The aim of this paper is to present a micro-mechanical damage model for quasi-brittle materials that accounts for friction effects on microcracks. We use homogenization based on asymptotic developments to deduce the overall damage behavior starting from explicit descriptions of elementary volumes with micro-cracks. A time-dependent propagation criterion is assumed for the evolution of cracks at the small scale. An appropriate micro-mechanical energy analysis is proposed leading to a damage evolution law that accounts for friction effects, strain rate dependency, stiffness degradation, material softening and size effects. Numerical results are presented in order to illustrate the local and structural effective damage response. Mesh-independency is proved for the finite-element solutions, as a consequence of the regularizing effect of time.