A Framework for Determining the Optimal Vibratory Frequency of Graded Gravel Fillers Using Hammering Modal Approach and ANN

To address the uncertainty of optimal vibratory frequency f_ov of high-speed railway graded gravel (HRGG) and achieve high-precision prediction of the f_ov, the following research was conducted. Firstly, commencing with vibratory compaction experiments and the hammering modal analysis method, the resonance frequency f₀ of HRGG fillers, varying in compactness K, was initially determined. The correlation between f₀ and f_ov was revealed through vibratory compaction experiments conducted at different vibratory frequencies. This correlation was established based on the compaction physical-mechanical properties of HRGG fillers, encompassing maximum dry density ρd_max, stiffness K_rd, and bearing capacity coefficient K₂₀. Secondly, the gray relational analysis algorithm was used to determine the key feature influencing the f_ov based on the quantified relationship between the filler feature and f_ov. Finally, the key features influencing the f_ov were used as input parameters to establish the artificial neural network prediction model (ANN-PM) for f_ov. The predictive performance of ANN-PM was evaluated from the ablation study, prediction accuracy, and prediction error. The results showed that the ρ_dmax, K_rd, and K₂₀ all obtained optimal states when f_ov was set as f₀ for different gradation HRGG fillers. Furthermore, it was found that the key features influencing the f_ov were determined to be the maximum particle diameter d_max, gradation parameters b and m, flat and elongated particles in coarse aggregate Q_e, and the Los Angeles abrasion of coarse aggregate LAA. Among them, the influence of d_max on the ANN-PM predictive performance was the most significant. On the training and testing sets, the goodness-of-fit R² of ANN-PM all exceeded 0.95, and the prediction errors were small, which indicated that the accuracy of ANN-PM predictions was relatively high. In addition, it was clear that the ANN-PM exhibited excellent robust performance. The research results provide a novel method for determining the f_ov of subgrade fillers and provide theoretical guidance for the intelligent construction of high-speed railway subgrades.