Two-Dimensional Numerical Modeling of the Effect of the Angle of the Dam with Support to the Parameters of the Flood Due to Partial Dam Break

Introduction In dam failure studies, prediction of its hydraulic components, including depth and velocity, has always been important for hydraulic engineers due to its impact on the severity of the disaster. There are various hydraulic, hydrological, geotechnical and geometric factors that affect the characteristics of the flow through the failure of the dam. In order to investigate the effect of the factors, research has been carried out especially in the field of laboratory, but little numerical research has been done. Resource surveys show that although the walls of concrete reservoir dams are not perpendicular to the lateral support, but so far, the effect of wall deflection on the hydraulic properties of the flood due to the dam failure has not been considered. Therefore, in this research, the effect of quarries of 2.5 to 10 percent of the wall of the dam was examined from the perpendicular to the base. Since the wall deviation of the dam from the normal state removes physical space from a rectangular state, the use of orthogonal coordinate system is not possible. Therefore, in this study, using the curvilinear coordinate system of the physical non- rectangular space studied, It is very accurately converted to computational space and the governing equations are solved. Materials and Methods In this research, the governing equations for shallow water were discritized in curvilinear coordinates by explicit finite difference method. For more stability Lax and Leap-Frog schemes on staggered mesh are utilized, too. For areas studied, in order to determine the coordinates of points in the physical space, by presenting a computer program, the computational mesh is created in Cartesian coordinates. Then, by converting the coordinates in the Cartesian system (x, y) to the curvilinear coordinates (ξ, η). Results and Discussion In order to validate the present model, its results were compared with experimental investigation by previous researchers. 1- Failure of the dam in the convergent-divergent channel without sloping and sloping: The water level profile of the laboratory model is presented for different times (zero, 4, 20, 60) seconds. The mean error in the results of the present numerical model is 4.02% for the results of the measurements for the non-slope channel and for the channel with a 0.01 slope, 1.65%. 2- Dam Failure in canal with dry bed with trapezoidal reservoir: The results of the model follow a similar trend to the experimental results, and the magnitude of the error in the peak areas that is more important is not significant. 3- The effect of the wall angle of the partial symmetric dam-break in the dry bed: It was observed that with the diversion of the wall angle of the dam from the perpendicular position in the failure site, depth and rate of flow decreased more. A closer examination shows that for diversion of 2.5, 5, 7.5 and 10 percent, peak discharge values were decreased  3.5, 6.1, 9.2, 11 percent, and the maximum water level was 2, 6, 9 and 12 percent.   Conclusions In simulating the ideal failure of the deformed reservoir on a dry bed, the results of this numerical model are adapted with the results obtained from the physical model. In another study, the results of the model were compared in the simulation of the dam failure phenomenon in the convergent-divergent channel without sloping and sloping with the results of the measurements. It was determined that a numerical model with an average error of less than 5% estimated the depth of the flow in the failure location.In order to achieve the main objective of the research, the results of the present numerical model in simulating the partial symmetric dam failure on dry bed have been investigated. It was observed that the diversion of the angle of the dam wall at the failer site affects the depth and discharge peak flow. The variations in “q” from the upstream of the reservoir to the failer site increase sharply and reach the maximum at the fracture site, then slowly decrease to the end of the reservoir wall. Similarly, changes in the water level with the distance from the upstream wall and moving towards the failer site are higher.  Keywords Dam-Break, Leap-frag and Lax schem, Curvilinear grid, Angel of Dam Wall  with Support.