###### Abstract
In addition, the aforementioned studies generally focus on the dynamic response of structures under explosive seismic action, and rarely consider the dynamic reliability evaluation of structural systems, which requires further investigation for engineering purpose. Due to the fact that the explosive ground motions are similar to the natural earthquake ground motions, the former can be simulated through the spectral representation method (SRM) [12; 13; 14; 15; 16], which is widely applied in the generation of stochastic processes and is already extensively used for the simulation of explosive ground motions [17; 18]. However, the conventional SRM is based on the Monte Carlo simulation method, which typically requires a large number of random variables and randomly generated sample functions to obtain a satisfactory level of simulation precision. In this end, it is difficult to use the Monte Carlo method for an accurate dynamic reliability evaluation and response analysis of complex civil engineering structures due to the large amount of computational costs and time expenses required to complete a dynamic time-history analysis of the investigated structure and the lack of assigned probability sampling [19; 20; 21]. Overall, current research on explosive ground motions has entered a relatively mature stage by analogy with natural ground motions, where the Sadovsky formula is a typical example. However, there are still three limitations in the existing research that require further exploration. * The research of the relation of charge quantity and the distance to the explosion source with the seismic characteristics of explosive ground motions only staying on the seismic energy level in the present stage, where the influence of that on the seismic spectrum and seismic duration is neglected. * The classic Monte Carlo method for simulating explosive ground motions faces the problems of high-dimensional random variables and the incomplete probability information of the generated sample set, which leads to great difficulty for the efficient and refined dynamic response and reliability analysis of randomly excited structural systems. * The method of using measured records for structural dynamic response analysis has two shortcomings. On the one hand, the number of measured records is limited, and the records are susceptible to the environment and the noise of the measurement instrument, which is difficult to meet the strict requirements of engineering structures. On the other hand, it is essentially a deterministic method that ignores the impact of the randomness of explosive ground motions on structures, which is not in line with reality. To overcome the challenges faced by the conventional Monte Carlo method, on the one hand, [PERSON] et al. [22; 23] proposed the stochastic harmonic function representation for simulating stationary and non-stationary stochastic processes in recent years. On the other hand, [PERSON] et al. [24; 25; 26; 27] recently offered a dimension-reduction technique wherein random functions are introduced as the constraints of random variables in order to generate stochastic (vector) processes for modeling the earthquake ground motions and the wind velocity fields. The computational costs associated with millions of random variables have been effectively reduced to the level of a few elementary random variables, demonstrating the commendable accuracy and efficiency of the dimension-reduction method. In addition, it is worth mentioning that each representative sample generated by the dimension-reduction method has an assigned probability and all the representative samples can constitute a complete probability set, making it possible to achieve the refined dynamic response analysis and reliability evaluation of randomly excited structural systems combining with the probability density evolution method (PDEM) [28; 29]. Consequently, it effectively bypasses the deficiencies of the conventional Monte Carlo method.