Numerical analysis of application limits of Vyalov’s formula for an ice-soil thickness

Artificial ground freezing is an efficient technique which allows one to sink the mine shafts under complex hydrogeological conditions. The aim of artificial ground freezing is a creation of a temporary wall of frozen soil around the intended excavation. To estimate an optimal thickness of an ice-soil wall, the Vyalov’s formula is widely used by engineers. The article is devoted to analysis of Vyalov’s formula on the basis of the numerical simulation. The numerical simulation has been conducted by the finite element method. For the simulation of a stress-strain state of an ice-soil wall a new computational scheme has been proposed. The scheme is based on Vyalov’s design layout for a vertical shaft sinking and takes into account a soil layer beyond the excavation bottom. A mechanical behavior of frozen soil is described by Vyalov’s constitutive relations. As a result, it has been shown that values of the wall thickness given by Vyalov’s formula do not agree with the ones obtained by the numerical simulation. In order to conform results given by Vyalov’s formula and the numerical simulation, two modifications of the formula have been proposed