Study of side slope effect on seepage rate in earthen canals using experimental model and gene expression programming

Seepage from the earth canals is considered as the main portion of water losses in the irrigation projects. Several empirical equations have been proposed by researchers to estimate the seepage losses in canals. Some of these equations estimate accurately but the others should be used with more cautious. Unfortunately, few previous practical formulas for estimating the seepage losses along the earthen canals are applicable and new design equations are needed. Because of complexity, more practical tools are required to model seepage processes. The geometric factors involved in the estimation of seepage are the shape and dimensions of the canal. Regression relations are most commonly used to predict the seepage rate from the earth canals; however the regression analysis can have large uncertainties. Thus, the computed seepage values can be far from the actual ones. Also, the regression analysis has some limitations by predefined equations for modeling. So, gene expression programming (GEP) has been used to model these processes, recently. Through the present paper, some experimental data measurements have been carried out, on trapezoidal earthen canals with different geometry for seepage analysis, and the equations were developed for relating the seepage losses, qs, to the flow and geometry canal parameters. The dimensional analysis of the seepage rate in the canals has shown that the parameters z, k and y are effective in the seepage discharge, qs. As is evident, the dimensionless parameter q/ kh, is a function of the channel side slope, (z), the water depth (y) and the hydraulic conductivity of soil (k) considered as variable parameters. For each of the three samples the hydraulic conductivity of soil was calculated from Darcy relationship, So that in each instance the measurement and estimation of seepage (by the volume method) and the water level measurement in the parameters were done, then the average hydraulic conductivity of soil was calculated and the seepage line was defined for each soils. In artificial intelligence, gene expression programming (GEP) is an evolutionary algorithm-based methodology inspired by biological evolution to find computer programs that perform a user-defined task. The effect of the side slope, the water depth and the hydraulic conductivity on seepage rate, qs, in the trapezoidal earthen canals was studied. This study presents gene expression programming (GEP), as an alternative tool in the prediction of the seepage losses in the earth canals. In GEP model they were used arithmetic operations like (*+ , − ,/ ,) and functions such as ( sqrt and power). The performance of GEP in training and testing sets is validated in terms of the common statistical measures R, the correlation coefficient, the root-mean-square error (RMSE). The R shows the degree which two variables are linearly related to. The experimental results showed that the seepage rate increased by increasing of the water depth in canal and hydraulic conductivity of soil, but the seepage rate was not directly related to the canal side slope. In small and narrow earthen canals, the seepage rate initially decreases and then increases with increasing the side slope, z. Considering that, the local features of seepage is a unique, the trapezoidal section with slope Z = 2 in the range of 1.5< Z< 2.5 had the minimum seepage rate. Also, the results of the sensitivity analysis indicated that the parameter k had the greatest impact on the rate of seepage. In general, the performance of GEP models was superior to the statistical regression schemes. These models could be successfully used in computation of the seepage in the canals. Based on the results, model performance can be evaluated as satisfactory, if R> 0.9 and less values of RMSE. The results of GEP were compared with measured values of experimental model. The comparison showed that this software had a good performance in modeling the seepage of earthen canals. The seepage rate calculated by GEP had little difference with the measured seepage. The GEP model performed well in simulating the seepage rate based on all parameters and for each of canal side slopes. The simplified analytic form of the proposed GEP model for qs can be expressed as a function of y, z and k parameters. The equation obtained by GEP is clear and precise function that can be used to calculate the seepage losses from earthen canals in similar situations.