An automatic procedure for calibrating the fracture parameters of fibre-reinforced concrete

Abstract

In this work a calibration procedure to obtain the material parameters that characterize the fracture behaviour of fibre-reinforced concrete (FRC) is presented. This procedure uses a recently proposed trilinear softening diagram implemented in a smeared crack model of the free finite element code OOFEM that allows reproducing the fracture behaviour of FRC and takes advantage of the optimization package of SciPy, with both pieces of software being open-source and of free access for anyone interested in this field. This work presents the calibration procedure, which uses the Nelder-Mead algorithm to adjust the numerical result with the experimental diagram and discusses some key aspects, such as the number of reference points used in the calibration process or the weighting factors used with them, including the possibility of making some reference points more relevant than others in the calibration process. The influence of the mesh size and the element type used in the FEM model is also analysed. To evaluate the quality of the numerical approximation, a deviation factor is defined, which provides an scalar value that becomes lower as the numerical adjustment is closer to the experimental diagram in the reference points. The proposed procedure allows calibrating six parameters automatically with a meaningful time reduction and good accuracy. Using a higher number of reference points may lead to a better adjustment, although this study suggests that a good selection of the reference points is more effective than using a high number of reference points or using weighting factors to make some points more relevant than others. This procedure is finally validated by applying it with experimental results obtained with other types of FRC materials (different fibres and different fibre proportions) and specimen geometries.