A Mathematical Model to Calculate River Bank Erosion RateCase Study: Zayande Rud River

Bank erosion consists of two processes: basal erosion due to hydraulic force and bank failure under the influence of gravity. Because riverbank resistance force varies with the degree of saturation of bank material, the probability of bank failure is the probability of the driving force of bank failure being greater than the bank resistance force. . The degree of saturation of bank material increases with river stage; therefore, the frequency of bank failure is correlated to the frequency of flooding. Consequently, the rate of bank is a probabilistic phenomenon. In this research, a mathematical model was developed to predict riverbank erosion rate. This model is based on Duan (2005) approach. The model was used to compute riverbank erosion rate of a meander reach in the Zayande Rud river. The model result indicates that the rate of bank erosion at the ZayandeRud river is approximately 0.4 m/year, and bank surfaces are not stable