Though the first five assumptions are either likely to hold, or deviation will have no discernible effect, experimental results contradict the final three. Darcy's law does not seem to hold at high hydraulic gradients, and both the coefficients of permeability and volume compressibility decrease during consolidation. This is due to the non-linearity of the relationship between void ratio and effective stress, although for small stress increments assumption 7 is reasonable. Finally, the relationship between void ratio and effective stress is not independent of time, again proven by experimental results. Over the past century several formulations have been proposed for the effective stress according to several work hypotheses (e.g. compressibility of grains, their brittle or plastic behavior, high confining stress etc.) and different approaches have been proposed to provide a theoretical proof of the Terzaghi's principle for several kinds of porous media. The main approaches were based on the Theory of Porous Media, the Homogenization Approach, and
Poroelasticity. Recently, a simple yet rigorous general proof was provided, based on classical elasticity theory. By way of example, at high pressures (e.g. in the Earth crust, at depth of some km, where the lithostatic load can reach values of several hundreds of MPa), Terzaghi's formulation shows relevant deviation from experimental data and the formulation provided by
Alec Skempton should be used, to achieve more accurate results. Substantially, the effective stress definition is conventional and related to the problem being treated. Among various effective stress formulations, Terzaghi's one seems particularly appropriate, for its simplicity and as it describes with excellent approximation a wide variety of real cases. ==See also==