We investigate, using a recently developed model of liquid state theory describing the rheology of dense granular flows, how a yield stress appears in granular matter at the yielding transition. Our model allows us to predict an analytical equation of the corresponding dynamical yield surface, which is compared to usual models of solid fracture. In particular, this yield surface interpolates between the typical failure behaviors of soft and hard materials. This work also underlines the central role played by the effective friction coefficient at the yielding transition.