Fuzzy Unsteady-State Drainage Solution for Land Reclamation

Very well-drained lands could have a positive impact in various soil health indicators such as soil erosion and soil texture. A drainage system is responsible for properly aerated soil. Until today, in order to design a drainage system, a big challenge remained to find the subsurface drain spacing because many of the soil and hydraulic parameters present significant uncertainties. This fact also creates uncertainties to the overall physical problem solution, which, if not included in the preliminary design studies and calculations, could have bad consequences for the cultivated lands and soils. Finding the drain spacing requires the knowledge of the unsteady groundwater movement, which is described by the linear Boussinesq equation (Glover-Dumm equation). In this paper, the Adomian solution to the second order unsteady linear fuzzy partial differential one-dimensional Boussinesq equation is presented. The physical problem concerns unsteady drain spacing in a semi-infinite unconfined aquifer. The boundary conditions, with an initially horizontal water table, are considered fuzzy and the overall problem is translated to a system of crisp boundary value problems. Consequently, the crisp problem is solved using an Adomian decomposition method (ADM) and useful practical results are presented. In addition, by application of the possibility theory, the fuzzy results are translated into a crisp space, enabling the decision maker to make correct decisions about both the drain spacing and the future soil health management practices, with a reliable degree of confidence.