Efficient meso-scale homogenisation and statistical size effect analysis of concrete modelled by scaled boundary finite element polygons

This study develops an efficient numerical homogenisation approach for meso-scale concrete samples with randomly generated and packed aggregates and pores. A simple algorithm is devised to discretize samples into meshes consisting of semi-analytical scaled boundary finite element (SBFE) polygons only. As each aggregate is modelled by one SBFE polygon and only polygonal boundaries are discretized into nodes, the degrees of freedom of a model is significantly reduced compared with conventional finite element models. The volumetrically averaged stress inside a SBFE polygon is semi-analytically integrated, leading to high accuracy in the homogenised elastic properties. The effects of model size and porosity are statistically studied by extensive Monte Carlo simulations. A size effect law taking porosity into account is proposed to predict effective elastic moduli in good agreement with experimental data up to 200 mm model size. The meso-models are found statistically homogeneous when the size is about 4.5 times the maximum aggregate size.