Finite Element Bayesian Inference Using Dual Ensemble Kalman Filters for Uncertainty Reduction in Geotechnical Models

The reliability of a geotechnical simulation depends strongly on the selection of material parameters and in recent years Bayesian Inference (BI) has become a popular coherent framework for this task. It has generally been used to reduce the uncertainties based on measurements, but it is challenging due to material non-linearity and paucity of measurement data. Applications to geotechnics of BI to date have struggled with the high dimensionality of the modelled problems (e.g. in 3D FEA) and many studies report considerable computational time needed to achieve the accuracy one might hope to get via an expert assessment. In this paper we introduce a Finite Element-BI (FE-BI) system for geotechnics using a two stage process where the material parameters and the simulation results themselves (the ``states'') are updated one after the other. The method is demonstrated on three examples with increasing complexity: parameter determination for undrained compression triaxial tests with the modified Cam clay model; parameter determination from FE simulation of cyclic triaxial tests with the Small Strain Overlay (SSO) model, and 3D FE simulations of a braced excavation. Results show that the FE-BI system can effectively infer both the parameters and states, reducing uncertainty in parameter and state distributions, giving good agreement with the reference solutions provided. The technique proposed in this paper provides a rigorous and efficient approach to obtain material parameters with greater certainty, and could have wide application in geotechnical engineering practice.