Physics-informed dictionary learning of time-varying 3D settlements from sparse monitoring data and 2D numerical models with consideration of complex stratigraphy

Digital twins of geotechnical structures replicate their physical counterparts, such as underground spaces developed from land reclamations. These spaces often exhibit intricate three-dimensional (3D) stratigraphic distributions, including irregular and interbedded soil layers. Developing a virtual 3D model, such as finite element model (FEM), with complex stratigraphy poses significant computational challenges due to the necessity for numerous stratum voxels, high-resolution meshing, and prohibitive analysis times. Incorporating field settlement data for model updating escalates the computational burden, as repeated evaluations of 3D FEM models are required for each model updating. To address this challenge, this study develops a novel approach for efficiently predicting time-varying 3D settlement from two-dimensional (2D) numerical models with sparsely measured monitoring data. Settlements from 2D FEM analyses, which account for complex stratigraphy, are compiled within a dictionary learning framework and combined with limited monitoring data to estimate time-varying settlements at multiple 2D cross-sections. The 2D settlements are then utilized to reconstruct high-resolution 3D settlements through 3D compressive sampling (3D-CS), eliminating a need for additional numerical model evaluations when integrating new monitoring data. The proposed approach is illustrated using a reclamation project in Hong Kong, China.