We present VIMOS-VLT spectroscopy of the Frontier Fields cluster MACS~J0416.1-2403 (z=0.397). Taken as part of the CLASH-VLT survey, the large spectroscopic campaign provided more than 4000 reliable redshifts, including ~800 cluster member galaxies. The unprecedented sample of cluster members at this redshift allows us to perform a highly detailed dynamical and structural analysis of the cluster out to ~2.2$r_{200}$ (~4Mpc). Our analysis of substructures reveals a complex system composed of a main massive cluster ($M_{200}$~0.9$times 10^{15} M_{odot}$) presenting two major features: i) a bimodal velocity distribution, showing two central peaks separated by $Delta V_{rf}$~1100 km s$^{-1}$ with comparable galaxy content and velocity dispersion, ii) a projected elongation of the main substructures along the NE-SW direction, with a prominent subclump ~600 kpc SW of the center and an isolated BCG approximately halfway between the center and the SW clump. We also detect a low mass structure at z~0.390, ~10 S of the cluster center, projected at ~3Mpc, with a relative line-of-sight velocity of $Delta V_{rf}$~-1700 km s$^{-1}$. The cluster mass profile that we obtain through our dynamical analysis deviates significantly from the universal NFW, being best fit by a Softened Isothermal Sphere model instead. The mass profile measured from the galaxy dynamics is found to be in relatively good agreement with those obtained from strong and weak lensing, as well as with that from the X-rays, despite the clearly unrelaxed nature of the cluster. Our results reveal overall a complex dynamical state of this massive cluster and support the hypothesis that the two main subclusters are being observed in a pre-collisional phase, in line with recent findings from radio and deep X-ray data. With this article we also release the entire redshift catalog of 4386 sources in the field of this cluster.
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