We investigate the nonlinear effective behavior of quasi brittle composites with evolving damage. To this end, we rely on an incremental variational approach for which we first introduce a linearization of the elastic-damageable constitutive law. The resulting Linear Comparison Composite (LCC) is then homogenized by using classical Hashin-Shtrikman bounds. We provide a theoretical and numerical assessment of the incremental variational procedure applied to a porous materials. For particulate composites with a damageable matrix, a complete validation by means of full-field simulations are available in [4] and will be shown during the oral presentation.