Research on the Elastoplastic Theory and Evolution Law of Plastic Zone Contours of Horizontal Frozen Walls under Nonuniform Loads

Abstract

The study of the changes in stress and deformation of frozen walls during excavation has always been a hot topic in underground freezing engineering, and the size of the plastic zone is an important basis for evaluating the stability of frozen walls. In response to the shortcomings in the current design of horizontal frozen walls, based on the internal excavation unloading conditions of the frozen wall in artificial ground freezing, an elastoplastic mechanical model for the interaction between a circular horizontal freezing wall and unfrozen soil mass is established under nonuniform loads to obtain the corresponding solutions for stress and displacement in the system. In this study, considering the shear stress of the plastic zone, the method for solving the traditional plastic zone contour equation is modified; consequently, the modified solution of the contour equation of the plastic zone for the frozen wall is obtained. Using this theoretical solution, the influence of the external load p0 and the lateral pressure coefficient λ on the contour line of plastic zone and tensile stress zone are analyzed by combining the project case, the calculation results show that: the λ=0.485 is the critical point where the inner edge of the frozen wall just happens to have tensile stress. When λ<0.485, the tensile stress zone is inevitable in the inner edge of the frozen wall vertical direction, and its range is only related to λ and increases with the decrease of λ. The p0 only affects the magnitude of tensile stress in the region, but does not affect its range. At this time, the frozen wall compression plastic zone contour evolves from crescent shaped to ear shaped with the increase of p0. When 0.485<λ<0.61, there will be no tensile stress zone, the frozen wall compression plastic zone contour also evolves from crescent shaped to ear shaped with the increase of p0. When λ>0.61, there will be also no tensile stress zone, with the increase of p0, the compression plastic zone contour evolves from the crescent shaped in the horizontal direction to the elliptical shaped, and there is no ear-shaped plastic zone in the whole evolution process. Based on our results, we show that our method can be used to provide a theoretical basis for the stability evaluation and parameter (thickness) design calculation of horizontal frozen walls under nonuniform loads.

Calculation Method of the Design Thickness of a Frozen Wall with Its Inner Edge Radially Incompletely Unloaded

“…The Mohr-Coulomb yield criterion describes the relationship between the first and third principal stresses, and the axial stress is generally regarded as the intermediate principal stress [29][30][31]. The relationship between the radial and circumferential stresses in the frozen wall plastic zone is [32][33][34]…”