solid we interpret the porewaterpressure as a Lagrange multiplier in the expression for the deformation energy,assuring that the saturation constraint is verified. We prove that thissaturation pressure is distributed among the constituents according theirrespective volume fraction (Delesse law) only if they are both truedensity-preserving.

A variational approach for the deformation of a saturated porous solid. A second-gradient theory extending Terzaghi's effective stress principle