A Bayesian-based framework for quantifying model-inherent uncertainties in soil constitutive models

Quantifying uncertainty in soil constitutive models is both challenging and essential for improving predictive reliability. While the Bayesian approach offers an effective framework for this purpose, previous studies have primarily focused on uncertainties in input parameters of standard “ideal” constitutive models. However, models such as the Mohr-Coulomb, Cam-Clay, and Modified Cam-Clay are based on simplified assumptions that do not fully capture real soil behaviour, making it impossible for them to match real-world data perfectly. This study introduces a novel Bayesian-based framework that transforms deterministic models into probabilistic ones, allowing for the quantification of model-inherent uncertainty. A modified maximum a posteriori (MAP) estimator is employed, incorporating a penalty term into the negative log-likelihood to form a new loss function, which enhances bias estimates and model reliability. Using this method, three assumptions about the model bias term are evaluated against triaxial test data from Karlsruhe sand and White clay. The results demonstrate that non-constant assumptions about the bias term significantly enhance model performance. Among the models tested, the probabilistic Modified Cam-Clay model with a nonlinear bias assumption exhibits the best performance. Conversely, the probabilistic Mohr-Coulomb model reveals certain limitations, including overpredicted peak deviatoric stress and overfitted volumetric strain, underscoring the need for further refinements.