Achieving a comprehensive and accurate understanding of the anchor reinforcement mechanism and a quantitative evaluation of the surrounding rock’s stability for an anchored underground cavern can provide an important theoretical basis for supporting and excavating the cavern. First, the composite bearing structure composed of the anchor and surrounding rock was defined as the surrounding rock reinforcement body by using the homogenization method, and a new method for evaluating the stability of surrounding rock by the surrounding rock reinforcement body deformation and damage degree was proposed. Second, based on the anchor reinforcement effect, the expression of the physical‐mechanical parameters of the surrounding rock reinforcement body was deduced, and the analytical solution of stress and displacement of the surrounding rock reinforcement body was obtained. Finally, the stability coefficient of surrounding rock indicating the degree of the surrounding rock reinforcement body damage was defined. The research showed that the theoretical solution agreed well with the results of the numerical simulation, and the difference between the theoretical solution and the monitoring value was less than 10%, which verified the reliability of the method and the results of this paper. The design of the length and spacing of the anchor followed the principle of long but sparse and short but dense, and the pretightening force of the anchor and the stability coefficient of surrounding rock varied linearly. The analytical solution of this paper provides a theoretical reference for understanding the mechanism of anchor support and provides a quantitative evaluation method for the stability of surrounding rock. Compared with the traditional support design, the theory of this paper gives full play to the self‐stability of the surrounding rock and the strength of the anchor, which is conducive to saving support costs and avoiding the construction limitations in some projects.

The traditional Coulomb’s earth pressure theory does not consider the effect of local surcharge on the lateral earth pressure and its critical failure angle. However, in practice, local surcharges commonly act on the surface of frozen backfill that is affected by freeze‐thaw actions in cold regions and tend to affect the active thrust and its position. In paper, analytical solutions for estimating the active thrust, critical wedge failure angle, and action position subject to a local surcharge in cold regions are proposed. Herein, the simplified equivalent moment of surcharge is adopted on the premise of maintaining Coulomb’s earth pressure assumptions. The formula derivation is provided as a typical example to obtain the active thrust, critical wedge failure angle, and its position under a strip surcharge. Compared with previous approaches, the proposed solutions lead to easier evaluation of all indexes associated with Coulomb’s active earth pressure. Meanwhile, the expressions of Coulomb’s earth pressure under other types of nonuniform loading acting on the wall are discussed. In addition, sensitivity is performed to assess the effect of some main parameters. The results indicate that the dip angle of retaining wall‐back and the friction angle of frozen backfill soil are two most significant indexes that influence the active thrust and its position.