A fuzzy set approach of an analytical solution of non-steady two-dimensional drainage

摘要

A new analytical solution for soil water two-dimensional movement to an orthogonal mesh of parallel drains is presented, as an extended case of the one-dimensional flow problem of the same nature. An equation is provided, that gives the profile of the water surface as well as the volume that has passed through the drains at a given time moment. Non-dimensional profiles of the piezometric surface are given for various values of time and space parameters. The water volume versus time derived from the respective equation is in very good accordance with the volume derived from surface profile integration. We also explore the possibility to solve this problem by using the fuzzy set approach, to cope with the uncertainties of the hydraulic parameters. Triangular fuzzy numbers are used to represent the hydraulic conductivity of the soil as well as the storativity of the aquifer. The drained water volume derived from the fuzzy set after denazification, approaches the one calculated by the analytical solution, included in the interval of presumption level a - 0.8.