A two-scale damage model for micro-fractured media is constructed using the asymptotic homogenization method. At the small-scale level, we consider locally periodic microstructures of two-types: micro-cracks nucleating from pores and wing-type micro-cracks. Based on an energy criterion for micro-crack propagation we deduce the macroscopic damage model, without supplementary assumptions on the overall behavior. We show that the resulting two-scale model has the property of capturing a micro-structural length - the distance between neighbor micro-cracks. The influence of the micro-structural parameters on the effective behavior is studied. We illustrate the capacity of the model to predict size effects under compression loadings.