We use a new backward evolution model to make predictions for the cosmological surveys in the far-infrared to be conducted by the SAFARI instrument on board of SPICA. The model, which is able to reproduce all the main constraints provided by ISO and Spitzer (source counts, redshift and luminosity distributions), considers different evolutionary properties for four IR populations, defined through a detailed SED-fitting analysis. The fraction of sources with identified AGN signature (~50%) is higher than in other models available in the literature, but is consistent with very recent Spitzer results. We discuss the extragalactic surveys that could be carried on for different scientific purposes (i.e. confusion limited, large and shallow) in the bands covered by SAFARI.