## 1 Introduction  
The launch vehicle is a complex and large-scale technology-intensive system and it plays an important role in the deep space exploration mission. Once an explosion occurs, it would threaten the safety of personnel and facilities around the launch site. Owing to its very low boiling point, liquid propellant is extremely hazardous and its leakage/sudden release from a pressurized tank would lead to vapor cloud formation resulting in subsequent fire and explosion. This point was amply demonstrated by a series of explosion accidents over decades [1]. The study of the rocket shock environment is an ongoing effort to characterize the environment resulting from catastrophic rocket explosion. The purpose is to develop the data and information required to allow launch vehicle designers to develop safer launch systems. Many workers have studied liquid propellant explosion characteristics by conducting experiments and analyzing experimental data [2; 3; 4; 5; 6; 7; 8; 9]. The liquid propellant explosion test has high risk and high cost, and the experimental conditions are strict and the repeatability is poor, which makes it difficult. With the development of computer simulation technology, numerical simulation has become the main means to solve such problems [10; 11; 12; 13; 14; 15; 16; 17]. Explosion hazard modeling is a challenging problem since it involves several physical, often complex, interacting aspects. In combustion explosions, the available quantity of energy changes rapidly and is constantly redistributed among heat, the kinetic and chemical energy forms. The problem becomes even more complex when the subsequent shock wave propagation is assumed to interact with the ground, which has a more destructive effect on the personnel and facilities at the launch site. Ground and shock waves interact closely since the shock wave impulses affect the ground, while the ground in turn modifies the shock wave's propagation patterns [18]. Therefore, it is of great significance to investigate different grounds effects on shock wave propagation resulting from near-ground explosion. It is difficult to deduce and calculate the shock wave parameters in theory, so most of the current research adopts the empirical formula based on a large number of tests for prediction. However, due to the limitation of experimental conditions, the results calculated by different empirical formulas often differ greatly, which will bring hidden dangers to the safety analysis of the launch site [19]. However, the explosion test has the characteristics of short time, poor repeatability, and high cost, so it is not convenient for research. Therefore, research on the propagation law of shock wave in complex environment has been investigated by many researchers [20; 21; 22; 23; 24; 25; 26; 27; 28]. When a rocket explodes on the launch pad, the shock wave does not travel through the infinite air. The ground has certain influence on the propagation of shock wave. The effect of the ground on the shock wave is reflected in two aspects. On the one hand, the ground will reflect and enhance the shock wave. On the other hand, the earth may absorb some energy of the shock wave [29]. Common types of launching site ground include concrete ground and soil ground. Concrete ground reflects more energy of the shock wave, while soil absorbs more energy of the shock wave and reflects less energy due to its looseness. In order to study the influence of different ground properties on the propagation law of shock wave, this paper considers two extreme cases, one is air material, the other is rigid ground. The air material simulates the shock wave propagation in free space without any obstruction. Rigid ground, on the other hand, absorbs no energy and reflects it all.