Analytical Approximation of Subsurface Total Drainage Quantity in Non-Steady State Drainage Flow, and its Verification in Heavy Soils

The subsurface total drainagequantity is one of the most importantindicators for the drainage policy of watermanagement. The methods of estimationof the subsurface total drainage quantityunder unsteady state drainage flow maybe different in consideration of the timeduration of the process and in relation tothe type, quality and quantity of the data used.Simple analytical approximation of thesubsurface total drainage quantity, whichwas developed by the operation of asubsurface pipe drainage system insaturated soil under unsteady statedrainage flow, is viewed in this paper.Derivation of the formula for subsurfacetotal drainage quantity is based onthe subsurface flow to drains with anapproximately horizontal impervious layer,where the Dupuit's assumptions and Darcy'slaw are applied. It is assumed that duringthe drainage process there will be no rechargeto the groundwater table.This analytical approximation of thesubsurface total drainage quantity at acertain time t was formed into a singleexponential equation. The correctness andapplicability of the analyticalapproximation of the subsurface totaldrainage quantity was verified with the help ofthe field measurements on the heavy soilsof an experimental watershed area of theResearch Institute for Soil and WaterConservation (RISWC) Prague-Zbraslav, CzechRepublic. The shape and the parameters ofthis subsurface total drainage quantityequation were also proved by nonlinearregression analysis, with application of themethod of Marquardt.This analytical approximation should serveas an elementary tool of water engineeringpractice for an immediate estimation of thevalues of subsurface total drainagequantities from field pipe drainagesystems in saturated soils. It shouldalso serve as a tool with only a minimumamount of information (the basic soilhydrology data and drainage system basicdesign parameters) and its application to awide range of drainage policies ispossible.