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• A three-dimensional coupled model is used to quantify seepage from lined canals. • The effects of cracks on the hydraulic conductivity of lining materials are evaluated. • A quantitative relationship between hydraulic conductivity and its factors is formed. • The accuracy of empirical formula and numerical model for canal seepage is improved. The equivalent saturated hydraulic conductivity of concrete lining (K sce) is a key parameter to estimate seepage loss, while few studies have quantified the effect of cracks on K sce , 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 K sce 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 (K sc), and underlying soil (K soil)), and the corresponding K sce values are estimated. Results show that the K sce value determined by the equivalent method is reliable in calculating seepage loss from concrete lined canals. K sce increases linearly with crack length with a slope C k , and C k 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 C k increases linearly with the mean value of the logarithmic crack width. The influence of crack location and K sc on K sce can be negligible. The maximum increment of K sce of a crack is proportional to K soil. Considering the variation of K sce with crack parameters and K soil , equations to determine the value of K sce are established by adding the increment of K sce caused by cracks to K sc. This study establishes a quantitative relationship between K sce and crack parameters, thereby enhancing the accuracy of seepage loss calculations in lined canal under different damage status. [ABSTRACT FROM AUTHOR]