In a concrete structure subjected to an explosion, for example a concrete slab, the material is subjected to various states of stress which lead to as many mode of rupture. Close to the explosive, a state of strong hydrostatic compression is observed. This state of stress produces an irreversible compaction of the material. Away from the zone of explosion, confinement decreases and the material undergoes compression with a state of stress, which is slightly triaxial. Finally, the compression wave can be reflected on a free surface and becomes a tensile wave, which by interaction with the compression wave, produces scabbing. We present in this paper a model aimed at describing these three failure modes. It is based on visco-plasticity and rate dependent damage in which a homogenisation method is used in order to include the variation of the material porosity due to compaction. The model predictions are compared with several experiments performed on the same concrete. Computations of split Hopkinson tests on confined concrete, a tensile test with scabbing, and an explosion on a concrete slab are presented.