###### Abstract  
In the present study, a stochastic model of explosive ground motions applying the dimension-reduction method is proposed, and the reliability evaluation of a nonlinear frame structure under such excitations is realized by means of the probability density evolution method and an equivalent extreme-value-based reliability evaluation strategy. Firstly, the evolutionary power spectrum density function of the explosive ground motions is modeled by respectively identifying the normalized total energy distribution function and the frequency  
abundant frequency components, which would perform a noticeable impact on typical engineering structures. In the 1920s, [PERSON] [1] took the lead in studying the impact of the ground motions caused by mine blasting on nearby building structures, and initially proposed the concept of structural anti-explosion. As a matter of fact, the explosion has significant randomness, and applying the random vibration theory to identify and study the spectral characteristics of explosive ground motions is crucial for exploring the damage mechanism and the anti-explosion strategy of the engineering structures affected by such excitations. In this regard, [PERSON] [2] presented the bispectrum analysis of both natural earthquake ground motion signals and explosive ground motion signals. He found that the sample bispectrum of the signals with Gaussian distribution is lower than that of the signals with skewed distribution. [PERSON] and [PERSON] [3] proposed empirical formulas for estimating the ground peak particle velocity and the dominant frequency of explosive ground motions based on data recorded in the field and found that explosive ground motions on the ground surface and in the free field are remarkably different due to the effect of surface reflection. In addition, with the rapid development of numerical analysis technologies such as finite element strategy, significant progress has been achieved in the investigations of the effects of explosive ground motions on structures. [PERSON] and [PERSON] [4] studied the dynamic response of reinforced concrete frame structures under the action of the simulated explosive ground motions, and they compared the numerical results of structural damage with some test results obtained in previous studies and codes. [PERSON] et al. [5] analyzed the dynamic response and the damage state of a four-story masonry building utilizing measured explosive ground motion records, and they concluded that the structure suffered brittle failure due to tensile stress. With the help of the measured data, [PERSON] et al. [6] investigated the possibility of evaluating the damaging effect of explosion sources on the ground by utilizing the actual explosive ground motion records through experimental tests, which showed that the treatment was feasible in the case of the same formation condition and within a certain distance. Obviously, explosive ground motion is a special form of ground motion that has attracted widespread attention [7; 8; 9; 10; 11]. Dynamic response and damage analysis of structures induced by explosive ground motions are primarily based on measured recordings at present, according to the research described above, which undoubtedly belong to the deterministic analysis scheme. However, due to the limited number of measured explosive ground motion time-histories, as well as the limitations of site conditions and explosion environment, it is difficult for the existing measured records to completely satisfy the requirements of structural dynamic response analysis. Considering the nature of the random dynamic characteristics of explosive ground motions, the application of random vibration theory and method to conduct the artificial synthetic method for reasonable stochastic explosive ground motion model, as well as structural dynamic response and reliability analysis, plays a significantly important role in the anti-explosion analysis and design of engineering structures.