A STUDY OF RILL DEVELOPMENT PROCESS BASED ON FIELD EXPERIMENTS

Abstract

Two rectangular experimental slopes are set on a bare slope in order to study the development process of rills (Figs. 1 and 2, Photo. 1). One slope is aimed to observe mainly the development pattern of rills (A-slope in Fig. 2) and another to measure the hydraulic conditions (B-slope in Fig. 2). Both have concrete partition walls except the lower end to eliminate the inflowing of water and sediment from outside the experimental slopes. The electrical resistivity survey, the cone penetration test and the grain-size analysis are also carried out to survey the soil conditions (Figs. 3, 4, 5 and 7). The results of them show that the soil conditions are nearly homogeneous in the traverse and change remarkably from the middle part to the lower part along the longitudinal profile. As for the hydraulic conditions, iL is recognized that the surface erosion occurrs when the rainfall intensity is above 1 mm/10 min (Fig. 8) and surface discharge is more closely related to the rainfall in 30 min than the rainfall in 60 min (Figs. 9 and 10). It is also observed that the sediment discharge per unit width at the end of the slope is nearly proportional to the square of the surface discharge (Fig. 13). Therefore, it can be considered that the sediment discharge per unit area at a certain place in such slopes is proportional to the length from the upper end to the place in a given rainfall intensity if the surface run-off coefficient is constant on the whole slope. Next, we shall discuss the erodibility of the slope by using _??_ where _??_ is the average erodibility coefficient, _??_the sediment discharge and the surface discharge at the end of the slope respectively and S the gradient of the slope. Using the values of _??_ and S obtained from the field experiment for the equation, we can obtain values of the coefficient key (Fig. 15). The figure shows that the value (_??_) decreases almost exponentially with the passing of time. This means that the erosible material of the slope decreases in the course of time. Then, let us investigate the relationship between the slope of the experiment plot and the model slope in order to examine the theoretical model which can validly apply to the development of rills in the model slope (Kashiwaya, 1979). The relationship between variables which play important roles for the rill morphology can be expressed as follows ;_??_(8-2) with D; drainage density, υ; flow velocity, ke; erosion proportionality factor, w; width of rill, ρ; density fluid, μ, viscosity of fluid and g; acceleration of gravity. Assuming that p, p and g take the same values both in the prototype and in the model, we can obtain_??_(9-1) and_??_ with RA; stream area number and Ho; Morton number, from eq. (8-2) by employing dimensional analysis. Therefore, it is said that the law of similarity can be established by using the above two equations. As for the number of rills in the steady state, let us introduce the next equation which is valid for the model slope; _??_ with k; the number of rills, p ; the coefficient expressing the relationship between the number of rills and the total width of rills, r; the ratio of the branching coefficient to the joining coefficient and N; the number of initial rills. It is derived from the stochastic differential equation based on the two hypotheses; the joining probability is proportional to the number of rills and the branching probability is proportional to the relative width (width/depth). In the present slope, assuming that the number of initial rills N is proportional to the slope length and r is in inverse to N (Fig. 17) and using the value of p given in the field experiment (Fig. 16), we can obtain the theoretical number of rills in the steady state of this slope.