AbstractA novel statistical framework was developed to quantify the variability of the fitting parameters of the soil–water characteristic curve (SWCC). Reliable estimation of the mean, standard deviation, and associated probability density function (PDF) of the fitting parameters of SWCC is an important tool for addressing reliability-based designs in unsaturated soil mechanics. The assumption of either Gaussian or lognormal distributions may not be valid for representing a high degree of variability associated with fitting parameters. This study aimed to provide the most appropriate continuous PDFs by optimizing the mean and standard deviation such that errors associated with quantile, percentile, and cumulative distribution function (CDF) were as low as possible. A total of 261 and 111 sample points were collected from the most comprehensive experimental works on the fitting parameters of SWCC for clayey and silty soils, respectively. Optimum distributions suitable to the model fitting parameters of SWCC are highly dependent on the type of soil. The most appropriate PDFs for representing the fitting parameters af, nf, and mf of Fredlund and Xing’s model were gamma, Weibull, and inverse Gaussian distributions, respectively. Similarly, fitting parameters af, nf, and mf for silty soils were represented by inverse Gaussian, Gumbel maximum, and Gumbel maximum distributions, respectively. This study found that the selection of inappropriate PDFs overestimated the probability of failure of unsaturated infinite slopes considerably, by 99.49% and 99.76%, respectively, for clayey and silty soils. Recommended mean, coefficient of variation (COV), and PDF are useful in the reliability-based design of unsaturated soil slopes and in judging the performance of existing infinite and finite slopes.

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