A fractal analysis of the water retention curve

Abstract

The dependence of the soil water content ϑ upon the matric potential ψ is studied within a fractal approach that regards the water retention curve as a sequence of well defined fractal regimes. Each of such regimes accounts for a given functional dependence ϑ≡ϑ(ψ), which in turn is characterized by a fractal dimension. The difference between the double fractal (observed into sandy soils) and multifractal (observed into clay soils) regime is explained by recalling that, for a sandy soil, the transition from saturated to dry conditions is driven by a steep reduction of ψ. To the contrary, for a clay (where the change from the highest water contents to the smallest ones is characterized by a large range of the matric potential), the multifractal behaviour is observed. These results are also confirmed by the analysis of experimental data. In particular, we show that the intermediate regime, generally accounting for the fractal multimodality, is due to the sandy nature of the soil at stake, practically immaterial. Finally, we demonstrate that our model can be also regarded as the straightforward generalization of that of Millán and González‐Posada ().

A scale‐invariant property of the water retention curve in weakly heterogeneous vadose zones

“…This question has been (in part) positively answered by means of the fractal geometry (a general overview can be found in Hunt, Ewing, & Ghanbarian, , and references therein). In particular, the fractal approach has proven to be a valuable tool to determine the scale‐invariant exponents of the water retention curve for a large set of soils (De Bartolo, Fallico, & Severino, ). The present study aims at underlining that some remarkable properties of scale invariance of the effective water retention curve can be detected even within a stochastic approach.…”

Modelling soil hydraulic properties with an improved pore‐solid fractal (PSF) model through image analysis

“…S1-S3, only one changepoint occurred in the SWRC of silty loam soil, and the application of biochar did not significantly change the suction value at the changepoint. De Bartolo,Fallico, and Severino (2018) extended the model proposed by Mill an and Gonz alez-Posada (2005) and found that for sandy soil, soil water movement demonstrated double fractal regimes, whereas in clay soils, soil water movement had multifractal regimes. The experimental soil in this study was closer to sandy soil, and the hydraulic parameters could be predicted with one changepoint.…”

Direct Scaling of Measure on Vortex Shedding through a Flapping Flag Device in the Open Channel around a Cylinder at Re∼103: Taylor’s Law Approach

“…Our approach is based on a direct scaling since analyses do not fit any specific model of . This empirical approach is well-known in literature, see for example [ 52 ] and in other contexts as to estimate the rate of sea level rise at some selected tide gauges around the world [ 53 ], in porous media [ 54 , 55 ], and in the framework of fluid mechanics [ 56 , 57 ].…”