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Article

Order Out of Chaos in Soil–Water Retention Curves

Department of Civil and Environmental Engineering, University of Brasilia, Brasilia 70910-900, Brazil
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Academic Editor: Maria Clementina Caputo
Water 2022, 14(15), 2421; https://doi.org/10.3390/w14152421
Received: 19 May 2022 / Revised: 15 July 2022 / Accepted: 25 July 2022 / Published: 4 August 2022
Water flow in porous media is one of many phenomena in nature that can demonstrate both simple and complex behaviors. A soil–water retention curve (SWRC) is needed to characterize this flow properly. This curve relates the soil water content and the matric potential (or porepressure), being fundamental for simulating unsaturated soil behaviors. This article proposes a new model based on simple assumptions regarding the saturated and unsaturated branches of soil–water retention curves. Despite its simplicity, the modeling capability of the proposed SWRC is shown for two types of soil. This new SWRC is obtained as a logistic function after solving an ordinary differential equation (ODE). This ODE can also be solved numerically using the Finite Difference Method (FDM), which indicates that the discrete version of the SWRC can be represented as the logistic map for specific parameters. On the other hand, this discrete representation is known to encompass chaotic and fractal behaviors. This link is used to investigate the stability and convergence of the FDM scheme, indicating that for values pre-bifurcation, both the FDM and the analytical solution of the ODE represent the new SWRC. This way, the present paper is the first step to better understating how a chaotic framework could be related to SWRCs and geotechnics in general. View Full-Text
Keywords: soil–water retention curve; unsaturated flow; complex systems; chaos; logistic map soil–water retention curve; unsaturated flow; complex systems; chaos; logistic map
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MDPI and ACS Style

Borges, L.P.d.F.; Cavalcante, A.L.B.; Ozelim, L.C.d.S.M. Order Out of Chaos in Soil–Water Retention Curves. Water 2022, 14, 2421. https://doi.org/10.3390/w14152421

AMA Style

Borges LPdF, Cavalcante ALB, Ozelim LCdSM. Order Out of Chaos in Soil–Water Retention Curves. Water. 2022; 14(15):2421. https://doi.org/10.3390/w14152421

Chicago/Turabian Style

Borges, Lucas Parreira de Faria, André Luís Brasil Cavalcante, and Luan Carlos de Sena Monteiro Ozelim. 2022. "Order Out of Chaos in Soil–Water Retention Curves" Water 14, no. 15: 2421. https://doi.org/10.3390/w14152421

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