This chapter examines the basis of theories dealing with saturation with water in simple 1D applications and in the more complex very deep borehole (VDH) case of interaction of dense smectitic clay contacting clay mud. Clay mineral particle surfaces exposed to water in voids carry electrical double-layers, representing the osmotic potential, while the interlamellar space has the highest hydration potential: water entering dry clay is first sorbed on external surfaces from which it diffuses into the interlamellar space, causing expansion. A key question in the design of VDH is whether there are limits respecting the ratio of the diameter of the dense clay core to be submerged in mud, and of the borehole. This matter has been treated by application of the described numerical model for predicting the evolution of the upper part of the boreholes where there will be no waste.