## 1 Introduction  
A reliability analysis of unsaturated soils is an important field in geotechnical engineering. Considering the unsaturated characteristics of soil in geotechnical design, a safer and more reliable solution can be obtained. The SWCC indicates the ability of the soil to maintain itself relative to the change in matric suction, and contains the basic information needed to describe the mechanical behavior of unsaturated soil [1]. The soil-freezing characteristic curve (SFCC) is a mathematical description of the relationship between unfrozen-water content and negative temperature in frozen soil. During soil freezing and thawing, unfrozen water and porous ice coexist in the soil, and temperature is the main factor determining their respective amounts [2]. Some studies have discussed the similarity between the SWCC and the SFCC [3]. During the wetting and drying process of unsaturated soil, soil-water-potential energy will decrease with the increase in soil water content, which is similar to the change in the potential energy gradient when liquid water turns into ice in saturated frozen soil. In addition, the SWCC also shows hysteresis behavior similar to SFCC [4]. Some characteristic parameters, such as AEV, slope at the inflection point, residual moisture content, and residual suction, are often used to correlate the SWCC and some soil properties such as shear strength and permeability. In addition, these parameters also play a key role in the seepage analysis and the soil balance humidity estimation [5; 6]. [PERSON] et al. [7] studied the influence of soil shrinkage on AEV by constructing a shrinkage curve, and proposed a method to determine the AEV of soil with shrinkage during drying. The matric suction of unsaturated residual soil varies with the change in climatic conditions, while the change in climatic conditions is related to the cyclic dry and wet conditions, resulting in hysteresis of SWCC. The hysteretic effect of the unsaturated residual soil slope is studied by [PERSON] et al. [8], and the difference of pore water pressure and water content under dry and wet conditions is studied by means of numerical seepage and stability analysis. The results show that no matter whether the soil is wet or dry, the numerical analysis results incorporated with the combined SWCC are more consistent with those with only wetting the SWCC than those with drying the SWCC only. A bimodal SWCC model considering a dual-porosity structure to describe the drying process of granular soil was proposed by [PERSON] et al. [9]. The new SWCC model shows a strong ability to fit the SWCC from gravel to silt. Because it takes a lot of time to measure the SWCC, many previous studies [10; 11; 12; 13; 14; 15] have focused on modeling the SWCC and other unsaturated-soil properties in order to find a method to estimate the SWCC accurately. One of the most influential is the equation established by [PERSON] et al. [10] which describes the relationship between suction and soil-pore characteristics through the induction and analysis of the experimental data. It is widely used in a variety of soils and has a good fitting effect in the whole suction range. Some studies [16; 17] have shown that the parameters for the grain size distribution with bimodal soil of the SWCC equation can be calculated by the dry density and volumetric water content in the grain size distribution. The reliable estimation of the mean value, standard deviation, and correlation probability density function of the SWCC fitting parameters are important tools to solve the problem of the reliability design of unsaturated-soil mechanics. By optimizing the average and standard deviation, [PERSON] et al. [18] make the error of quantile, percentile, and cumulative distribution functions as low as possible, so as to provide the most suitable continuous probability density function. The mean, coefficient of variation, and probability density function are recommended for the reliability design of unsaturated soil slopes.