Shakedown analysis of cavities in cohesive-frictional materials and its application to underground energy storage caverns

In this paper, a shakedown analysis is conducted for both cylindrical and spherical cavities in cohesive-frictional materials subjected to cyclic internal pressures. Based on Melan's lower-bound shakedown theorem, theoretical shakedown conditions for a two-layered cavity system are developed using the stress and strain solutions obtained from cavity expansion and contraction analyses. The shakedown limits are investigated in relation to the dimensions of the two-layered cavity system and the elastic/plastic material parameters. Numerical validation is conducted through a comparison of the stress path of the critical element and the failure lines of the materials. In addition, closed-form solutions for special cases, namely, the analytical shakedown conditions of cavities in an unbound cohesive-frictional material and in a bound material with different boundary conditions, are explicitly expressed. Finally, the shakedown solutions are applied to solve the thickness design problem of underground compressed air energy storage in lined and unlined caverns.