Morphology and gully erosion caused by sediment transport

Mt. Sakurajima, one of the most active volcanoes in the world, produces abundant volcanic ash in abundance and this was especially true in the 1980s. The mountainside is composed of fallen pumice and deposited ash, and its slope is as steep as 20 - 30 degrees. Many people are living close to this volcano and several typhoons visit here every summer. And debris-flow due to heavy rainfall often causes great damage to the surrounding areas. Therefore further investigations on the forecast of outflow of the debris have been needed. Meanwhile, it is well known that Scheidegger described a topographical model for the longitudinal profile of river basins. However, his model appears to have some disadvantages when river engineers attempt to apply it, partly because the model has several unknown parameters which denote the topographical properties, and partly because the physical meaning of the parameters concerning precipitation is not clearly defined. In a river basin where the concept of entropy is accepted, through the method of Horton-Strahler, stream numbers are calculated as a function of a distance from the watershed. The purpose of this study is to obtain a fair-working solution to the problem of the profile of a river basin, especially a gully process with sediment transportation caused by precipitation. The eroded cross section is to have a logarithmic similarity from the field data. Consequently a new differential equation of profile variation was derived from the equations of continuity and motion with respect to water and sediment. The computed results show a close agreement with the experimental and field data. As a result of this study, we obtained a method to estimate the amount of debris outflow in a volcanic area where the upstream basins are bare, yet therefore yield abundant sediment at the mouth of a river.