ANALYTICALLY COMPUTED RATES OF SEEPAGE FLOW INTO DRAINS AND CAVITIES

The known formulae of Freeze and Cherry, Polubarinova-Kochina, Vederni kov for flow rate during 2-D seepage into horizontal drains and axisym metric flow into cavities are examined and generalized. The case of an empty drain under ponded soil surface is studied and existence of dra in depth providing minimal seepage rate is presented. The depth is fou nd exhibiting maximal difference in rate between a filled and an empty drain. 3-D flow to an empty semi-spherical cavity on an impervious bo ttom is analysed and the difference in rate as compared with a complet ely filled cavity is established. Rate values for slot drains in a two -layer aquifer are 'inverted' using the Schulgasser theorem from the P olubarinova-Kochina expressions for corresponding flow rates under a d am. Flow to a point sink modelling a semi-circular drain in a layered aquifer is treated by the Fourier transform method. For unsaturated fl ow the catchment area of a single drain is established in terms of the quasi-linear model assuming the isobaric boundary condition along the drain contour. Optimal shape design problems for irrigation cavities: re addressed in the class of arbitrary contours with seepage rate as a criterion and cavity cross-sectional area as an isoperimetric restric tion. (C) 1997 John Wiley & Sons, Ltd.