Fuzzy Estimators of Drain spacing in Subsoil Drainage using Fuzzy Logic and Possibility Theories

In the permanent flow of subsoil drainage, a lot of equations are used, most of them based on the Dupuit assumption. All related mathematical models present uncertainties and fuzziness, which create problems in the design of drainage networks. Fuzzy Logic deals with this problem and allows the management of uncertain information. This paper presents the solution of the Hooghout equation based on Fuzzy Logic and Possibility theories, using the Reduced Transformation Method for the related numerical calculations. This results in a fuzzy estimator for the drain spacing, whose α-cuts, provide, according to Possibility Theory, the confidence intervals of the drain spacing with a certain strong probability. Results on subsoil drainage in the case of soils with parallel drains located at any position from the impermeable bottom are presented. The possibility theory application enables the engineers and designers of irrigation, drainage, and water resources projects to gain knowledge of hydraulic properties (e.g., water level, outflow volume) and make the right decision for rational and productive engineering studies.