Order Out of Chaos in Soil–Water Retention Curves

Abstract

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.