A series of flow experiments were performed on matched fractures to study the problem of non-Darcy flow in fractured media. Five rock fractures of different roughness were generated using indirect tensile tests, and their surface topographies were measured using a stereo topometric scanning system. The fracture was assumed to be a self-affine surface, and its roughness and anisotropy were quantified by the fractal dimension. According to the flow tortuosity effect, the nonlinear flow was characterized by hydraulic tortuosity and surface tortuosity power law relationships based on Forchheimer’s law. Fracture seepage experiments conducted with two injection directions (0° and 90°) showed that Forchheimer’s law described the nonlinear flow well. Both the proposed model and Chen’s double-parameter model gave similar results to the experiment, but the match was closer with the proposed model. On this basis, a new formula for the critical Reynolds number is proposed, which serves to distinguish linear flow and Forchheimer flow.

Gypsum rock is highly sensitive to a water environment due to its unique physical and chemical properties, such as high solubility. After wetting, the internal microstructure of gypsum rock is damaged, and the mechanical properties deteriorate accordingly, leading to serious engineering problems for gypsum-bearing geotechnical structures. Therefore, it is particularly necessary to investigate the mechanical deterioration behavior of gypsum rock after wetting. In this paper, the mechanical behavior of gypsum rocks with different water contents were studied. The relationship between the rock water content and the water immersion time was established through the water content test. The scanning electron microscope (SEM) images of the gypsum rock after the water immersion showed that the internal microstructure of the gypsum rock became looser and more complex as the immersion time increased. The fractal dimensions of the SEM images were calculated to quantify the degree of damage to the gypsum rocks after wetting. These images showed that the degree of damage increased with the increasing immersion time, but the increase rate tended to be slow. The relationship between the rock water content and the mechanical responses of gypsum rock were established by triaxial compression tests, and the concomitant acoustic emission (AE) characteristics in the loading processes showed that the immersion time had a positive correlation with the AE frequency and a negative correlation with the AE cumulative count. Based on the AE characteristics, a damage constitutive model of gypsum rock as a function of immersion time was developed and this can reproduce the mechanical responses of gypsum rock after wetting.

The stability of the goaf support system is the key to safe production in gypsum mines. Therefore, this study constructed a pillar‐beam support system which contained pillar plastic zones. In this support system, the beam and pillar were taken as energy releaser and energy dissipater, respectively. Through establishing a cusp catastrophe model based on energy theory, the new criterion for instability was obtained which is related with geometric stiffness and system energy dissipation. The results indicate the instability of the support system is caused by the incompatibility of energy release, dissipation, and geometric deformation. When K > 1, the energy released by the support system is compatible with geometric deformation. The support system experiences a quasistatic process from the static state in bottom page to the static state in top page along Path I. When K < 1, the energy released by the support system cannot be in tune with geometric deformation. The support system experiences a catastrophe process along Path II. The evolution from the static state in bottom page to the static state in top page is not progressive, but catastrophic. The redundant energy released in this process leads to mechanical instability of the support system. This study provided theoretical foundation for the mining and treatment of mines. Based on actual engineering examples, the sensitivity of the geometric parameters of the support system was analyzed as well. These parameters are ranked by their sensitivity from high to low, as is shown below: beam thickness, plastic zone width, room span, pillar width, and pillar height. Then, the goaf was classified according to the geometric parameters. Energy catastrophe theory was applied to analyze the stability of the support system in different classes of goaf. The analysis results showed that Class D goaf should be labeled as the unstable zone, which was consistent with the result of field research. To conclude, energy catastrophe theory can be used to demonstrate the nonlinear mechanical mechanism of support system instability in room‐pillar mining goaf.