A physics-informed and SHAP-enhanced modeling framework for predicting strength of cement-stabilized soil

This study presents a hybrid modeling framework for predicting the unconfined compressive strength (UCS) of cement-stabilized soils by integrating data-driven and physics-informed approaches. Two physics-informed machine learning (PIML) strategies were developed: Hybrid Corrector (HC) Framework and Physics-Informed Neural Networks (PINN), both of which are embedded with a physical model using the concept of modified water-cement ratio. In the HC framework, shallow (e.g., support vector regression and random forest) and deep learning models (e.g., feedforward neural network and multi-scale deep neural network) were trained to learn residuals between physical model outputs and observed UCS values, which were then added to physical predictions to form physics-informed models. In the PINN framework, the physical model was embedded directly into the loss functions of FNN and Multi-scale DNN to enforce physical consistency during training. Modeling results demonstrate that both PIML frameworks significantly improved prediction accuracy and generalization compared to purely data-driven or physical models. Among all models, the PINN-based Multi-scale DNN achieved the best performance with R 2 of 0.941 on the test set. SHAP analysis of the model PINN-based Multi-scale DNN indicated that the mean absolute feature contributions of cement, water content, and clay content to UCS are 42 %, 37 %, and 21 %, respectively. To enhance practical applicability, a graphical user interface (GUI) was developed using the Tkinter framework, integrating the trained PI-Ms model with SHAP-based interpretability. The tool enables rapid UCS prediction, visual explanation of feature effects, and provides mix design recommendations, offering a user-friendly platform for engineering design and decision-making in soil stabilization.