In this work we measure the merger fraction, f_m, of L_B >= L*_B galaxies in the VVDS-Deep spectroscopic Survey. We define kinematical close pairs as those galaxies with a separation in the sky plane 5h^-1 kpc < r_p = 1/4 and 1/10 = mu) proportional to mu^s. The value of s evolves from s = -0.60 +- 0.08 at z = 0.8 to s = -1.02 +- 0.13 at z = 0.5. The fraction of minor mergers for bright galaxies evolves with redshift as a power-law (1+z)^m with index m = -0.4 +- 0.7 for the merger fraction and m = -0.5 +- 0.7 for the merger rate. We split our principal galaxies in red and blue by their rest-frame NUV-r colour, finding that i) f_m is higher for red galaxies, ii) f_m^red does not evolve with z, and iii) f_m^blue evolves dramatically. Our results show that the mass of normal L_B >= L*_B galaxies has grown ~25% since z ~ 1 because of minor and major mergers. The relative contribution of the mass growth by merging is ~25% due to minor mergers and ~75% due to major ones. The relative effect of merging is more important for red than for blue galaxies, with red galaxies subject to 0.5 minor and 0.7 major mergers since z~1, which leads to a mass growth of ~40% and a size increase by a factor of 2. Our results also suggest that, for blue galaxies, minor mergers likely lead to early-type spirals rather than elliptical galaxies. These results show that minor merging is a significant but not dominant mechanism driving the mass growth of galaxies in the last ~8 Gyr (Abriged).
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