Time-dependent plastic analytical solutions for spherical cavity considering loading-unloading paths and temperature effects

Abstract

Geomaterials generally exhibit time-dependency and plasticity, meanwhile, significantly influenced by the loading-unloading paths and temperature settings. Furthermore, the mechanical properties heavily depend on temperatures. In this study, an alternative viscoelastic-plastic analytical solution for stress and displacements is developed for spherical cavity closure, innovatively taking into account the time-dependent plastic behaviours of geomaterials, the loading-unloading paths, and the unsteady heat conduction and its effect on the mechanical behaviours.

In order to do that, the Burgers viscoelastic model and plastic slider characterised by the Mohr-Coulomb model are selected to characterise the time-dependency and plasticity of geomaterials, respectively. As a verification and validation step, the developed analytical solutions are compared with numerical predictions and experimental tests. After that, comprehensive parametric analyses are performed and some significant conclusions are achieved: (1) The critical supporting pressure for cavity stability increases linearly with both temperature and elastic modulus of rock. (2) Moderate heating is beneficial for stability, while excessive heating may cause secondary plastic yielding. The cavity reaches its most dangerous state during the early stages of storage. (3) The thermal conductivity and viscosity coefficient primarily affect the transient stress paths and stability of the cavity but do not impact the initial or final stress states. The developed time-dependent plastic analytical solution provides an alternative and efficient tool with a high potential for application to several relevant case studies, such as nuclear waste storage constructed in salt rocks.