3D combined stratigraphy and geo-properties modeling using probabilistic machine learning

Subsurface soil variability is inherently three-dimensional (3D), making 3D modeling of stratigraphy and geo-properties crucial in geotechnical engineering. Because stratigraphy and geo-properties are interdependent and subsurface data is often sparse, their uncertainties must be characterized together. This paper presents a new 3D probabilistic approach that jointly models stratigraphy and geo-properties using a Conditional Random Field (CRF) at any point in the domain, while quantifying their uncertainties. To efficiently capture complex spatial patterns, Radial Basis Functions (RBFs) are used to augment spatial coordinates, serving as the CRF’s inputs. The model’s simple structure allows fast inference via the junction tree algorithm, and parameter learning from borehole data using Maximum Likelihood Estimation. The method is demonstrated on a real-world project site, validated against an artificial benchmark geological model and on independent boreholes, and compared to an existing coupled uncertainty method. Its application to settlement risk assessment illustrates its practical relevance. The results confirm that the model captures spatial variability realistically, reflects uncertainty, and supports more informed decision-making in geotechnical engineering.