The fragmentation of (3.7 A GeV) and (14.6 A GeV) is investigated as a function of the degree of disintegration of different components of photoemulsion nuclei. The experimental measurements show nearly energy-independent behaviour throughout the studied charge, size and multiplicity distributions of fragments produced from the two projectile beams. The various stages of the interactions, from the initial impact through to the final formation of clusters, are theoretically treated as follows. (i) The first stage of the interaction is modelled by the Glauber approach, using Reggeon parametrization for the nucleon-nucleon scattering amplitude. (ii) The additional inelastic interaction of secondary particles, produced in the primary stage, with other nucleons of the nucleus is analysed in the framework of a Reggeon-theory inspired model. (iii) The phenomenological percolation-evaporation model is used to describe the spectator part of the nucleus.