Plastic design theory of frozen soil wall based on interaction between frozen soil wall and surrounding rock

The design theory of frozen soil wall (FSW) is one of the core technologies for mine shaft freezing sinking. The conventional plastic design formula for the thickness of FSW is deduced under loading conditions. It does not take into account the interaction between FSW and surrounding rock and the effect of angle of internal friction, and it has a greater error compared with the actual situation. For a more rational design of FSW, considering the excavation unloading effect and the interaction between FSW and its surrounding rock, an elastic-plastic mechanical model is established, and analytical solutions for stress and displacement are derived. The influences of various factors on the thickness of FSW are discussed. A new formula for the thickness of plastic FSW is developed on the basis of the solutions. The analyses show that the new formula is more reasonable than the traditional one, and the use of the Coulomb-Mohr yielding criterion for calculating the thickness of FSW is suggested.