STEADY INFILTRATION IN UNSATURATED SOIL FROM A BURIED CIRCULAR-CYLINDER - THE SEPARATE CONTRIBUTIONS FROM TOP AND BOTTOM HALVES

Waechter and Philip (1985) obtained the asymptotic expansion of the mean infiltration rate for large s from a buried circular cylinder using a scattering analog. Here s(= alpha l/2) is defined as the ratio of the characteristic length l of the water supply surface (in fact, its radius) to the sorptive length 2 alpha(-1) of the soil and alpha satisfies the relationship K(psi) = K(0) e(alpha psi), where K is the hydraulic conductivity, and psi is the moisture potential. This exact solution cannot be used directly to obtain the separate contributions to the mean infiltration rate from the top and the bottom halves of the cylinder; our analysis is based on a new class of special functions derived from the modified Bessel equation with a forcing term. In this paper, we obtain the separate asymptotics for the two halves for large s to make a comparison with the results of the trench problem (Waechter and Mandal 1993). The asymptotic expansions for top and bottom halves are (2/pi)(0.69553s(-2/3)) and (2/pi)(1 + 0.30066s(-2/3)), respectively, whereas for a semicircular trench, the mean infiltration rate is given by (2/pi)(1 + 0.30066s(-2/3)).