## 5 Fragility and Leakage Risk Assessment of the NCS  
### Fragility Assessment Process  
In the PSA framework, one of the main focuses is placed on identifying potential stochastic phenomena within the NCS and quantifying the associated risks to the failure of the NCS. A fragility assessment of the NCS under accident pressure is an essential part of the PSA (Level 2), which provides a quantitative description of the structural performance and limit state of the NCS from a probabilistic perspective [18]. The results of the fragility assessment are typically expressed in the form of a fragility curve, as shown in Figure 11. The center of the fragility curve is determined by the pressure capacity of the NCS, and the slope of the fragility curve depends on the uncertainty associated with the pressure capacity. Figure 11: Fragility curves under different uncertainty levels. Fragility curves for the NCS under accident pressure are typically derived using an analytical method, which is fulfilled by performing structural analyses of the NCS with consideration of the associated uncertainties. In this paper, the primary uncertainties in the NCS are taken into account, including material uncertainty (reflecting the stochastic nature of material properties), modeling uncertainty (reflecting the difference between the analytical model and the actual structure), and load uncertainty (reflecting the variability of accident load) [32]. The basic steps of the analytical method for assessing the fragility of the NCS are as follows: Firstly, random samples describing the components of the NCS are generated by random sampling. Then, a nonlinear FE analysis is performed on each random sample, in conjunction with the sub-modeling technique. Finally, a statistical analysis of the calculated results is carried out to construct the fragility curve of the NCS under different degrees of liner corrosion. In this paper, the Latin Hypercube Sampling (LHS) method is employed to produce random samples of the NCS. The LHS method is an improved technique from the traditional Monte Carlo simulation, which utilizes an equal probability sampling method for sampling random variables. Firstly, the cumulative probability distribution of each random variable is divided into N intervals. Subsequently, a random selection is made from each interval to obtain a set of variables. Finally, the original sample values are calculated by utilizing the inverse function of the probability distribution associated with each random variable. Assuming that the sampling space is M-dimensional (where M represents the total number of random variables), the completion of the LHS simulation yields an N \(\times\) M design matrix. Each column in this matrix comprises a random arrangement of a specific random variable, while each row represents a set of random samples for the NCS. The utilization of this equal probability sampling method in LHS enables coverage of a broader probability space with a relatively small number of simulation samples. Consequently, computational efficiency can be significantly enhanced [33]. To clarify the material uncertainty, the mechanical property parameters of the materials employed in the NCS are treated as random variables. Table 2 summarizes the statistical characteristics of the random variables. It is important to note that these statistical parameters are derived from a comprehensive review of the relevant codes and published literature [32; 34; 35]. Additionally, the compressive strength of concrete is correlated with its elastic modulus and tensile strength, and thus only the compressive strength is treated as a random variable. Utilizing LHS simulation, 30 sets of random samples that describe the material uncertainty of the NCS are generated, and the detailed LHS sample values are provided in Appendix A. In accordance with the sub-modeling simulation program described in Section 4.1, it is imperative to sequentially perform nonlinear FE analyses for both the overall model of the NCS and the gusset sub-models with different corrosion degrees.