Data-Driven and Physics-Informed Machine Learning for Geotechnical Engineering Practice: A Systematic Review, Mathematical Formulation, and Comparative Case Study Analysis

Geotechnical engineering practice has traditionally relied on empirical and semi-analytical correlations that struggle to represent the non-linear, spatially variable behaviour of soils and rocks. This paper synthesizes evidence from 221 peer-reviewed studies (2020-2026) on the application of machine learning (ML) and deep learning (DL) to soil mechanics, rock mechanics, and earth structures, and formally derives the governing mathematical formulations of the principal algorithm families, including ensemble trees, artificial neural networks, and physics-informed neural networks (PINNs). Secondary quantitative synthesis of the reviewed corpus shows ensemble methods such as extreme gradient boosting achieving coefficients of determination of 0.90-0.96 for geomaterial property prediction, compared with 0.65-0.75 for conventional correlations. Three operational case studies from Singapore, Hong Kong, and China illustrate measurable safety and economic gains from field deployment. The review concludes that physics-informed, ensemble-based ML constitutes a statistically and practically significant advance over classical empirical methods, while data scarcity, interpretability, and cross-site transferability remain the principal barriers to unconditional adoption in regulated design practice.