In this work, we develop a micro-mechanics inspired constitutive model for lightly cemented granular materials, whose internal variables have a clear physical interpretation. It builds on our previous work, which was able to predict several aspects of the behavior of bonded geomaterials ( e.g. , macroscopic stress-strain responses, localization patterns) but did not explicitly account for porosity nor could it predict dilatancy at low mean stress levels. In the present work, we extend the original formulation by Tengattini (2015), formulating a model that is able to predict the material response across a broad range of mean stress while maintaining the same number of parameters as the original model, all of which have a clear physical interpretation, which helps guide their calibration.