Document Type

Dissertation - Open Access

Award Date


Degree Name

Doctor of Philosophy (PhD)


Agricultural Engineering

First Advisor

John L. Wiersma


A numerical method and model were developed to simulate soil moisture during steady-state and transient flow toward a tile drain. Intermittent application of water by drip irrigation and rainfall were simulated by use of finite difference approximation equations. No known analytical solution for these flow situations exists because of the complex mathematics describing unsaturated flow in the soil. The computer model is based on the electrical resistance network analog. The explicit finite difference equations were solved by the successive over-relaxation method for steady-state flow and by iteration for transient soil moisture flow. The computer program for the model consists of specialized subroutines which solve transient flow problems by a series of steady-state solutions. This series of solutions requires iterative application of the unsaturated flow equation to all unsaturated nodes and successive over-relaxation to all saturated nodes for each unsaturated iteration. Small time steps must be used during unsaturated flow to avoid an unstable solution. The computer model was used to simulate soil moisture movement under three different regimes: (1) drip irrigation, (2) intermittent rainfall, and (3) rainfall on an inclined soil profile when hysteresis xiii W3S considered. An immediate response was obtained during irrigation or rainfall applications. The water table decline prior to water application and after the application was the typical exponential recession curve. The water table receded rapidly above the tile drain and drawdown progressed slowly toward the midplane boundary in the horizontal profile. This numerical technique and model could be a useful design tool to simulate soil moisture movement for evaluating proposed designs of drainage, irrigation, leach bed systems and other soil moisture flow problems.

Library of Congress Subject Headings

Soil moisture
Numerical analysis




South Dakota State University