Artificial intelligence approaches to jet grouting column diameter prediction

Jet grouting is a widely employed ground improvement technique that involves injecting liquid cement slurry with high kinetic energy to enhance soil properties. The diameter of the resulting jet grout columns is a critical factor in determining the overall effectiveness of the jet grouting process. Accurate prediction of this diameter is crucial for optimizing design, minimizing material waste, and ensuring the long-term performance and stability of the treated ground, ultimately leading to cost savings and improved confidence in engineering applications. Currently, empirical equations are widely used for predicting jet grout column diameter. However, these deterministic approaches face significant limitations: they often rely on limited datasets, fail to account for inherent variability in soil properties and jet grouting processes. While recent studies demonstrate that machine learning models can offer improved predictive capability over these empirical equations, these models also present challenges, including unknown reliability, robustness, susceptibility to overfitting due to small training datasets, and neglect fundamental physics governing submerged jet flow. This study addresses these limitations by developing and evaluating advanced data-driven methods to improve accuracy, reliability, and robustness of jet grout column diameter prediction, complemented by physics-informed models for jet grout flow simulation. The research employs four complementary approaches that progressively enhance predictive capabilities. First, this study introduces Transformer-based model using the largest available dataset and compares its performance against widely used machine learning models (ANN, XGBoost, ANN Mixture model, Random Forest) and empirical equations. Results demonstrate that the Transformer model outperforms all compared approaches in terms of predictive accuracy and generalization capability, highlighting the potential of Transformer-based models for capturing complex patterns in geotechnical problems. This study enhances the model's practical applicability through design charts and SHapley Additive exPlanations (SHAP) interpretations. Second, this study introduces a surrogate Physics-Informed Neural Network (PINN) model to predict jet grout flow diffusion characteristics that directly control jet erosive capacity and subsequent column formation. Unlike traditional data-driven approaches that ignore governing physics, the PINN model incorporates Reynolds Averaged Navier Stokes (RANS) equations coupled with k − turbulence model as physics-based loss functions. This study trains the model utilizing high-fidelity simulation data generated from ANSYS Fluent modeling of jet grout flow across varying jet velocities. To ensure stable convergence and mitigate gradient explosion, this study employs normalization of input parameters, curriculum training strategy, and balanced loss terms. Results demonstrate that the PINN model effectively predicts key jet grout flow parameters with acceptable accuracy and generalization capability, while simultaneously enhancing the model interpretability and demonstrating the potential of physics-informed approaches for geotechnical problems involving complex turbulent flows. Third, this study applies a Bayesian inference framework to calibrate existing empirical equations for coarse-grained soils, transforming deterministic outputs into probabilistic predictions that quantify uncertainty and incorporate prior knowledge. This approach provides insights into the expected variability of jet grout column diameter, supporting improved design reliability through probabilistic rather than deterministic estimates. Finally, this study introduces Bayesian deep learning models to overcome the uncertainty quantification limitations and overfitting risks of conventional ANNs. The framework quantifies both aleatoric and epistemic uncertainties, offering a structured probabilistic approach for the prediction of jet grout column diameter under variable site conditions. This study presents design charts for predicting the jet grout column diameter based on SPT N-value, specific energy, soil type, and jet grout type, enabling risk-informed decision-making and improving the reliability of jet grouting design under variable ground conditions. Collectively, these four complementary approaches – advanced deep learning, PINN, Bayesian calibration, and Bayesian deep learning – provide practitioners with more accurate, reliable, and risk-informed tools for jet grouting design, advancing both theoretical understanding and practical application of jet grouting.