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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 total energy distribution function on the basis of the measured motion records. In addition, an exponential model is constructed to forecast the seismic characteristics of the explosive ground motions based on the given distance to the explosive source and the charge quantity. Then, the representative samples of the explosive ground motions are simulated using the dimension-reduction method. The simulation results show that the generated acceleration samples have significant seismic characteristics of the explosive ground motions, and the accuracy is verified by comparing the second-order statistics with the sample set and the corresponding targets. Due to the fact that the probabilities of the representative samples simulated by the dimension-reduction method can compose a comprehensive probability set, it contributes to the refined dynamic response analysis and reliability evaluation of complex structures combining with the probability density evolution method. The accurate dynamic response analysis and reliability evaluation of a nonlinear frame structure illustrates the effectiveness of the proposed model and the dimension-reduction method for simulating the explosive ground motions. The numerical results demonstrate that the explosive ground motions have a substantial effect on the nonlinear behavior and the security of engineering structures.