Verification of impermeable barrier depth and effective radius for drain spacing using exact solution of the steady state flow to drains

Abstract

The steady-state drainage equation ofHooghoudt (1940) has adrawback that tables for the determination of the so-called’’equivalentlayer, d_e‘‘ are needed. These calculations arecumbersome as d_e is dependenton the unknown spacing. Moreover, additional head islost due to theconvergence of stream lines towards the finite numberof perforations withinthe pipe wall. Therefore, corrections are required byreplacing the actualdrain radius by its effective radius. The designers inEgypt assume that thedepth of impermeable layer is infinity which resultsin an over estimationof drain spacing that will affect the ability of thedrainage system.Van der Molen and Wesseling (1991) have developed aseries solution toreplace the Hooghoudt‘s approximation method for theequivalent depth by anexact solution. A comparison between this solution andthose of Lovell andYoungs (1984) and Hooghoudt (1940) showed that theexact solution proved tobe very accurate and efficient solution. The mainobjective of this study isto verify an accurate depth of the impermeable barrierand an effectiveradius of drain pipes which should be used in thedesign process using theexact solution.A field investigation was conducted in a study area of33,138 ha in theNorthern Delta of Egypt within Daqahliya Governorate.The results indicatethat a 5 m depth instead of infinity for theimpermeable layer in Nile Deltaand an effective radius of 90 mm should be used in thedesign process. Theuse of the exact solution for equivalent depth is acrucial issue especiallywith the high rate of on-going drainage projects inEgypt.