Title: A theoretical treatise of drainage and seepage in bottom land areas adjacent to incised channels: the J. J. van Deemter analysis Author
Submitted to: International Symposium on River Sedimentation
Publication Type: Proceedings
Publication Acceptance Date: March 1, 2013
Publication Date: September 2, 2013
Citation: Romkens, M.J. 2013. A theoretical treatise of drainage and seepage in bottom land areas adjacent to incised channels: the J. J. van Deemter analysis. Proceedings of the 12th International Symposium on River Sedimentation. 2049-2058. (CD ROM) Interpretive Summary: Seepage is an important but underappreciated mode of soil erosion. Seepage may also undermine dams and levees, facilitate gully development, and can serve as a conduit for pollution of open water bodies from contaminated fields. Seepage is part of the realm of groundwater flow problems and often occurs at the lower part of slopes, where water exits the soil profile. In quantifying seepage knowledge is required of the nature of the groundwater flow regime. This article revisits solutions to groundwater flow that are capable of predicting seepage losses based on conformal theory. This technique was developed in the 1920s and used to a limited degree in the 1930s, but has not received the attention it deserves. J. J. van Deemter applied this theory in addressing drainage and infiltration problems, including seepage. This article revisits his work to determine whether it can be used to solve certain groundwater flow problems involving seepage.
Technical Abstract: Saturated groundwater flow research on agricultural land in early times was mainly concerned with drainage of excessive rain. The key issue then was the spacing of drains or ditches to provide the efficient and effective removal, within a given time, of excessive water for a given soil. The focus was almost exclusively on flat land areas and for homogeneous, isotropic soils. In this context, the analytical and experimental works by Hooghoudt, Kirkham, Gustafsson, Childs, and others in the 1930s and 1940s come to mind in which various aspects of this problem were studied. Since those days, drainage research has shifted to a host of other issues involving soil profile heterogeneity, soil layering, drainage technologies, etc. Perhaps the most significant, but least recognized, contribution to drainage theory under steady flow regimes through homogeneous isotropic soils during those early years was the work by J. J. van Deemter (1950) in the Netherlands. His work represents an analytical approach of finding exact solutions for a host of situations of 2-dimensional flow using conformal theory. His work represented a major advancement at that time but never received the recognition it deserved because: (1) it was written in Dutch; (2) upon completing his work, Dr. van Deemter joined the Royal Dutch Shell and did not continue or publish this work; and (3) the mathematical complexity of his work was beyond the competency of many drainage practitioners. This paper revisits his work and the analytical solutions obtained for a number of scenarios involving drainage by drains, ditches, and stream channels. The significance of this work today is that it allows the evaluation of seepage forces in streambank instability issues, sediment production in stream channels, and water quality source problems from land adjoining streams.