## 1 Introduction  
Coarse-grained soils (CGSs) are defined as soils in which particles with diameters ranging from 0.075 to 60 mm constitute more than 50% of the total mass [1, 2, 3]. They are widely used in the construction of geotechnical structures such as dams and embankments, as well as various permeable structures and facilities, due to their favorable engineering properties, including high compaction performance, large permeability coefficient, and high shear strength. Permeability is a fundamental soil property that plays a critical role in determining the stability and functionality of geotechnical structures. It is commonly characterized by the permeability coefficient, the accurate determination of which has been a longstanding focus and challenge in both academic and engineering communities [4, 5, 6]. The permeability coefficient of soils is typically obtained through experimental testing [7, 8, 9]. The permeability coefficient of CGS is typically determined through experimental testing [10; 11; 12]. However, permeability tests for CGSs present challenges such as large specimen size, difficulties in specimen preparation, and long testing durations. Consequently, extensive efforts have been made to develop predictive formulas for the permeability coefficient. Existing studies indicate that key factors influencing the permeability of CGSs include particle size distribution [13; 14], particle shape [15; 16; 17], pore characteristics [18; 19], mineral composition [20; 21], temperature [22; 23], and fluid properties [24]. For a given type of CGS (i.e., soils with similar genesis and mineral composition, which are generally considered to be of the same type), the particle shape tends to be relatively consistent. Under such conditions, particle size distribution and pore characteristics become the two most critical factors governing permeability [25], as they largely determine the permeability coefficient. Therefore, in principle, the permeability coefficient of any given CGS should be computable based on parameters describing its particle size distribution and pore characteristics. Based on these parameters, numerous empirical models for predicting the permeability coefficient of CGSs have been developed by researchers worldwide. Notable examples include the [PERSON] model [26], [PERSON] model [27], the modified Hazen model [28], as well as the Chapuis model [29]. Empirical models exhibit distinct advantages in predicting the permeability coefficient of coarse-grained soils, primarily due to their engineering applicability and rapid assessment capabilities. Empirical models, exemplified by the Kozeny-Carman equation, establish explicit mathematical relationships between permeability and particle size characteristics (e.g., effective particle size \(D_{10}\)) as well as void ratio (\(e\)). These models require only a limited set of readily obtainable soil parameters, making them particularly suitable for on-site engineering decision-making. By leveraging statistical correlations derived from extensive laboratory test data, such models serve as efficient tools for the preliminary selection of coarse-grained fill materials and the early assessment of seepage risks, especially when applied to soils with relatively uniform gradation (e.g., well-graded sandy soils) and simple pore structures. However, the limitations of empirical models become particularly pronounced under complex conditions. The oversimplified physical assumptions hinder the accurate representation of multiscale pore connectivity in continuously graded coarse-grained soils. For instance, these models often neglect the nonlinear influence of particle angularity on tortuosity, leading to permeability coefficient prediction errors exceeding 50%. Second, model parameter sensitivity is highly dependent on boundary conditions.