## 1 Introduction  
Floating offshore wind turbines (FOWT) have recently shown great potential due to the considerable wind resources and more flexible installation sites they provide compared to onshore wind turbines [1]. As a result, FOWT capacity has obtained significant progress in the last decade [2, 3]. According to Offshore Wind Market Report: 2021 Edition ii, in 2020 alone the global floating offshore wind capacity grew by more than three times, from 7663 MW (2019) to 26,529 MW [4]. This higher wind energy density brings with it new challenges for the offshore wind industry, particularly the mooring system [2, 3]. One of the main challenges with mooring systems is their high rate of failure, as experienced in the oil and gas industry with 296 mooring system accidents in a roughly 40-year period [5], and an annual probability of failure during 2001-2011 estimated at 3.0 \(\times\) 10\({}^{-3}\)[6]. Similar challenges exist with respect to FOWT, and further comprehensive studies based on specific FOWT properties are required [2].  
The floating wind industry currently applies three conventional mooring configurations from the oil and gas industry: catenary mooring systems, tension-leg mooring systems, and semi-taut mooring systems, shown in Figure 1[7, 8]. A catenary mooring system mainly houses steel chains, and hangs freely between the floating structure and anchor to form a catenary shape. The relaxed catenary of the system leads to flexible vertical and horizontal motion of the floating platform [9, 10]. The mooring lines of tension-leg mooring systems are pre-tensioned, allowing them to be fully tautened by the floating body [9]. The semi-taut mooring system combines the taut mooring system and catenary mooring system [9, 10]. The advantages and disadvantages of the three mooring systems are summarized in Table 1. Current offshore floating wind projects such as the spar type foundation (Hywind Scotland [11], Hywind Tampen [7], TODA Hybrid Spar [12]),  
wind energy industry specifically, studies are very limited. [PERSON], et al. [24] used a numerical tool that combines a floater-mooring-coupled dynamic analysis program (CHARM3D) with an aero-hydro-servo-elastic wind turbine simulation tool to model the failure case of an FOWT and report its dynamic motion during the accident. Their results suggested the need for a more comprehensive study with additional scenarios. Most of the above-mentioned previous studies on the effects of mooring failure considered TLP; however, for semi-submersible floating wind turbines the dynamic response of the platform following mooring line failure and the impact of various incident wind and wave angles have not been thoroughly discussed in the literature and require dedicated studies. Furthermore, a non-operational wind turbine as considered in this research compares to the [PERSON], [PERSON] and [PERSON] [24] operational model. In the present study, a fully nonlinear numerical model was built with consideration of the Quadratic Transfer Function (QTF), added mass, and damping matrices of the platform. The hydrodynamic model of an FOWT [25; 26] with the three-leg mooring configuration is investigated under mooring failure along with the dynamic response in detail, including platform performance, drift area, and tension in the remaining mooring lines.  
The remainder of this paper is organized as follows: Section 2 introduces the analytical model of the FOWT, floating platform and the mooring system; Section 3 presents the numerical modelling of the FOWT, including the numerical tools and validation; Section 4 presents the hydrodynamic performance of the FOWT under the mooring filature conditions; Section 5 discusses the main findings and considers potential industrial applications; finally, the main findings and conclusions are drawn in Section 6.