The classical methodology of the scalar potential is used to develop the theory of equilibrium moisture distribution in the vertical in swelling soils. In addition to the well-known moisture potential � and the gravitational potential -z (z being the vertical ordinate, taken positive downward), the total potential � includes a further component �, the overburden potential. It is shown that � = de/d� [P(Zo) + ?zzo] (A) where e is the void ratio, 6 is the moisture ratio, P(zJ is the load (if any) at the surface z = z,, and y is the apparent wet specific gravity. The equilibrium condition that � be constant in depth reduces to a first-order differential equation, the solutions of which represent equilibrium moisture profiles. The singular solution � = �pt for all z > zo (B) separates two distinct classes of non-singular solutions. �p, designated the pycnotatic point, is the moisture ratio at which � assumes its maximum value. Swelling soils satisfying certain conditions (which appear to be theoretically reasonable and agree with the data of soil physics and soil mechanics) possess one, and only one, pycnotatic point. In such soils, then, three distinct types of equilibrium profile occur: (i) Hydric profiles, for which the surface moisture ratio �o > �p. 6 decreases with increasing z, asymptotically approaching 8, at great depths. (ii) Pycnotaticprojiles, for which 8, = aP and equation (B) is satisfied. (iii) Xeric profiles, for which �o < �p. � increases with z, asymptotically approaching �p at great depths. The physical significance of this result is discussed with the aid of calculations for an illustrative example. The hydrology of swelling soils is entirely different in character from classical hydrological behaviour, which ignores the consequences of volume change. Contrary to a common notion, the effects of overburden potential manifest themselves right to the surface of the soil: it is not the magnitude of n, but that of d�/dz, which is important. The effect of swelling on the behaviour of the soil water may be crudely summarized as follows: Gravity operates completely in reverse to the expectations of classical theory in the 'normal' part of the hydric range; its effect diminishes to zero at the pycnotatic point; and it approaches classical behaviour at the dry end of the xeric range. Applications of the analysis to equilibrium states in hydrology and soil mechanics are treated in Part II. In later papers the concept of the overburden potential is applied to steady vertical flows and to infiltration in swelling soils.
Classical behaviour of Q-balls in the Wick–Cutkosky model
