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We aim at reproducing the mass- and sigma-[alpha/Fe] relations in the stellarpopulations of early-type galaxies by means of a cosmologically motivatedassembly history for the spheroids. We implement a detailed treatment for thechemical evolution of H, He, O and Fe in GalICS, a semi-analytical model forgalaxy formation which successfully reproduces basic low- and high-redshiftgalaxy properties. The contribution of supernovae (both type Ia and II) as wellas low- and intermediate-mass stars to chemical feedback are taken intoaccount. We find that this chemically improved GalICS does not produce theobserved mass- and sigma-[alpha/Fe] relations. The slope is too shallow andscatter too large, in particular in the low and intermediate mass range. Themodel shows significant improvement at the highest masses and velocitydispersions, where the predicted [alpha/Fe] ratios are now marginallyconsistent with observed values. We show that this result comes from theimplementation of AGN (plus halo) quenching of the star formation in massivehaloes. A thorough exploration of the parameter space shows that the failure ofreproducing the mass- and sigma-[alpha/Fe] relations can partly be attributedto the way in which star formation and feedback are currently modelled. Themerger process is responsible for a part of the scatter. We suggest that thenext generation of semi-analytical model should feature feedback (eitherstellar of from AGN) mechanisms linked to single galaxies and not only to thehalo, especially in the low and intermediate mass range. The integral starformation history of a single galaxy determines its final stellar [alpha/Fe] asit might be expected from the results of closed box chemical evolution models.(abridged)

GalICS II: the [alpha/Fe]-mass relation in elliptical galaxies