An analytical model for variation of exit gradient downstream of a hydraulic structure with inclined downstream cutoff resting on infinite anisotropic soil

Abstract

ABSTRACT An analytical solution is developed for the variation of the exit gradient along the downstream side of hydraulic structure with downstream-inclined cut-off resting on an anisotropic soil. The model is presented using dimensionless variables to demonstrate the relationship between the exit gradient rate and the ratio of the cut-off length to the seepage driving head (Ie*S/h), as well as the ratio of the distance from the structure toe to the cut-off length (X/S). Various ratios of the dam base length to the length of cut-off (b/S = 2, 3, 5, 10, and 15) are considered, along with different degrees of anisotropy of the underneath soil (Kr = 1, 0.5, 0.25, and 0.1). A MATLAB code is developed to implement the model. The results indicate that the maximum exit gradient is observed at an inclination angle of 75°, while the minimum exit gradient is observed at a 30° cutoff inclination angle for all cases. The variation of the exit gradient exhibits an increasing linear trend from X/S = 0 up to a certain distance (between 1 and 2). Beyond this distance, a non-linear decreasing trend is observed. The relationship between the exit gradient and the inclination angle cases after a distance of approximately 5X/S. The range of maximum exit gradient decreases with a decrease in the degree of anisotropy (Kr); with a significant reduction observed for Kr values of 0.25 and 0.1. Furthermore, for all degrees of anisotropy, the range of maximum exit gradient decreases as b/S increases.