Bayesian calibration of NorSand Model Parameters using triaxial test data

The NorSand constitutive model is a relationship between stresses and strains that has gained attention in geotechnical engineering for tailings due to its ability to numerically represent brittle materials in a critical state framework. Current calibration practices typically rely on visual fitting that is undertaken on a test-by-test basis, to identify trends across different loading conditions imposed on a single material. This approach is often time-consuming, inaccurate, and introduces subjective bias. This study presents a Bayesian approach for calibrating the elasticity (G_ref, m, ν) and plastic hardening (H₀, H_y) parameters of the NorSand model, utilising triaxial compression test data for a selected soil material. The approach is also extended to include the plasticity parameters N and χtc as variables for inference. The Bayesian framework integrates the NorSand model, experimental triaxial data, and predefined parameter ranges (priors) to create a posterior probability function. This posterior is then evaluated using the Markov Chain Monte Carlo (MCMC) method to estimate the most likely parameter values that best match observed soil behaviour. Additionally, this approach provides insights into parameter correlations and uncertainty, streamlining parameter estimation objectively and rationally. The methodology is demonstrated with a case study on the Fraser River sand, validated against established literature, and includes Python scripts for model implementation and Bayesian calibration.