According to the deep beam model, the bury conditions, the geometry characteristics and the load condition, we established a load transfer model based on the tie rod arch and an internal force model for the loaded and anchored segments of the anti-slide pile. Then, we analyzed the shear, bending shear and local compressive failures of the pile, caused by the equivalent concentrated thrust force, the lateral frictional force, active earth pressure, and passive earth pressure, etc. With the laboratory results of the deep beam model, the relation between the shear span ratio and the tie rod arch was presented. According to the mechanical balance conditions of the cantilever beam, we obtained the power function curve of the tie rod arch and the influence factors. Subsequently, we established the equations of the horizontal displacement and the deflection angle at the bearing segment by superposing the load and the displacement of the strip nodes. According to the deformation characteristics of the Timoshenko deep beam element, the equations of the horizontal displacement and the deflection angle at the anchored segment were proposed. With the established calculation model and the material mechanics, the displacement, shear force and bending moment curves at the loaded and anchored segment of the anti-slide pile were proposed. Finally, the case study indicates that the displacement and the internal forces are nonlinear in the pile. The results obtained using the preliminary beam are larger than the numerical results, which is the smallest results than the other two methods.

For improving the toughness and long‐term strength of the fractured rock mass reinforced with epoxy resin and reducing the opening displacement of the crack tip, three types of converging cracks are established according to the deformation and failure characteristics of the rock mass, structural planes, and epoxy resin composite structure. The stress intensity factor of the type II compound crack and the analytical formula of the crack surface tip opening displacement are obtained. An improved Kelvin nonlinear creep model is proposed. Through the creep isochronous curve, the time and long‐term strength of accelerated creep failure are obtained, as well as creep rupture coupling characteristics. The ductile plastic deformation is used to characterize the toughness, and the toughness of epoxy resin is enhanced by adding mud powder, and the relationship between toughness and long‐term strength is established. Combined with experimental verification, when the drying mud powder content is 20%, the toughness of the epoxy resin has a good correlation with the long‐term strength; when the mud powder content exceeds 30%, its ductility and long‐term strength decrease, and at the same time the toughness effect is significantly weakened. The research results can provide a useful reference for toughened epoxy resin to strengthen fractured rock mass engineering.

Based on the theory of limit and the unified strength theory, the three-dimensional failure pattern and the corresponding velocity field on the heading face for cyclical footage are proposed, considering the influence of the cyclical footage and the intermediate principle stress on the heading face stability. Addition, the influence of various parameters on the heading face stability is analyzed. The present study shows that the first increase in internal friction angle (lower than 25°) can promote the heading face stability. Then, the increase in the cohesion can promote the stability when the internal friction angle is higher than 25°. In addition, for the relatively intact instead of the poor surrounding rock, the promotion of the stress conditions of the heading face, caused by by the intermediate principle stress, indicates that the Mohr-Coulomb criterion is conservative.