Multiple failures in or around a stiff inclusion embedded in a soft matrix under a compressive loading

As well as cavities, embedded concretions and fossil inclusions are known to be possible sites of fracture initiation in rocks under compressive loadings. Parallel cracks can be observed in stiff inclusions surrounded by soft sediments. The crack spacing is often small and strictly incompatible with a mechanism of successive failures and reloading because of a shielding effect. The explanation proposed here is that these failures occur almost simultaneously thus avoiding this effect. A mixed criterion developed by one of the authors and involving both energy and stress conditions is able to predict such a fracturing mechanism. It is strongly related to a size effect: the larger the inclusion diameter, the higher the number of cracks. There is a competition between this mechanism and other fracture events like matrix failure or interface debonding. It is shown that, depending on the material properties and the concretion size, one of them can become predominant.