Maximum entropy principle in geotechnical engineering: a state-of-the-art review

Purpose This paper aims to explore the application of the Maximum Entropy (MaxEnt) principle in geotechnical engineering for uncertainty modeling and reliability analysis. It focuses on reviewing robust methods for estimating quantile functions and probability distributions of geotechnical variables using fractional moments and probability-weighted moments, addressing challenges such as data scarcity and overfitting. Design/methodology/approach The study uses a comprehensive review of MaxEnt-based methods, numerical simulations and case studies. Novel techniques, such as fractional probability-weighted moments and partial maximum entropy, are introduced and validated through real-world applications such as slope stability and soil property characterization. Computational tools and programming languages facilitating MaxEnt implementation are also discussed. Findings The proposed MaxEnt-based methods demonstrate superior accuracy and efficiency in estimating quantile functions and probability distributions, particularly in tail regions. Case studies show significant improvements over traditional empirical distributions, offering better fits to sample data while avoiding overfitting or underfitting uncertainties in geotechnical applications. Originality/value This review paper provides a comprehensive synthesis of existing literature on the application of the Maximum Entropy (MaxEnt) principle in geotechnical engineering, filling a gap in consolidating knowledge on its theoretical foundations, advancements and practical implementations. By systematically reviewing recent developments, it offers a detailed guide for researchers and practitioners, including an extensive list of computational tools and programming platforms (e.g. Python, R, MATLAB, Julia, STAN, Gurobi) to facilitate MaxEnt implementation. Additionally, the inclusion of a real-world case study demonstrates the practical utility of MaxEnt in modeling uncertainty, serving as a benchmark for future research and applications in geotechnical projects.