Voids ratio dependent soil-water characteristic curves: Theoretical derivations using fractals

Abstract

The way water is retained in soils is described mathematically using a Soil-Water Characteristic Curve (SWCC). Many equations have been proposed for SWCCs which link degree of saturation, suction and voids ratio. They are empirical or phenomenological in origin and rarely incorporate both the particle size distribution and a description of pore geometry. Here, focusing on fractal soils, by setting particle and pore surface areas equal and constant, analytical derivations are presented linking all parameters defining SWCCs to particle and pore geometries. Descriptions of how pore shapes and volumes depend on voids ratio are incorporated. The derivations show key parameters, the air entry value and air expulsion value, are linked to the voids ratio in power laws, giving theoretical justification to what is observed in experiments. The power exponent is the fractal dimension of the particle size distribution. The voids ratio dependant SWCCs provide very good fits to data for eight soils, three of which are demonstrated here. This discovery means that a SWCC for a single voids ratio can be made applicable to another voids ratio using the particle size distribution.