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Inverse Formulation and Finite Difference Solution to Partially Saturated Seepage from Canals¹

ABSTRACT

The mathematical model describing Darcian flow of water through soils approximates actual occurrences more closely when it permits regions of the flow to be partially saturated. A generally accepted relationship between effective permeability and capillary pressure is utilized to formulate and solve by inverse methods with finite differences the steady-state flow system of water through soils. The inverse formulation considers the cartesian coordinates x and y as the dependent variables and the potential function and the two dimensional stream function as the independent variables (i.e. the problem is solved for x and y in the plane). The approach is applied to the problem of seepage from a canal to a water table and a computer program (FORTRAN IV) has been written for solving this problem.

¹ Contribution from the Utah Water Research Laboratory, Utah State University, Logan.

² Associate Professor, Civil Engineering, Utah State University, Logan, Utah and Staff Specialist, Computer Sciences Corporation, Richland, Wash., respectively.

Received for publication April 18, 1969. Accepted for publication September 19, 1969.