A Physics-constrained, Data-sparse Framework for Heave Risk Categorization of Shallow Foundations on Expansive Soils

This paper presents a physics-constrained computational framework for heave risk assessment in shallow foundations on expansive soils, specifically designed for data-limited conditions. The proposed methodology employs Physics-Informed Neural Networks (PINNs) to predict swell pressure (P s) using routinely accessible index properties: plasticity index (P I), dry density (γ d), and initial moisture content (w 0), with optional inclusion of liquid limit (w L) as a fourth parameter. The primary innovation lies in embedding monotonicity constraints, derived from unsaturated soil mechanics and diuse double-layer theory, directly into the loss function to enforce physical consistency and ensure stable learning with sparse data. Training and validation are conducted using Leave-One-Out Cross-Validation (LOOCV) on a database of 218 experimental samples from Algerian expansive soils. From this dataset, 44 complete records allow comparative LOOCV analyses using three input features versus four features incorporating w L. The three-feature PINN achieves a coecient of determination (R 2) of 0.699 and Root-Mean-Square Error (RMSE) of 58.3 kPa, with marginal improvement upon adding w L (R 2 = 0.706, RMSE = 57.6 kPa). These results conrm that the three basic index properties capture the essential predictive information, while w L provides negligible additional benet. Although conventional machine learning algorithms such as XGBoost and Random Forest yield superior accuracy (R 2 > 0.95), they lack physical guarantees. The PINN ensures predictions remain mechanically consistent, enhancing reliability for engineering practice. Finally, the estimated swell pressures are integrated into a PTI-based displacement model to classify foundation heave risk into low, moderate, and high categories, oering a transparent preliminary screening tool to assist geotechnical engineers in planning site investigations and mitigation strategies.