A GMM–MRF–HBM framework for stochastic geological modeling and soil parameter estimation: case study on the Tokyo Airport soft soil benchmark

Accurate, reliable, and geological stratification and associated soil property estimation is critical for the safe and cost-effective design of geotechnical infrastructure. However, the inherent spatial heterogeneity of geomaterials, coupled with the scarcity, incompleteness of site investigation data, poses significant challenges for conventional site characterization methods. This study presents an integrated probabilistic framework that integrates Gaussian Mixture Models (GMM), Markov Random Fields (MRF), and a Hierarchical Bayesian Model (HBM) to address these challenges. The proposed framework first applies GMM to classify borehole records into probabilistic geological clusters in the feature space, followed by MRF-based three-dimensional stratigraphic modeling to incorporate spatial continuity and geological prior knowledge. For each cluster, soil parameters are inferred at unobserved locations using an HBM calibrated with relevant Big Indirect Data (BID), and the final predictions are obtained through probability-weighted aggregation across clusters. The framework is validated using two benchmark problems from the Tokyo Airport soft soil dataset: (i) reconstruction of undrained shear strength profiles from partial observations, and (ii) estimation of missing mechanical parameters under incomplete-testing scenarios. Comparative evaluations against existing benchmark approaches show that the proposed GMM–MRF–HBM framework captures depth-dependent variability more effectively, achieves lower prediction errors. These findings highlight the potential of the framework as a robust and generalizable tool for data-driven site characterization in sparse and heterogeneous geotechnical settings.