## 5 Reliability Evaluation of the Nonlinear Frame Structure
### Reliability Evaluation Analysis  
Figure 10 shows the PDFs and CDFs of the story drift ratio at each story and those of the EEV \(\Phi_{\max}\) of the frame structure under the generated explosive ground motions in the case of \(\rho=0.04\). It can be clearly seen in Figure 10a that with the increase of the story, the opening of the PDF curve of the story drift ratio becomes larger and the peak value shifts to the right, indicating that the dynamic responses of the higher stories are often larger than that of the lower stories. Figure 10b describes the CDFs of the story drift ratio at each story and that of EEV, which are also referred to as the structural seismic reliability. Correspondingly, a similar phenomenon can also be observed in Figure 10b, where under the same threshold conditions the CDF value of the story drift ratio gradually decreases as the height of the frame structure increases in total.  
The corresponding threshold of the story drift ratio of moderate and minor ground motions is \(1/550\) and \(1/100\), according to reference [48]. Since the simulated explosive ground motions are between the moderate and minor ground motions, the corresponding threshold of the story drift ratio is taken as \(1/300\) in this study. Table 7 lists the component and global reliability of the \(10\)-story nonlinear frame structure at the threshold of \(1/300\) under the action of the explosive ground motions with scaled charge quantities of \(0.03\) and \(0.04\). In essence, the reliabilities presented in Table 7 are the area between the threshold line and the PDFs to left of the threshold, and the specific values are the vertical coordinates corresponding to the line focus of CDFs and the threshold line, which are also clearly pictured in Figure 10b. Moreover, it can be easily seen in the table that the weak stories are the eighth story and ninth story which have the lowest seismic reliabilities in all the \(10\) stories, of which the values are \(0.903\), \(0.906\) in case of \(\rho=0.03\) and \(0.860\)  
Figure 10: The PDFs and CDFs of story drift ratio of each story and those of EEV in the case of \(\rho=0.04\): **(a)** PDFs of story drift ratio of each story and that of EEV; **(b)** CDFs of story drift ratio of each story and that of EEV.  
0.882 in case of \(\rho=0.04\). Table 7 also points out that the global dynamic reliability is lower than the minimum single-story dynamic reliability, which indicates that the global dynamic reliability is not equivalent to the weakest chain reliability, and the failure events of each story are not completely related. What is more, it can be further observed from the table that as the scaled charge quantity increases, the reliability of the structure decreases under the same threshold conditions. This indicates that the scaled charge quantity can affect explosive ground motions, thereby affecting the safety performance of the structure. The reliability analysis of this nonlinear frame structure sufficiently verifies the effectiveness of the dimension-reduction modeling method and the EEV-based reliability evaluation strategy, which provide a theoretical basis for the design of structural explosion resistance analysis.  
In this section, the reliability evaluation of the investigated 10-story nonlinear frame structure is realized by the EEV-based reliability evaluation strategy. From this, it is easy to acknowledge the weakest chain of the frame structure by presenting the refined dynamic reliability of each story and also obtain the global dynamic reliability of the whole structure, which can provide a theoretical basis for the anti-explosion design of structures.