An Analytical Plane-Strain Model for Frozen-Wall and Stratum Interaction During Shaft Excavation

Artificial ground freezing is widely used for shaft sinking in deep water-rich alluvium, but conventional frozen-wall design often treats the wall as an isolated thick cylinder loaded by the full horizontal ground pressure. This paper develops an analytical plane-strain model in which the frozen wall and surrounding stratum interact during radial unloading caused by excavation. The frozen wall is modeled as a finite cylinder and the stratum as an infinite cylinder. Both are described as linear elastic or ideal elastic-plastic Mohr–Coulomb materials, and radial stress and displacement continuity are imposed at their interface. General thick-cylinder solutions are assembled into six possible frozen-wall/stratum state combinations, with explicit or iterative solution of the interface pressure and deformation. Finite element verification shows close agreement with the analytical solution, and a further axisymmetric comparison supports the plane-strain assumption. The results show that the interface pressure is generally lower than the horizontal ground pressure, while frozen-wall deformation is bounded by the unsupported stratum and infinitely thick wall limits. The model provides a rational basis for frozen-wall design as an interacting ground-support system.