A new formula for calculating the required thickness of the frozen wall based on the strength criterion

Abstract

The study delves into the elastoplastic deformation of a frozen wall (FW) with an unrestricted advance height, initially articulated by S.S.Vyalov. It scrutinizes the stress and displacement fields within the FW induced by external loads across various boundary scenarios, notably focusing on the inception and propagation of a plastic deformation zone throughout the FW's thickness. This delineation of the plastic deformation zone aligns with the FW's state of equilibrium, for which S.S.Vyalov derived a formula for FW thickness based on the strength criterion. These findings serve as a pivotal launchpad for the shift from a one-dimensional (1D) to a two-dimensional (2D) exploration of FW system deformation with finite advance height. The numerical simulation of FW deformation employs FreeFEM++ software, adopting a 2D axisymmetric approach and exploring two design schemes with distinct boundary conditions at the FW cylinder's upper base. The initial scheme fixes both vertical and radial displacements at the upper base, while the latter applies a vertical load equivalent to the weight of overlying soil layers. Building upon the research outcomes, a refined version of S.S.Vyalov's formula emerges, integrating the Mohr – Coulomb strength criterion and introducing a novel parameter – the advance height. The study elucidates conditions across various soil layers wherein the ultimate advance height minimally impacts the calculated FW thickness. This enables the pragmatic utilization of S.S.Vyalov's classical formula for FW thickness computation, predicated on the strength criterion and assuming an unrestricted advance height.

Keywords

• frozen wall
• artificial ground freezing
• stress-strain state
• ultimate equilibrium
• mohr – coulomb criterion
• mechanical analysis
• modeling
• freefem