An elastic-plastic solution for the optimal thickness of a frozen soil wall considering an interaction with the surrounding rock

The technology of artificial ground freezing has been widely applied in geotechnical engineering to support underground spaces, whereas the effects of excavation-induced large deformation and frictional and dilatant behavior of geomaterials are neglected in the current design. In this paper, a rigorous elastic-plastic solution of cavity contraction is proposed using a non-associated Mohr-Coulomb failure criterion to provide the optimal thickness of the frozen soil wall for excavation using artificial ground freezing technology, considering an interaction between the frozen soil wall and the surrounding soil/rock. After validation of a case study on a deep mine shaft against a numerical simulation, a thorough parametric study investigates the variation in the optimal thickness with the soil properties and initial stress conditions, as well as the effects of interaction and the critical condition. Compared to the existing solution, the proposed optimal thickness of the frozen soil wall is shown to contribute to both the design and cost-effectiveness in practical engineering, including tunneling and mine shaft construction.