One of the main issues about Internal Transport Barriers (ITBs) and their relevance to a reactor scenario regards the possibility of creating and maintaining them at plasma densities close to the Greenwald limit. One of the main candidates to create and fuel high-density ITB plasmas is pellet injection. The question then arises as whether an ITB can survive the strong perturbation induced by the pellet and the fuelling of the interior of the ITB is possible without destroying the barrier itself. To investigate this subject, experiments were performed on JET where high-density plasmas with an Internal Transport Barrier (ITB) were created by means of combined use of Lower Hybrid Current Drive (LHCD) and pellet injection before the barrier formation. Attempts were then made to use pellets to fuel the plasma and sustain its density during the ITB phase. It was found that shallow pellets ablating within 15cm from the plasma edge and far from the foot of the barrier (located at about 50cm from the plasma edge) did not destroy the ITB, whereas deeper pellets with penetration length of 30-40cm affected the barrier and led to its disappearance. Modelling of these experimental scenarios has been performed with transport and fluid turbulence codes. The codes used in the analysis were: JETTO, a 1.5 dimensional transport code, TRB, a global electrostatic fluid turbulence code and CUTIE, a global electromagnetic fluid turbulence code. In this paper the result of the simulation are presented and the physics of the interaction between the pellet and the ITB is discussed.