This work aims at assessing the loads and the fatigue estimates computed using an advanced actuator disk (AD) method coupled to large eddy simulation, at a resolution appropriate for large wind farm calculations. In order to compute pertinent fatigue loads, blade trajectories are replicated through the disk, and the AD aerodynamic forces are interpolated onto these "virtual blades" at each time step. This approach, denoted AD-B, is verified against a Vortex-Particle Mesh (VPM) method coupled to immersed lifting lines at a fine resolution, through simulations of an isolated rotor in a turbulent wind. Two different methods are used to evaluate the fatigue damages: the widely used Rainflow counting (RFC) procedure and the spectral Dirlik's approach (DK), both combined with a Palgrem-Miner rule. In the present work, the DK counting method is considered to further investigate the potential of extrapolating some loading data in the high frequencies, uncaptured by the AD-B model at a coarse resolution. The results show that the fatigue estimates computed using the RFC procedure are very similar for the VPM and the AD-B methods, thus without any modeling of the unresolved scales for the disk. Indeed, the AD-B model captures the loads of middle and large amplitudes that contribute the most to the rotor damage. The use of extrapolated loading data makes the AD-B fatigue estimates closer to the VPM ones, but the DK counting method globally leads to results that are quite different from those obtained using the RFC procedure. Further investigations are thus required for the combination of extrapolated loading information and spectral counting methods.