Abstract: The design and validation of effective protection systems for large leak sodium-water reaction (LLSWR) accidents in sodium-cooled fast reactors (SFRs) require a comprehensive understanding of the complex long-term thermohydraulic responses following the initial pressure wave propagation process. Due to the strong coupling among sodium-water chemical reactions, gas generation, pressure evolution, discharge processes, and protection system actions, the accurate prediction of the long-term accident behavior remains a critical issue for the safety assessment and engineering design of SFR steam generator systems. In this study, a long-term effect model for LLSWR accidents was developed to describe the system response during the transition from the initial steady operating condition to the long-term transient stage. The proposed model incorporates the major physical phenomena involved in accident progression, including reaction-induced gas production, pressure propagation, rupture disk activation, and accident discharge processes. Based on the configuration and operating parameters of a sodium-water reaction experimental facility, numerical simulations covering the entire accident process, including the initial steady state, transient pressure evolution, and long-term system response, were performed. The calculated pressure histories at key locations agreed well with the experimental measurements in terms of both overall trends and characteristic response features, demonstrating the validity and applicability of the proposed model for long-term LLSWR analysis. Furthermore, the response characteristics of the rupture disk protection system under different leakage rates were systematically investigated. The results show that, under relatively small leakage conditions, the buffering effect of the system volume prevents rupture disk activation. When the leakage rate reaches 0.6 kg/s, only the reactor-side rupture disk is activated, initiating the corresponding protection action. As the leakage rate further increases to 2.5 kg/s, the significantly intensified reaction source causes a rapid pressure rise, leading to the activation of both rupture disks, with the system pressure reaching the safety limit of the experimental facility. In addition, the pressure responses of the two-stage accident discharge tanks were evaluated under various leakage scenarios. The results indicate that the pressure fluctuations in both discharge tanks remain at an extremely low level throughout the accident process, demonstrating sufficient discharge capacity and safety redundancy of the protection system. Overall, the developed model successfully reproduces the complete evolution process from steady-state operation to the long-term transient stage and provides a reliable numerical tool for LLSWR accident analysis, protection system optimization, and safety evaluation of sodium-cooled fast reactor steam generator systems.