A global gyrokinetic toroidal full-f five-dimensional Vlasov simulation GT5D (Idomura et al 2008 Comput. Phys. Commun.179 391)is extended including sources and collisions. Long time tokamak micro-turbulence simulations in open system tokamak plasmas are enabled for the first time based on a full-f gyrokinetic approach with self-consistent evolutions of turbulent transport and equilibrium profiles. The neoclassical physics is implemented using the linear Fokker–Planck collision operator, and the equilibrium radial electric field Er is determined self-consistently by evolving equilibrium profiles. In ion temperature gradient driven turbulence simulations in a normal shear tokamak with on-axis heating, key features of ion turbulent transport are clarified. It is found that stiff ion temperature Ti profiles are sustained with globally constant Lti ≡ |Ti/Ti'| near a critical value, and a significant part of the heat flux is carried by avalanches with 1/f type spectra, which suggest a self-organized criticality. The Er shear strongly affects the directions of avalanche propagation and the momentum flux. Non-diffusive momentum transport due to the Er shear stress is observed and a non-zero (intrinsic) toroidal rotation is formed without momentum input near the axis.