Robust probabilistic calibration of a stochastic lattice discrete particle model for concrete

Abstract

Numerical modelling of quasi-brittle materials arising from lattice or particle formulations is based on “a priori” discretisation of a medium according to an idealization of its granularity. This paper concentrates on the so-called Lattice Discrete Particle Model (LDPM), which provides accurate modelling of damage initiation and crack propagation at various length scales. However, its simulations are computationally demanding. We propose an automated identification procedure that would facilitate widespread utilisation without requiring deep expert knowledge about details of the model. Such an automated procedure is complicated, namely due to stochasticity of the LDPM related to the random generation of the particle configuration. The particle size distribution is generated so that it statistically corresponds to prescribed concrete granulometric distributions, but each realisation of particle configuration is created at random. For the proposed identification procedure, probabilistic Bayesian formulation is used to obtain robustness and stability, and time requirements are kept at a reasonable level thanks to the LDPM’s polynomial chaos approximation. The Bayesian formulation solves such an inverse problem as well–posed and provides a quantitative assessment of the underlying uncertainty for the values of material properties identified. The procedure is applied to identify seven material parameters from an unconfined compression cube test and notched three-point bending test. Its efficiency is verified on synthetic data with known parameter values in order to quantify the accuracy of the estimates and it is also validated using experimental data to prove its robustness.