Numerical estimation of the equivalent hydraulic conductivity for canal concrete lining with cracks

Abstract

The equivalent saturated hydraulic conductivity of concrete lining (Ksce) is a key parameter to estimate seepage loss, while few studies have quantified the effect of cracks on Ksce, potentially leading to significant errors in canal seepage estimation. A three-dimensional numerical model is employed to simulate seepage loss from canals lined with concrete, and then to obtain the value of Ksce by an equivalent method. A total of 58,400 scenarios are simulated for different concrete lining and crack conditions (e.g., crack length, crack width, crack location, hydraulic conductivity of concrete (Ksc), and underlying soil (Ksoil)), and the corresponding Ksce values are estimated. Results show that the Ksce value determined by the equivalent method is reliable in calculating seepage loss from concrete lined canals. Ksce increases linearly with crack length with a slope Ck, and Ck exhibits a power function relationship with crack width, reaching a maximum value when the crack width surpasses the critical threshold, which ranges from 0.424 to 0.435 mm. When the crack width follows a log-normal distribution, the logarithmic value of Ck increases linearly with the mean value of the logarithmic crack width. The influence of crack location and Ksc on Ksce can be negligible. The maximum increment of Ksce of a crack is proportional to Ksoil. Considering the variation of Ksce with crack parameters and Ksoil, equations to determine the value of Ksce are established by adding the increment of Ksce caused by cracks to Ksc. This study establishes a quantitative relationship between Ksce and crack parameters, thereby enhancing the accuracy of seepage loss calculations in lined canal under different damage status.