Predicting frost heave in soil-water systems using the generalized regression neural network optimized with particle swarm optimization algorithm

Frost heave poses a serious hazard to geotechnical engineering. However, conventional experimental and theoretical methods, which have limitations in accurately describing the deformation behavior of soils during frost heave, struggle due to the nonlinear and uncertain nature of the process. For this reason, the study leverages the advantages of the Generalized Regression Neural Network (GRNN) in handling nonlinear problems and small sample datasets. The structure of the GRNN model is further optimized using the Particle Swarm Optimization algorithm (PSO) and K-fold Cross Validation (K). The input variables for the model include water content (W), temperature (T), dry density (ρ), and plasticity index (I_p) under various working conditions. The frost heave rate (η) is considered as the output variable. Meanwhile, the model also considers the effects of both one-factor and two-factor interactions among the input variables on frost heave behaviors. Finally, a prediction model for η based on the K-PSO-GRNN is established. The results demonstrate that the K-PSO-GRNN model exhibits greater robustness and stability in predicting η compared to PSO-GRNN and GRNN (R² = 0.94, MAE = 0.14), and the prediction residuals for η range from 0 to 0.4. Among these variables, W has the most significant influence on η, followed by T, ρ, and I_p. Moreover, both ρ and I_p have significant interactions with T and have a notable impact on the soil's frost heave behavior. At high ρ, the soil shows reduced sensitivity to frost heave in response to changes in T, while at high I_p, the soil becomes more sensitive to frost heave with changes in T. η generally shows a positive correlation with W and ρ, and a negative correlation with T. The aforementioned K-PSO-GRNN model can be utilized for predicting η, which is valuable in forecasting non-uniform deformation hazards caused by frost heave and studying preventive measures.