It is assumed that: 1) a projectile particle invokes into target nucleus a cascade of quark-gluon exchanges; 2) the nucleons involved in the cascade are ejected from the nucleus which leads to the nuclear destruction. On these bases a simple model to estimate the nuclear destruction at the fast stage of the interactions is proposed. The allowed region of the model parameters is determined at the proton-emulsion high energy interaction data analysis: an analysis of gold interactions with nuclei at an energy of 600 MeV/nucleon fixes the parameter values. The distributions on the energy in Zero-Degree-Calorimeter (ZDC) in the interactions of Si+Al, Cu, Pb (14 GeV/nucleon) and Au+Au (10 GeV/nucleon) calculated in the framework of the model and in the cascade evaporation model (CEM) are presented. The proposed model describes the nuclear distribution at intermediate and high energies better than CEM does. The estimation of the average values of impact parameter and the number of intra-nuclear collisions for Au+Au interactions in the events with different ZED is given