Abstract:  The energy development projects in western China require the construction of a large number of vertical shafts in weakly cemented gravel layers with poor stability. Anchor rod support is an important means of controlling the deformation of surrounding rock. However, most of the current theories on anchor reinforcement have overlooked the lagging support of anchor rods. Therefore, based on the spatial constraint effect of the working face, elastic-plastic theory, and the anchor rod stress uniform distribution method, this study proposes a semi-analytical calculation method for the deformation and stress of the surrounding rock of vertical shaft anchor bolts considering the lag support of anchor bolts. The correctness of this method was verified by finite element method. Based on the proposed semi analytical solution, the influence of anchor parameters was further explored. The research results show that the larger the lag distance of the anchor rod, the greater the deformation of the surrounding rock, and the smaller the surrounding rock pressure borne by the anchor rod and other supporting structures. When the lag distance x_gs of the anchor rod is less than 1.5r_A (r_A represents the excavation radius of the vertical shaft), the deformation u_r(r=r_A) and safety factor s of the surrounding rock change greatly. When the lag distance x_gs of the anchor rod is greater than 3.0r_A, the deformation u_r(r=r_A) and safety factor s of the surrounding rock remain basically unchanged. Increasing the diameter of the anchor rod improves the shear strength, but the impact gradually decreases. When the length of the anchor rod L is less than 1.0r_A, the deformation of the surrounding rock u_r(r=r_A) and the safety factor s change greatly. When the length of the anchor rod L is greater than 1.0r_A, the change is slow, so it is not recommended to excessively use long anchor rods. Research suggests that when selecting support parameters, consideration should be given to the support lag distance to ensure the stability of the surrounding rock. This study successfully applied this theory to the vertical shaft engineering of pressure pipelines, and the research results provide a solid theoretical basis for the design of anchor rod support for the surrounding rock of the vertical shaft.

Key words: vertical shaft support, anchor rod lag support, lag support distance, stress distribution method