Efficient probabilistic multi-fidelity calibration of a damage-plastic model for confined concrete

Abstract

This detailed study investigates Bayesian inference with material model parameters, exemplified using an advanced damage-plastic model with parameters identified from recently proposed innovative tests of concrete cylinders subjected to confined compression. The study has two main objectives—one specific and the other more general: (i) to evaluate the potential and benefits of the elaborated experimental setup for estimating 15 material parameters in the damage-plastic model for concrete (CDPM2) and (ii) to demonstrate the robustness and efficiency of the numerical tools applied to the problem of simultaneous probabilistic identification for a large number of parameters from limited and noisy data. The paper therefore provides sufficient detail about all steps included in the identification procedure, allowing its application to any other material model calibration problem.The computational burden connected to probabilistic analysis based on Markov chain Monte Carlo method is mitigated here by using a surrogate model based on polynomial chaos expansion. As a benefit, this type of surrogate allows global sensitivity analysis to be performed easily, and it also facilitates analysis of complexity in the relationship between particular material parameters (or pairs of parameters) and simulated material response components. The description also includes strategies for the construction of an efficient anisotropic polynomial expansion with varying degrees in particular parameters.As a problem-specific acceleration of the surrogate construction, two variants of the model simulating the confined compression experiment are described. One is a high-fidelity model that considers detailed specimen geometry, while the other is a computationally faster and more stable low-fidelity variant which simulates the test on the level of a single material point.The robustness and efficiency of the elaborated identification strategy are illustrated by calibration from synthetic as well as from experimental data obtained for four distinct sets of specimens made of the same concrete and equipped with aluminum hoops. The consistent results of particular calibrations, sensitivity analysis and also expert expectations based on deep understanding of material laws confirm the robustness of the identification strategy and its ability to simultaneously estimate 11 out of 15 parameters in a complex damage-plastic model from relatively inexpensive failure tests.