The Final Distribution of Retained Liquid in an Ideal Uniform Soil

Abstract

If liquid, initially saturating the pores of a soil, is allowed to drain from that soil, no such complete drainage as occurs in a simple capillary tube is observed; large quantities of liquid are retained. The quantity of liquid held by the soil immediately after drainage gradually alters; it decreases to a stationary value and the liquid so held finally arranges itself in a stable distribution. Whatever be the distribution, the bounding liquid surfaces are capillary ones and subject to the laws of thermodynamics and capillarity; the Kelvin relation, in general determines the curvatures. The problem is considered for an ideal soil, that is an assemblage of spheres, of a single size, packed at random. There are in the ideal soil three types of distribution. First, there is a pendular region where the liquid is retained in the form of single rings of liquid wrapped around the axis of each pair of adjacent grains in contact. Second, there is a funicular region, which may be considered to arise by coalescence of the rings; we have two or more grain contacts imbedded in a single liquid mass, that is, webs of liquid enmeshing two or more grain contacts and which may involve many grains of the packing. There is, finally, a saturation region in which all pores are completely filled. The limits of each of these zones are determined. The funicular zone is a zone of hysteresis and all values between a normal minimum and complete saturation are usually possible. To calculate the normal minimum distribution the actual packing is replaced by an average packing of grains in hexagonal array and equally spaced to give the required porosity. The funicular distribution is now in the form of single rings wrapped around the axis of each pair of grains of the packing. The volume of each type of ring is determined in terms of (σ/ρghr), where σ is the surface tension of the liquid and ρ its density, r the grain radius, and h the height of the ring above a free liquid reference plane. The average volume of each type of ring is obtained for all rings confined between two given planes. From the average ring volume and the number of such in each cc of packed space, the total retention in each zone above saturation is found. The distribution, that is, the liquid retained in any lamina at a height h above the free liquid, is also given. The results are compared with the data of King.