The energydevelopment projects in western China require the construction of a largenumber of vertical shafts in weakly cemented gravel layers with poor stability.Anchor rod support is an important means of controlling the deformation ofsurrounding rock. However

most of the current theories on anchor reinforcementhave overlooked the lagging support of anchor rods. Therefore

based on thespatial constraint effect of the working face

elastic-plastic theory

and theanchor rod stress uniform distribution method

this study proposes asemi-analytical calculation method for the deformation and stress of thesurrounding rock of vertical shaft anchor bolts considering the lag support ofanchor bolts. The correctness of this method was verified by finite elementmethod. Based on the proposed semi analytical solution

the influence of anchorparameters was further explored. The research results show that the larger thelag distance of the anchor rod

the greater the deformation of the surroundingrock

and the smaller the surrounding rock pressure borne by the anchor rod andother supporting structures. When the lag distance of the anchor rod is less than 1.5 ( represents the excavation radius of the vertical shaft)

the deformation (=)and safety factor of the surrounding rock change greatly. When the lagdistance of the anchor rod is greaterthan 3.0

the deformation (=)and safety factor of the surrounding rock remain basically unchanged.Increasing the diameter of the anchor rod improves the shear strength

but theimpact gradually decreases. When the length of the anchor rod is less than 1.0

the deformation of the surrounding rock (=)and the safety factor change greatly. When the length of the anchorrod is greater than 1.0

the change is slow

so itis not recommended to excessively use long anchor rods. Research suggests thatwhen selecting support parameters

consideration should be given to the supportlag distance to ensure the stability of the surrounding rock. This studysuccessfully applied this theory to the vertical shaft engineering of pressurepipelines

and the research results providea solid theoretical basis for the design of anchor rod support for thesurrounding rock of the vertical shaft.