PROBABILISTIC CALIBRATION OF A SOIL MODEL
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A constitutive model is a relationship between material stimuli and responses. Calibration of model parameters within well-defined constitutive models is thus key to the generation of accurate model-based predictions. One limitation of traditional material calibration is that only a few standardized tests are performed for estimating constitutive parameters, which makes the calibration process eminently deterministic. Moreover, measurements taken during standardized tests are usually global readings, which implicitly assume a ‘homogeneous’ material composition, smearing out the influence of any local effects. This work introduces the Functional Bayesian (FB) formulation as a probabilistic methodology for the calibration of constitutive models that incorporates material random responses and local effects into the assessment of constitutive parameters. This particular calibration process is known as the probabilistic solution to the inverse problem. Estimates of the statistics required for the Bayesian solution are obtained from a series of standard triaxial tests which are coupled with 3-Dimensional (3D) stereo digital images allowing for the capturing of material local effects. In addition, the probabilistic method includes the spatial representation of elemental ‘material’ properties by introducing spatially varying parameters within a 3D Finite Element Model (3D-FEM) to reproduce to the extent possible the actual heterogeneous response of the material. The sampling of spatial ‘material’ realizations is performed by the Polynomial Chaos (PC) method, which permits the simulation of multi-dimensional non-Gaussian and non-stationary random fields. Integration of the random parameters is performed via Markov Chain Monte-Carlo and Metropolis-Hastings algorithms. The calibration of a soil iii sample is presented as a case study to illustrate the applicability of the method when the soil response lies within the linear elastic domain. Calibration results show a probabilistic description of the spatially distributed parameters and of the coefficients of the chaos representation that defines it. Inferences retrieved from the MCMC sampling include the analysis of the ‘material’ properties and of the coefficients of the PC representation which enhances understanding of the randomness associated with the material composition and response.