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It is of great significance for the improvement of grouting technology and engineering practice to master the flow law of grout between parallel plates. However, the traditional calculation model ignores the influence of the inertia term and only considers the stable flow of slurry, so there is a big error in some cases. It is difficult to solve the motion equation of a Bingham fluid considering the inertial force term directly. Combined with the relationship between the steady-state flow equation of a Bingham fluid and a Newtonian fluid, the approximate unsteady-state flow equation of a Bingham fluid suitable for describing slurry flow is constructed. In addition, according to the unsteady flow equation, the relationship between the time and distance of slurry flow in parallel plate fractures can be obtained, and the simplified conditions of the Bingham fluid unsteady flow model are given. Finally, the accuracy of the flow equations and the simplified conditions are verified by experiments and numerical calculations.

Pore water pressure has an important influence on the stresses and deformation of the surrounding rock of deep tunnels in water-rich areas. In this study, a mechanical model for deep tunnels subjected to a nonuniform stress field in water-rich areas is developed. Considering the pore water pressure, a new unified solution for the stresses, postpeak zone radii, and surface displacement is derived based on a strain-softening model and the Mogi-Coulomb criterion. Through a case study, the effects of pore water pressure, intermediate principal stress, and residual cohesion on the stress distribution, postpeak zone radii, and surface displacement are also discussed. Results show that the tangential stresses are always larger than the radial stress. The radial stress presents a gradually increasing trend, while the tangential stress presents a trend of first increasing and then decreasing, and the maximum tangential stress appears at the interface between the elastic and plastic zones. As the pore water pressure increases, the postpeak zone radii and surface displacement increase. Because of the neglect of the intermediate principal stress in the Mohr-Coulomb criterion, the postpeak zone radii, surface displacement, and maximum tangential stress solved by the Mohr-Coulomb criterion are all larger than those solved by the Mogi-Coulomb criterion. Tunnels surrounded by rock masses with a higher residual cohesion experience lower postpeak zone radii and surface displacement. Data presented in this study provide an important theoretical basis for supporting the tunnels in water-rich areas.

Mining-induced fractures in underground coal mining face affect the stability of overburdens and provide preferential channels for water and material transfer in the underground environment. Therefore, to study the development of water-flowing fracture zones in overburdens of working face and goaf is of great significance for roof control, gas drainage, water resistance, disaster reduction, and efficient mining from the mining. In this study, a new method for predicting the development of overburden water-flowing fracture zone height (DHOWFFZ) was proposed based on the characteristics of overburden rock in No. 3 coal seam of Xin’an Coal Mine. First, the stope of No. 3 coal seam exhibits a rock stratum structure of mudstone and sandstone overlapping. Considering this characteristic, the overburden strata of No. 3 coal seam are divided into several “mudstone-sandstone” rock stratum groups. Furthermore, the ultimate tensile deformation of soft rock is greater than that of hard rock. It is proposed to judge the development degree of penetrating fracture in each rock stratum by adopting the elongation rate of mudstone intermediate layer. Meanwhile, the DHOWFFZ of “mudstone sandstone” composite rock stratum structure in the 3402 working face of No. 3 coal seam is calculated to be smaller than 43.1 m according to the actual situation. Finally, the DHOWFFZ in the 3402 working face was measured in the field, which verifies the rationality of the new DHOWFFZ prediction method. The research results provide new ideas for the prediction of DHOWFFZ and are helpful for future research in related fields.