محاسبات مربوط به فرسایش شیاری
Erosion Equations
RILL EROSION
The DuBoys channel scour equation as developed by sedimentation engineers (Vanoni, 1975) has been modified for rill erosion (Meyer, 1964). In the WEPP model (Lane et al., 1987) rill detachment is expressed as:

Both research (Graf, 1971) and field observations (Foster and Meyer, 1972b) have shown that the rate of sediment detachment is reduced as the concentration of sediment being carried by a channel increases. This effect was observed immediately downstream from major reservoirs, where relatively clear water caused accelerated erosion on the channel floor. The same phenomenon was also observed by the authors during erosion research in 1987 and 1988, when it was noted that more severe scouring occurred at the top of rills immediately below the point of adding clean water than further downrill. At some highly erodible sites, deposition was observed at the downstream end of some of the rill plots. Because of the effect of sediment load on rill erosion the rill detachment subroutine in the WEPP model includes algorithms to account for a decrease in detachment due to increased amounts of sediment load. Hence, it was necessary to examine the effect of sediment load on the rill erosion rates observed during this experiment.
According to Foster and Meyer (1972b), an intuitive expression for the effect of suspended sediment on rill detachment by scour is:

The above expression allows for the increase of sediment load due to rill detachment only. If the interrill contribution per unit length and width of rill (E), is added to the rill sediment load, then the following equation can be used to relate the change in rill load to sediment load, sediment transport capacity, and interrill sediment contribution:

Equation {8} cannot be solved directly, but an approximate solution (Elliot, 1998) which included dividing increases in sediment load between interrill and rill sources, and assumed a constant shear along a rill, was:
