State space model of undrained triaxial test data for Bayesian identification of constitutive model parameters

Soil constitutive model parameters can be identified from triaxial test data. The identification is frequently performed by fitting a constitutive model to triaxial test data from a purely statistical or probabilistic perspective based on an assumption that measurements are independent. This ignores the sequential attribute of triaxial test data and is, hence, not realistic. In this paper, a probabilistic state space model (SSM) is proposed for undrained triaxial test data analysis, with which the sequential data attribute is explicitly considered and a constitutive model (physics) is linked to the SSM model (statistics) in a natural way. Then, constitutive model parameters can be rigorously learned under a Bayesian framework based on the SSM without artificially augmenting them into hidden variables of SSM. Without loss of generality, the modified Cam Clay (MCC) model is taken as an example to develop the SSM and to demonstrate the proposed Bayesian framework, which is illustrated using simulated and real-life data. Results from the proposed Bayesian framework based on the SSM include not only the best estimates of MCC model parameters but also their posterior distributions for quantifying the identification uncertainty, based on which the identifiability of MCC model parameters is discussed and highlighted.