The drilling of offshore oilwells in deep and ultra-deep waters is done by floating drilling rigs, which connect to the well in the seabed through the drilling riser. This connection transmits dynamic efforts to the wellhead and casings, causing fatigue in this structure. We formulated the hypothesis that dynamic characteristics of the system change when a high load is applied if the rig drifts after a blackout, changing the accumulated damage from fatigue. At first, we have simulated the consequences of this extreme load using a soil-pile model in Abaqus, a 3D finite element software. Based on the results obtained, a dynamic analysis was performed for two different soil types and two different water depths. It was concluded that the less rigid soil is only a little sensitive to the degradation of soil condition, meanwhile the more rigid soil increases the accumulated damage by about 50 percent.