## 1 Introduction  
Embankment dams are the most widely used dam style in the world. A core-rockfill dam is a type of embankment dam and is widely used, and core rockfill dams are increasingly being built and put into use. Core-rockfill dams such as Changhe dam (240 m), Nuozhadu dam (261.5 m), and Lianghekou dam (293 m) have been built. Gushui dam (305 m) and Shuangjiangkou dam (314 m) are under construction [1]. Penetration damage is one of the most common forms of damage to embankment dams due to defects in the foundation and body of the dam itself or the effect of dam-penetrating structures, 25% of embankment dam failures [2] are caused by dam failure worldwide, and about 30% of embankment dam wrecks in China are due to penetration damage [3]. In these wrecks, infiltration damage often occurs in the early stage of water storage [4]. When the reservoir first fills with water, the core wall is in a non-saturated state, there is a rapid rise of the reservoir water level, the pore water pressure in the rock pile area increases, the heart wall inside and outside undergo a sudden change in water pressure, and it is prone to infiltration damage. Teton Dam in the United States formed a gradual internal source and developed pipe surges at the contact area of the dam material in the core wall during the initial impoundment of water, leading to breach damage of the dam [5]. An abnormal permeability coefficient of dam-building materials leads to excessive water seepage, which may lead to dam failure. This tragedy might not have happened if the permeability coefficient could have been calculated from monitoring data in time. The coefficient permeability of unsaturated soils is determined by the water of the soil, which is a function of saturated permeability coefficients and the soil-water characteristic curve (SWCC) [6]. [PERSON] raised an equation of the relative permeability coefficient \(k_{r}\) from the SWCC [7]. [PERSON] [8] combined the SWCC formula derived by himself with the [PERSON] model, raising the specific van-Genuchten model, which is widely used in the calculation of saturated-unsaturated seepage. The Brooks-Corey model [9] is also widely used in the calculation of saturated and unsaturated seepage. [PERSON] [10] used a piece of FEM software named Geo-slope to perform a saturated-unsaturated numerical simulation of a dam during the descent of the reservoir water level; due to the existence of an unsaturated area, the percolation line in the dam is convex and the pore water pressure dissipation becomes slower. [PERSON] [11] simulated slope seepage with variations in the reservoir water level and rainfall intensity based on saturated-unsaturated theory, offering some guidance for slope ability. [PERSON] [12] solved the complicated saturated-unsaturated seepage problem caused by rain infiltration by using the finite element method. [PERSON] [13] built a 3-D FEM calculation model, carrying out a physical model experiment on composite geomembrane defect leakage based on saturated-unsaturated theory. Though the theory of saturated-unsaturated soil seepage has been developed for a long time, there is still a big problem in calculating the pressure in the dam and slope. In order to accurately determine the pore pressure in the soil, it is necessary to know the seepage calculation parameters of the soil. In saturated-unsaturated seepage analysis, laboratory testing and engineering analogies are the methods for determining the analysis parameters [14; 15; 16], but these cannot accurately avoid the impact of the size effect, engineering quality, and actual operating environment [17; 18; 19; 20]. Many large-scale projects cannot accurately obtain permeability parameters through experiments, but they can be obtained by inversion through dam monitoring data, while inversion analysis has become an effective method for determining seepage parameters [21]. Many scholars have studied the effect of the water storage rate on the seepage of dams based on saturated-unsaturated theory.