Empirical Regression Modelling of Acoustic Emission Signatures to Infer the Geotechnical State of Sands Subjected to Symmetrical Compression

This research presents a robust multivariate statistical framework for the non-destructive prediction of geomechanical state parameters in quartz-rich coastal sands through acoustic emission (AE) monitoring. Granular media under symmetrical compressive stress function as complex natural systems, where microscopic energy dissipation—arising from particle rearrangement and grain microcracking—radiates as transient elastic waves. To decode these stochastic processes, 24 confined uniaxial compression tests were conducted across diverse soil typologies and moisture contents (0–12%). A high-dimensional data matrix was constructed, integrating 13 geotechnical variables with 48 acoustic descriptors formulated through three distinct temporal aggregations: stage-specific, history average and weighted history average. The statistical results identify the logarithmic effective vertical stress (log10(σ′v)) and the cumulative axial strain (ε) as the most significant geomechanical drivers, exhibiting Pearson correlation coefficients |p| ≥ 0.85 with acoustic activity. In the acoustic domain, the analysis reveals that Signal Strength (Ss) and cumulative energy (E) flux are the most reliable predictors for volumetric deformation, while the amplitude (A), b-value (b), and average frequency (F) emerge as critical indicators for identifying the transition between spatial rearrangement and the onset of grain fragmentation. Furthermore, the inclusion of dimensionless parameters, particularly earliness (earl), enhances model stability by standardising waveform symmetry across varying stress regimes. High-order polynomial regression models (up to the third degree) were derived, demonstrating that the statistical complexity of acoustic signatures allows for the high-fidelity inference of the soil matrix’s initial and state parameters. This methodology establishes a unified mathematical architecture for the in situ characterisation of granular skeletons, balancing computational efficiency with predictive power in intricate geological domains.