Seepage rate function establishment and validation for trapezoidal canal based on dropping head ponding test

Abstract: Dropping head ponding test is a typical method for canal seepage measurement, particularly under variable canal capacities during irrigation. This study analyzed the limitations of traditional method for seepage rate calculation and proposed a new method based on dropping head ponding test (DHPT). Based on dropping head ponding test results and a standard method in Technical Code for Seepage Control Engineering on Canal, seepage rates were calculated, and a power function was established to describe the relationships between water-level and seepage rate. The standard calculation method had two inaccurate hypotheses. One was the linear variation of water-level dropping speed between a pair of contiguous measurements. However, water-level dropping speed slowed down while water level dropping down, and dropping speed change was obviously nonlinear in trapezoidal canals. The other hypothesis was the power functions that restricted regression precision. In addition, calculation error increased while measurement interval was prolonged, and it resulted in an integral error to the power functions. The new DHPT function was developed with 3 components in this study: the relationship between water level and its dropping speed, water surface width variation due to water level, and wetted width variation due to water level. The DHPT function development process was simplified to 6 steps: 1) Making plot of water-depth vs measuring time to generate a water variation function; 2) Deriving an inverse function of water-depth variation and its first derivative expressed as water level dropping speed; 3) Deriving a function between water surface width and water depth; 4) Deriving a function between wetted width and water depth; 5) Establishing a seepage rate function; and 6) subtracting evaporation from total lost water, and then correcting seepage rate function. In a case study, test canals were designed for 6 types of lining forms with a cross-section form of trapezoid in side slope angle for 32° and bed width 1.2 m. The dropping head ponding test was applied on all the types. The DHPT seepage rate functions and traditional power functions were both established. Function errors were examined. In order to decrease the influence of linear variation, total seepage depths were discretized into millimeters using a traditional method to calculate unit seepage time. The test seepage time was between 81.25 -176.92 h. By DHPT seepage rate function, the largest error was 2.102 h and the minimum error was 0.308 h. While by traditional power function, the largest error was 9.433 h and the minimum error was 1.137 h. Error analysis showed that the DHPT seepage rate function described seepage characteristics of trapezoid canals well and gained higher accuracy in seepage rate estimation. Finally, the traditional method and the DHPT functions were applied to 6 types of lining canals calculation. The traditional calculation used day as measuring interval and its result was expressed as seepage rate of average water depth in day. Average water depth was used as an independent variable in the DHPT function. For 27 samples, the calculated seepage rates were higher by traditional method than those by DHPT function generally. The traditional method was averagely 0.248 L/（m2·h）higher than the DHPT function results. Compared with the traditional method, the DHPT functions showed higher accuracy. This study indicates that the new function is better than the standard function in dropping head ponding test, and the method provides a better technical support for seepage estimation in irrigation system management.