Predicting Clay Swelling Pressure: A Comparative Analysis of Advanced Symbolic Regression Techniques

Abstract

Swelling pressure is a key geotechnical property that influences the behaviour and stability of engineering structures built on expansive clayey soils. This pressure can be measured directly through laboratory tests or estimated using indirect methods. This paper analyses a dataset of undisturbed clay samples from southeastern Spain using advanced symbolic regression techniques, namely: deep symbolic regression (PhySO), high-performance symbolic regression (PySR), multi-objective symbolic regression (MOSR), and physics-guided symbolic regression (PGSR). These methods provide interpretable results as equations, unlike standard machine learning models. All generated equations showed high performance (R2 > 0.91 and MAE < 23 kPa) and simplicity, making them suitable for practical engineering applications. PySR yielded the best overall metrics (R2 = 0.933, MAE = 20.49 kPa), particularly excelling in high-pressure ranges, while PhySO demonstrated the most balanced performance, especially for low to medium pressures. MOSR minimized edge-case bias, and PGSR, despite lower overall performance, remained competitive. The plasticity index (PI) was identified as the most influential factor in all models, followed by the percentage of fines. The use of undisturbed samples enhanced the reliability of the findings, and the resulting equations enable a flexible estimation of swelling pressure based on commonly available geotechnical parameters.