This direction paper explores the evolving landscape of physics-informed machine learning (PIML) methodologies in the field of geotechnical engineering, aiming to provide a comprehensive overview of current advancements and propose future research directions. Recognising the intrinsic connection between geophysical phenomena and geotechnical processes, we delve into the inter of physics-based models and machine learning techniques. The paper begins by elucidating the significance of incorporating physics-informed approaches, emphasising their potential to enhance the interpretability, accuracy and reliability of predictive models in geotechnical applications. We review recent applications of PIML in soil mechanics, hydrology, geotechnical site investigation, slope stability analysis and foundation engineering, showcasing successes and challenges. Furthermore, we identify promising avenues for future research in geotechnical engineering, including the integration of domain knowledge, model explainability, multiphysics and multiscale problems, complex constitutive models, as well as digital twins and large AI models within PIML frameworks. As geotechnical engineering embraces the paradigm shift towards data-driven methodologies, this direction paper offers valuable insights for researchers and practitioners, guiding the trajectory of PIML for sustainable and resilient infrastructure development.

Global warming accelerates permafrost degradation, compromising the reliability of critical infrastructure relied upon by over five million people daily. Additionally, permafrost thaw releases substantial methane emissions due to the thawing of swamps, further amplifying global warming and climate change and thus posing a significant threat to more than eight billion people worldwide. To mitigate this growing risk, policymakers and stakeholders need accurate predictions of permafrost thaw progression. Comprehensive physics-based permafrost models often require complex, location-specific fine-tuning, making them impractical for widespread use. Although simpler models with fewer input parameters offer convenience, they generally lack accuracy. Purely data-driven models also face limitations due to the spatial and temporal sparsity of observational data. This work develops a physics-informed machine learning framework to predict permafrost thaw rates. By integrating a physics-based model into machine learning, the framework significantly enhances the feature set, enabling models to train on higher-quality data. This approach improves permafrost thaw rate predictions, supporting more reliable decision-making for construction and infrastructure maintenance in permafrost-vulnerable regions, with a forecast horizon spanning several decades.

Data-driven constitutive models are increasingly addressing non-elastic and three-dimensional scenarios. However, their robustness can be significantly impacted by the inadequate integration of physical information. Accordingly, this study introduces a tensor-based physics-encoded neural network to characterize the constitutive behavior of soil, exemplified by isotropic hypoplasticity with dependency on pressure and porosity. The framework ensures strict adherence to fundamental physical laws for small strain, rate-independent isotropic constitutive behavior. The network utilizes stress tensor invariants and soil state parameters (porosity) as inputs, and outputs crucial coefficients for the tensorial constitutive relations. The model has been calibrated using only symmetric triaxial test data (both drained and undrained). The effectiveness of the neural network-based constitutive model has been validated through simulations of drained and undrained triaxial tests under various initial conditions, as well as boundary value problems with complex loading. The results demonstrate that the proposed model offers the following distinguishing advantages: 1) Applicability to both two- and threedimensional non-elastic cases, even when trained with two-dimensional data; 2) Strict adherence to fundamental physical laws, avoiding soft constraints; 3) An incremental, tensor-based architecture, suitable for integration in numerical software for boundary value problems.