Scale-Invariance Ideas Explain the Empirical Soil-Water Characteristic Curve

The prediction of the road’s properties under the influence of water infiltration is important for pavement design and management. Traditionally, this prediction heavily relied on expert estimates. In the last decades, complex empirical formulas have been proposed to capture the expert’s intuition in estimating the effect of water infiltration on the stiffness of the pavement’s payers. Of special importance is the effect of water intrusion on the pavement’s foundation – known as subgrade soil. In this paper, we show that natural scale-invariance ideas lead to a theoretical explanation for an empirical formula describing the dependence between soil suction and water content; formulas describing this dependence are known as soil-water characteristic curves.