A Semi-empirical Model of Air Waves Induced by Falling Rock in a Closed Goaf

In this paper, a semi-empirical model of air waves induced by falling rock is described. The model is composed of a uniform motion phase (velocity close to 0 m·s-1) and an acceleration movement phase. The uniform motion phase was determined based on experimentally and the acceleration movement phase was derived by theoretical analysis. A series of experiments were performed to verify the semi-empirical model and elucidated the law of the uniform motion phase. The acceleration movement phase accounted for a larger portion with a greater height of the falling rock. Experimental results of different falling heights of the goaf showed close agreement with theoretical analysis values. The semi-empirical model could accurately and conveniently estimate the velocity of air wave induced by falling rock. Thus, the semi-empirical model can provide a reference and basis for estimating the speed of air waves and designing protective measures in mines.