Abstract—A mathematical model is constructed to describe erosion from the features formed after the ‘first’ erosion on gravel or dirt roads. The model was based on parameters such as the nature or make of the road, erosion effect, and the effect of repairs. The rill/dune effects on the road were assumed to be proportional to the repairs that are necessary to neutralize them. The repairs model was first analyzed then the general erosion model. Finally, an erosion model that combines all the parameters was developed and analyzed with a numerical example. The main methods used included experimental designs and numerical techniques for the formulation and analysis. Results show that the approximate time required for road repairs given a remarkable effect, reduces with the size of the initial effect. A bigger initial effect reduces the time required to initiate a repair on such roads. Results further showed that erosion effects resulting from the rill/dune development effects are tremendously reduced. Once correct measurements are taken and historically followed, good road maintenance may be experienced in order to enhance economic development in developing countries.

Index Terms—Erosion, features, model, repairs, rill, dune.

T. Semwogerere is with the College of Engineering Design Art and Technology (CEDAT), Makerere University. P. O. Box, 7062, Kampala, Uganda (e-mail: semwogereretwaibu@yahoo.co.uk).
S. B. Kucel is with the Mechanical Engineering Department, Makerere University. P. O. Box, 7062, Kampala, Uganda (e-mail: sbkucel@gmail.com).
P. O. Lating is with the Department of ICT, CEDAT, Makerere University. P. O. Box, 7062, Kampala, Uganda (e-mail: plating@tech.mak.ac.ug).

Cite: Twaibu Semwogerere, Samuel B. Kucel, and Peter O. Lating, "Modeling the ‘Second’ Soil Erosion on Non-Paved Roads," International Journal of Applied Physics and Mathematics vol. 4, no. 4, pp. 290-295, 2014.