Abstract: Mechanical parameters of gypsum rock are influenced by the relative humidity in the mine atmosphere. Based on failure characteristics of the roof bed in gypsum mines, we proposed a simplified three-hinged arch analysis model under the uniform load q. Then a cusp catastrophe model was established to investigate instability mechanisms of the roof bed system influenced by the relative humidity. Experimental results show that mechanical parameters of gypsum rock are greatly reduced due to the influence of relative humidity. Analysis and calculation results show that the increase of the relative humidity around the roof bed leads to the instability of support system and the appearance bifurcation set. Therefore, it is more likely that the roof bed undergoes a catastrophic event. The algebraic value of control parameter (a) of the three-dimensional space gradually increases with the increase of relative humidity in the mine atmosphere (i.e., absolute value decreases and changes from negative to zero), and the control parameter (b) gradually increases as well. The path of the control parameter (a, b) of system instability shows the northeast direction, which is the probable path for the system to lose stability.

Key words: gypsum mine, roof bed, a cusp catastrophe model, relative humidity, control parameter