The possible formation mechanisms of massive close binary black holes (BHs) that can merge in the Hubble time to produce powerful gravitational wave bursts detected during advanced LIGO O1 and O2 science runs include the evolution from field low-metallicity massive binaries, the dynamical formation in dense stellar clusters and primordial BHs. Different formation channels produce different source distributions of total masses ${M_\mathrm{tot}}$ and effective spins $χ_\mathrm{eff}$ of coalescing binary BHs. Using a modified \textsc{bse} code, we carry out extensive population synthesis calculations of the expected effective spin and total mass distributions from the standard field massive binary formation channel for different metallicities of BH progenitors (from zero-metal Population III stars up to solar metal abundance), different initial rotations of the binary components, stellar wind mass loss prescription, different BH formation models and a range of common envelope efficiencies. The stellar rotation is treated in two-zone (core-envelope) approximation using the effective core-envelope coupling time and with an account of the tidal synchronization of stellar envelope rotation during the binary system evolution. The results of our simulations, convolved with the metallicity-dependent star-formation history, show that the total masses and effective spins of the merging binary black holes detected during LIGO O1-O2 runs but the heaviest one (GW170729) can be simultaneously reproduced by the adopted BH formation models. Noticeable effective spin of GW170729 requires additional fallback from the rotating stellar envelope.

18 pages, 11 figures, accepted to MNRAS after taking into account star-formation rate history for comparison of the calculated BH-BH coalescences with observed systems, LIGO/Virgo GWTC-1 sources added