Modeling of geometric-hydraulic cross-sectional relationships and transmission capacity Khorramabad river sediment

Introduction
Due to the need for space, high cost, and a long time to perform experiments, the use of physical models is often not recommended. For this reason, many river engineering issues are examined with mathematical models (Azizi et al., ­2019).
Kalami et al. (2019) in detecting geometric-hydraulic relationships of river cross-sections using an inverse solution of Venant equations showed that after identifying the relationships and comparing them, hydraulic-hydrological process methods have high efficiency and accuracy in simulating river floods. Ouda (2019) in modeling and multi-phase reviewing of sediment transport and bed erosion and changes in river morphodynamics using numerical modeling and analysis of sediment production and transfer mechanisms showed that the current numerical model performs well in most cases of Multiphase test shows sediment transport and erosion.
Data and Method
The study area is located in Khorramabad city of Lorestan province in western Iran From Cham-Anjir station, 12 km from Khorramabad, with an area of ​​1650 km² up to Doab Vissian station with an area of ​​2450 km², which in this study includes a part of the permanent river of Khorramabad with a length of approximately 40 km. After entering geometric and flow data into the model, boundary conditions including sediment measurement curve for upstream range and discharge-Ashle curve were performed for downstream range in HEC-RAS hydraulic model and sensitivity results were extracted. Then, using SPSS software, the regression relationship between the dependent variable of Discharge (Q) and independent variables (W), river water surface width (D), average and hydraulic depth of flow, (A) flow cross-section, and (V) velocity The average cross-section (flow) was calculated based on the values ​​of significance level, coefficient of determination and standard error. Based on the results, various simple linear models, degree 2, degree 3, and exponential, and the relationships governing the geometric properties and factors related to the processes affecting the river were investigated. Among them, the relationship with the highest coefficient of determination and the lowest standard error was selected as the appropriate relationship.
 
Results and Discussion
Sensitivity analysis of the model shows that with increasing the number of cross-sections, the rate of change of hydraulic parameters along the river has been clearer. Also in Khorramabad River, the number of sections is 421 and the model estimation accuracy is 20.73% for the water level width parameter, 79.65% for the flow depth parameter, and 74.07% for the flow velocity parameter.  In the exponential model, there is no problem with the variables collinearity and the variables do not interact with each other. In models grades 2 and 3, due to the problem of collinearity, these models do not have sufficient validity. In addition, models grades 2 and 3 did not have sufficient validity in terms of both significance level and standard error. Therefore, the exponential model is introduced as a suitable model due to its non-collinearity, P-value less than 1%, and standard error less than other models. In the obtained function, the discharge flow as a dependent variable is directly related to the width of the river. Also has a more direct connection with the flow cross-section. The Discharge also shows a more direct relationship with the flow cross-section. Because the flow cross-section parameter includes two parameters of flow width and depth (geometric variables of the river). In the obtained exponential function, the sediment capacity as a dependent variable has a direct relationship with the average flow velocity, shear stress, and flow rate as an independent variable. According to the relationship obtained between the independent variables of sediment capacity, it is more dependent on the flow rate. As the flow rate increases, the sediment capacity also increases and vice versa.
 
Conclusion
Studies show that Grade 2 and 3 models did not have sufficient validity due to the problem of being co-linearity and significant level and standard error.In the sediment simulation section, the coefficient of determination obtained in the exponential function for V, Q, SH is less than the values ​​of 2 and 3 degrees regression functions and higher than simple linear regression functions and all variables are meaningful at the level of 1% (99% confidence interval). Also in this function, the variables have the lowest standard error and a significant level compared to the simple linear, grade 2, and grade 3 models. Therefore, they are considered suitable models for the river. The results of the study of exponential functions show that the sediment transport capacity is directly related to the flow rate, flow velocity, and shear stress, and also the flow rate is directly related to the flow cross-section, river width, and flow depth inversely.  This means that with increasing flow, the cross-sectional area of the stream, which includes the width of the river and the depth of the stream, gradually decreases, and also with increasing flow and changes in river morphology, flow velocity and shear stress increase, which results in increased sediment transport capacity and vice versa.