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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]

• A fully coupled numerical model is used to quantify canal seepage from lined canal. • Effects of lining material and damage parameters on reduction factor are evaluated. • The main factors influencing seepage from canal with 3 lining materials are quantified. • Three empirical formulas are developed for the reduction factor of damaged lining. • The accuracy of empirical formula to calculate seepage from lined canal is improved. An increasing number of canals are designed with liners to decrease canal seepage. As the lining material and cracks or holes were previously considered equivalent porous media, few studies have quantified the effects of lining parameters on canal seepage, and the relationships between the reduction factor (β) of the lining and the crack width (d f) and hole density (h d) are not explicit, leading to large errors in the estimation of seepage loss. A three-dimensional numerical model is employed to simulate seepage loss from canals lined with concrete and geomembrane material in a total of 1159 scenarios, focusing on the crack locations, saturated hydraulic conductivity (K s) of concrete material and geomembrane material (K sc and K sg , respectively), thickness (T c), concrete lining d f , and geomembrane lining h d. For canals lined with concrete, d f is the main factor affecting canal seepage, followed by K sc and T c. Cracks with widths smaller than 0.02 mm have minimal influence on β, where β is reduced by a decrease in K sc or an increase in T c. When d f ranges from 0.02 to 0.2 mm, β increases gradually to a maximum value, while the impacts of K sc and T c weaken. For canals lined with geomembranes, β increases slightly with h d from 0 to 4.2 × 10−5, increases nearly linearly with log h d from 4.2 × 10−5 to 8.4 × 10−3, and then approaches 1.0. β is weakly influenced by K sg for particular h d values when K sg is smaller than 10−11 m/s, increases rapidly with K sg from 1 × 10−11 to 1 × 10−8 m/s, and then exceeds 0.938. For a canal lined with both concrete and a geomembrane, the trends in β with changes in d f and h d are identical to those of a canal with a single lining. Based on these results, the damage degree is proposed to evaluate the influence of cracks and holes on the lining effectiveness and as an intermediate variable for calculating β from d f and h d. Three empirical equations are proposed to calculate the β value of the concrete lining, geomembrane lining and combined lining with different d f and h d. The results show that the proposed equation improves the accuracy of the estimation of β compared with the multiplication model and can be further used for calculations of seepage loss from lined canals. [ABSTRACT FROM AUTHOR]