Comparison of the VIMOS-VLT Deep Survey with the Munich semi-analytical model. II. The colour-density relation up to z=1.5

[Abridged] We perform on galaxy mock catalogues the same colour-density analysis made by Cucciati et al. (2006) on a 5 Mpc/h scale using the VVDS-Deep survey, and compare the results from mocks with observed data. We use mocks with the same flux limits (I=24) as the VVDS (CMOCKS), built using the semi- analytic model by De Lucia & Blaizot (2007) applied to the Millennium Simulation. From CMOCKS, we extracted samples of galaxies mimicking the VVDS observational strategy (OMOCKS). We computed the B-band Luminosity Function LF and the colour-density relation (CDR) in the mocks. We find that the LF in mocks roughly agrees with the observed LF, but at z<0.8 the faint-end slope of the model LF is steeper than the VVDS one. Computing the LF for early and late type galaxies, we show that mocks have an excess of faint early-type and of bright late-type galaxies with respect to data. We find that the CDR in OMOCKS is in excellent agreement with the one in CMOCKS. At z~0.7, the CDR in mocks agrees with the VVDS one (red galaxies reside mainly in high densities). Yet, the strength of the CDR in mocks does not vary within 0.2