Variationally consistent derivation of the stress partitioning law in saturated porous media

The linearized version of a recently formulated Variational Macroscopic Theory of biphasic isotropic Porous Media (VMTPM) is employed to derive a general stress partitioning law for media undergoing flow conditions under prevented fluid seepage and negligible inertia effects, typically met in biphasic specimens subjected to jacketed tests.The principle of virtual work, relevant to the specialization of VMTPM to such characteristic flow conditions, naturally yields a stress partitioning law, between solid and fluid phase of a saturated medium, that exactly matches with the celebrated Terzaghi’s principle. It is also shown that the stress tensor of the solid phase work-associated with the strain measure of the VMTPM naturally corresponds to the Terzaghi’s effective stress. Accordingly, under undrained conditions, Terzaghi’s law is proved to be a completely general stress partitioning law for a saturated biphasic medium irrespective of its constitutive and/or microstructural features as well as of the compressibility of its constituent phases.Since the developments reported are obtained ruling out thermodynamic constraints and any assumption on the internal microstructure and on the compressibility of the phases, the results obtained indicate that Terzaghi’s law could more generally apply to a broader class of biphasic media and be not restricted within the context of geomechanics.