An investigation on the propagation of underground-explosion-generated infrasonic waves is carried out via numerical simulations of the equations of fluid dynamics. More specifically, the continuity, momentum, and energy conservation equations are solved along with the Herzfeld-Rice equations in order to take into account the effects of vibrational relaxation phenomena. The radiation of acoustic energy by the ground motion caused by underground explosions is initiated by enforcing the equality, at ground level, between the component of the air velocity normal to the Earth's surface and the normal velocity of the ground layer. The velocity of the ground layer is defined semi-empirically as a function of the depth of burial and of the yield. The effects of the depth and of the source energy on the signals recorded in the epicentral zone are first discussed. The tropospheric and stratospheric infrasonic phases traveling at a long-range are then analyzed and explained. Synthesized ground waveforms are finally discussed and compared to those recorded at the I45RU station of the International Monitoring System after the 2013 North-Korean test. Good agreement is found between numerical results and experimental data, which motivates the use of infrasound technologies alongside seismic techniques for the characterization of underground explosions.