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Yellow River, the second longest river in China, exhibits the characteristics of wandering channel, more river branches and higher sediment concentration. Sandy-riverbank collapse in desert reach is very prominent in the fluvial processes of the upper Yellow River, especially during flood period. The study area has been selected as the lower part of the upperYellowRiver from Xiaheyan (Ningxia Province) to Toudaoguai (Inner Mongolia Province), which is called briefly as NM channel and located at the desert region with a total length of 1080 km. The riverbank collapse can be described schematically as in Figure 1.

Field data obtained from sandy riverbanks shows that the vertical riverbank profiles before and after collapse are similar. Both the slope angles are equal to the internal friction angle of the riverbank material, which is in agreement with the results of experiments on the riverbank scour process conducted by Nagata et al. (2000). Based on the field observations and theoretical analysis for the NM channel, calculation of the riverbank collapse volume can be simplified into the erosion volume by water flowing. In this paper, a method calculates the riverbank toe erosion volume is introduced. Only the interaction between flow and riverbank is considered in the process, and the riverbank height is not involved, which changes constantly with sand movement.

The amount of material eroded can be calculated using the residual shear force method, in which the erosion rate epsilon is related to the shear stresst and shear strength tau(c) by

epsilon = k(tau-tau(c)) (1)

where k is the soil erodibility and is determined experimentally. The amount of erosion is

E = integral(H)(Y) k (tau-tau(c))dy (2)

where H is thewater level and Y is the minimumwater depth at which riverbank erosion occurs.

At a sandy riverbank, it is a difficult and indeed dangerous task to survey the flow velocity vertically. Experiments were performed to obtain a relationship between the velocity at a given depth and the surface velocity, which can be expressed by

u/v = 0.56 (y/H)(2) + 0.76 y/H + 0.81 (3)

On the basis of residual shear stress and using an experimentally determined vertical velocity distribution, the amount of erosion is given by

E = integral(H)(Y) k {gamma alpha(2)nu(2)n(2) /H-1/3 [0.56 (y/H)(2) + 0.76 y/H + 0.81] - tau(c) }dy (4)

After all, the calculation was carried out using Matlab software.

The method above has been preliminarily presented for riverbank collapse volume C and verified by using measured date fromWuhai observation site, located at theYellow River passes through the Ulan Buh Desert. The results compared favorably with the measured values.