Foundation damping holds large potential for design optimisations of monopile-supported offshore wind turbine structures. However, the contribution of foundation damping is not well understood, in part due to lack of suitable method for incorporating foundation damping in the time-domain analysis of wind turbine structures. This paper presents a practical approach for this purpose in which a dashpot is attached in parallel to each p-y spring along the monopile. In this way, the distributed soil-pile interaction stiffness and damping are accurately modelled. To demonstrate the validity of the proposed approach, a case study exploring the influence of foundation damping on the dynamic response of an IEA 15 MW reference turbine founded on monopile is carried out. The results demonstrate that the foundation damping has relatively limited impact on the overall dynamic response and fatigue loads in power production states. However, inclusion of foundation damping is shown to significantly reduce the structural response after emergency shutdown and under parked conditions. The findings of the case study show promising potential for wind turbine structure design optimization through consideration of foundation damping.