Elastic-brittle-plastic analysis of the radial subgrade modulus for a circular cavity based on the generalized nonlinear unified strength criterion

When using the bedded-beam model based on Winkler springs for cavity lining design, it is always difficult for engineers to select an appropriate value for the radial subgrade modulus (k) due to the lack of related theoretical research. The solutions of k for a circular tunnel proposed by Wood (1975) and Zhang et al. (2014) have been found to be applicable only when a tunnel is in elastic ground. However, a rock mass will exhibit elastic, brittle and plastic states under different stress conditions. Considering that the plastic state can effectively improve the bearing capacity and reduce the engineering cost, to investigate the radial subgrade modulus in an elastic-brittle plastic rock mass, modified analytical solutions are derived that are compatible with a generalized nonlinear unified strength criterion. Using the maximum shear stress modulus, these solutions consider the comprehensive influences of the intermediate principal stress, the dilation characteristic and brittle plastic. Then, a comparative verification of the new solutions using a nonlinear Hoek-Brown yield criterion is conducted. The effects of the parameters are discussed in detail. The calculation results show that k is a comprehensive evaluation index for multiple factors, is significantly influenced by the geo-stress and support pressure, and increases with the geological strength index, elastic strain and Young's modulus in the plastic zone. During cavity contraction, the intermediate principal stress improves the magnitude of k more significantly than dilation, whereas dilation has a greater effect during cavity expansion. Using the perfectly plastic model without considering brittle-plastic behaviour will lead to an overestimation of k, and using different strength criteria directly affects the timing of the plastic deformation of a rock mass. The influence of various factors should be comprehensively considered to select a reasonable radial subgrade modulus to take full advantage of the latent potentialities of a rock mass. The deep-buried diversion tunnel at the Jinping II hydropower station is studied as an example to dernonstrate the practical application of the proposed model.