The research of design method for anchor cables applied to cavern roof in water-rich strata based on upper-bound theory

• We establish a failure mechanism of the cavern roof with anchor cable in water-rich stratum.
• A design method of anchor cable is obtained based on the upper-bound theory and Hoek–Brown criterion.
• We discussed the factors that affect the design parameters and corresponding recommendations.
• The design method is applied to determine the anchor cable parameter of a pump station.

In this study, we use the upper-bound method to develop a collapse failure mechanism of the roof surrounding rock of semicircle arched roadway, with a consideration of the water pressure in the stratum and the support from anchor cables. We consider a cavern with a semi-circular roof and straight walls in a water-rich stratum as a case study. A design method is presented for the required length of and the pre-tightening force of anchor cables on the cavern roof, based on the Hoek–Brown criterion. We analyse the effects of factors such as the cavern width, the pore-water pressure coefficient and the specific weight and the compressive and tensile strengths of the rock mass using established sensitivity indexes for the factors that affect the design parameters of anchor cables. We provide recommendations for controlling the surrounding rock in practical engineering applications for actual scenarios. The design method is used to determine the parameters of anchor cables for the roof of a primary drainage pump station in a mine. The designed anchor cables are used to effectively control the deformation of the surrounding rock. The results show that at the early stage of the excavation of a cavern, the collapse of the surrounding rock of the roof can only be effectively controlled using anchor cables with lengths that meet the design requirements and to which a sufficient pre-tightening force has been applied. In addition, the required length of anchor cables increases with the cavern width, the pore-water pressure coefficient and the specific weight of the rock mass and decreases as the compressive strength of the rock mass increases. The cavern width has the highest sensitivity among the influence factors for the length of anchor cable. Furthermore, the required pre-tightening force for anchor cable for the roof decreases as the tensile and compressive strengths of the rock mass increase and increases with the pore-water pressure coefficient, the cavern width and the specific weight of the surrounding rock. The cavern width also has the highest sensitivity among the influence factors for the pre-tightening force. Finally, the cavern shape and width should be carefully selected for the design and construction of a cavern with weak surrounding rock in a water-rich stratum. The intactness of the surrounding rock should be improved by using high-strength and high-toughness anchored supporting components, applying a high pre-tightening force to the anchored supporting components and using grouting reinforcement to mitigate the effect of water. In this way, relatively good control of the surrounding rock can be realised.