The dynamics of transport barrier relaxation oscillations in the presence of resonant magnetic perturbations (RMPs) is investigated with a 3D global fluid code which simulates resistive ballooning turbulence in tokamak edge plasmas. The results reproduce qualitatively the stabilizing effect of RMPs and share common characteristics with ELM control experiments. It is found that this stabilization is due to a modification of the geometrical properties of the barrier.