Analytical application of maximum sediment transport capacity to determine hydraulic geometry relationships in gravel bed rivers

Development of erosion and sedimentation processes due to human activities or natural changes will threaten the stability of the rivers and cause hydraulic and morphological changes. Continuous changes will result in a lot of damages including damage to structures constructed in the rivers. Therefore, preserving the rivers in the equilibrium (regime) state is of great importance. In other words, determination of the stable hydraulic geometry of the rivers is one of the most important cases on which the design, planning, management and training of the river are founded. Two basic approaches have been used to predict the hydraulic geometry of gravel-bed rivers: (1) Those based on empirical regime equations; and (2) those based on the simultaneous solution of the equations governing channel flow. Currently there are considerable restrictions with the use of both methods for channel design purposes. Existing experimental hydraulic geometry relationships have been obtained for particular field conditions and based on limited data, and can be used only under the same conditions. Equally theoretical methods are applicable only to straight or fixed width and with static stability channels, due to our lack of knowledge regarding the mechanisms controlling width adjustment and meander development, a large number of theories have been developed in this regard that the basic assumptions of all include a steady and uniform flow as well as stream changes toward the equilibrium state and the main difference between these theories is the hydraulic mechanisms employed by the models to describe how the stream reaches the equilibrium state. In this Paper, an analytical model for assessing the stable condition (static and dynamic stability) and predicting river response to the applied changes (such as hydraulic changes) was proposed and univariate and bivariate hydraulic geometry relationships to be applicable in the rivers with dominant bed load, were derived. For this purpose, after reviewing the previous researches in this field, the principles and concepts of the regime and hydraulic geometry were presented. In the next step, by using the analytical model, a system of equations was solved without including bank stability constraint (unconstrained model). Due to lack of required equations to solve the system, extremal hypotheses were used. According to these theories, the river behavior is justified in order to optimize a specific morphologic parameter. a good agreement was observed between the developed exponents of hydraulic geometry relationships in this paper and the results of the empirical and analytical hydraulic geometry relationships. This represents the self-adjusting mechanism of alluvial channels by introducing the channel shape factor (bed width/depth ratio) and the inclusion of extremal hypotheses in the flow governing equations (continuity, flow resistance and sediment transport equations). Finally, developed model were calibrated using the field data of the United Kingdom and the mean relative error of the bankfull width and depth calculation is obtained 47% and 35%, respectively. obtained results confirmed the efficiency of the proposed model. Development of erosion and sedimentation processes due to human activities or natural changes will threaten the stability of the rivers and cause changes