ANALYTIC SOLUTION TO A PROBLEM OF SEEPAGE IN A CHEQUER-BOARD POROUS MASSIF

A study is made of steady two-dimensional seepage in a porous massif c omposed by a double-periodic system of 'white' and 'black' chequers of arbitrary conductivity. Rigorous matching of Darcy's flows in zones o f different conductivity is accomplished. Using the methods of complex analysis, explicit formulae for specific discharge are derived. Strea m lines, travel times, and effective conductivity are evaluated. Defle ction of marked particles from the 'natural' direction of imposed grad ient and stretching of prescribed composition of these particles enabl es the elucidation of the phenomena of transversal and longitudinal di spersion. A model of pure advection is related with the classical one- dimensional advective-dispersion equation by selection of dispersivity which minimizes the difference between the breakthrough curves calcul ated from the two models.