Empirical simulations based on extrapolations from well-established low-frequency ($< 5$ GHz) surveys fail to accurately model the faint, high frequency ($>10$~GHz) source population; they under-predict the number of observed sources by a factor of two below $S_{18~rm GHz} = 10$ mJy and fail to reproduce the observed spectral index distribution. We suggest that this is because the faint radio galaxies are not modelled correctly in the simulations and show that by adding a flat-spectrum core component to the FRI sources in the SKA Simulated Skies, the observed 15-GHz source counts can be reproduced. We find that the observations are best matched by assuming that the fraction of the total 1.4-GHz flux density which originates from the core varies with 1.4-GHz luminosity; sources with 1.4-GHz luminosities $< 10^{25} rm W , Hz^{-1}$ require a core fraction $sim 0.3$, while the more luminous sources require a much smaller core fraction of $5 times 10^{-4}$. The low luminosity FRI sources with high core fractions which were not included in the original simulation may be equivalent to the compact `FR0 sources found in recent studies.
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