Research On Rational Formula Method For Design Flood Calculation Of Small Watershed

The rational formula method is currently one of the widely used methods for calculating design floods in small watersheds in China.In this paper,a method is proposed to solve the problems in the rational formula method such as the rectangular assumption of the confluence area curve.The method before and after improvement was applied to 15 small watersheds,and the feasibility of the proposed method was evaluated by comparing the calculation results of designed flood peaks.The main research content and achievements are as follows:（1）The application of traditional rational formula method15 small watersheds above Changtaiguan section in the Huaihe River Basin were selected as the study basin.DEM was used as the data source and GIS as the tool to extract the characteristic parameters of the watershed required by the rational formula.The rainstorm parameters and concentration parameters were calculated by the“Design Rainstorm and Flood Atlas of Small and Medium-sized Watershed in Henan Province”.The trial calculation method is used to calculate the design flood peak discharge of 15small watersheds with design frequency of 50%.The results show that 1 watershed has full basin runoff concentration and 14 watersheds has partial runoff concentration.（2）Rational formula method based on the length of concentration pathIn the formula for calculating the design discharge peak using the original rational formula method,a correction coefficient is introduced to eliminate the influence of the rectangular assumption of concentration area curve.Based on DEM,the length of drainage path of each point in the basin to the outlet is calculated,and the relationship between F_tc and L_tc is calculated by programming.The spatio-temporal distribution of the flow velocity in the watershed is assumed to be uniform,that is to say L_tc?L equal to t_c?τ.The relationship betweenα_tc and t_c?τin the watershed is obtained through formula transformation,and then a rational formula is obtained for partial confluence based on the length of concentration path.The improved rational formula was applied to the design discharge peak calculation of 14 watersheds,and the results were compared with that of traditional methods.The results show that the peak discharge of improved method is greater than that of traditional method and that the time of concentration of watershed of improved method is less.It is thought that the concentration parameter being obtained based on the rectangular generalization of the concentration area curve in traditional methods is one of the main reasons for the difference in results.It is concluded that the concentration parameter cannot be used directly to the method in which the concentration area curve is generalized as other shapes.（3）Rational formula method based on the time of concentrationUsing DEM as data source and velocity calculation formula considering the influence of rainfall intensity,the runoff velocity of each grid point in the watershed corresponding to different rainfall intensity were obtained;According to the flow velocity and the drainage path,the time of concentration of each grid point to reach the watershed outlet were calculated;Based on the time of concentration,the relationship between the excess rainfall duration t_c and the peaking area F_c corresponding to different rainfall intensity（F_c～t_c）was obtained;the rational formula method based on the time of concentration is obtained by combining the basic form of rational formula with F_c～t_c.The improved rational formula is used to calculate design flood peaks of 14watersheds,and the results are compared with those of traditional methods.The comparison results show three situations:the difference in calculation results between the two methods is not significant,and the improved method’s calculation results are greater than the original method and smaller than the original method.Based on the distribution of confluence area or isochronous area of each watershed obtained from the time of concentration,the causes of the three results were analyzed.It is shown that the improved method is completely based on the real concentration characteristics of the basin to calculate the peak building area F_c corresponding to t_c.It can be concluded that the method is feasible and can be directly applied to the design flood calculation of small watershed in hilly area.