Prediction on Permeability Coefficient of Continuously Graded Coarse-Grained Soils: A Data-Driven Machine Learning Method

Accurately predicting the permeability of coarse-grained soils is crucial for ensuring geotechnical safety and performance. In this study, 64 coarse-grained soil (CGS) samples were designed using a negative exponential gradation equation (NEGE), and computational fluid dynamics–discrete element method (CFD-DEM) coupled seepage simulations were conducted to generate a permeability coefficient (k) dataset comprising 256 entries under varying porosity and gradation conditions. Three machine learning models—a neural network model (BPNN), a regression model (GPR), and a tree-based model (RF)—were employed to predict k, with hyperparameters optimized via particle swarm optimization (PSO) and four-fold cross-validation applied to improve generalization. Gray relational analysis (GRA) revealed that all input parameters (α, β, dmax, n) significantly influence k (R > 0.6). The interquartile range (IQR) method confirmed data suitability for modeling. Among the models, BPNN achieved the best performance (R2 = 0.99, MAE = 1.5, RMSE = 2.9, U95 = 0.4), effectively capturing the complex nonlinear relationship between gradation and permeability. GPR (R2 = 0.92) was hindered by kernel selection and noise sensitivity, while RF (R2 = 0.97) was limited by its discrete regression nature. Compared to a traditional empirical model (R2 = 0.9031), BPNN improved prediction accuracy by 10.13%, demonstrating the advantage of data-driven methods for evaluating CGS permeability.