Issue 53

A. Kostina et alii, Frattura ed Integrità Strutturale, 53 (2020) 394-405; DOI: 10.3221/IGF-ESIS.53.30 394 Applicability of Vyalov’s equations to ice wall strength estimation A. Kostina, M. Zhelnin, O. Plekhov, I. Panteleev Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science, Russia kostina@icmm.ru , http://orcid.org/0000-0002-5721-3301 zhelnin.m@icmm.ru, http://orcid.org/0000-0003-4498-450X poa@icmm.ru, http://orcid.org/0000-0002-0378-8249 pia@icmm.ru , http://orcid.org/0000-0002-7430-3667 L. Levin, M. Semin Mining institute of the Ural Branch of Russian Academy of Science, Russia aerolog_lev@mail.ru , http://orcid.org/0000-0003-0767-9207 seminma@outlook.com , http://orcid.org/0000-0001-5200-7931 A BSTRACT . A simple analytical relations are commonly used in engineering practice to calculate ice wall thickness. One of them is Vyalov’s relation that takes into account the features of a real technological process of tubing lining and the inelastic deformation associated with frozen soil creep. An estimation of applicability and margin of safety of this equation is an issue of engineering mechanics. In this paper, we propose a mathematical model for description of ice wall deformation under natural external loading and present the results of the computational experiments in which an optimal thickness for the ice wall is determined. Based on this simulation, we modify the existing analytical relation, which makes it possible to calculate the thickness of an ice wall of unlimited height. K EYWORDS : Ice wall; Frozen soil; Mine shaft; Vyalov’s equation. Citation: Kostina, A., Zhelnin, M., Plekhov, O., Panteleev, I., Levin, L., Semin, M., Applicability of Vyalov’s equations to ice wall strength estimation, Frattura ed Integrità Strutturale, 53 (2020) 394-405. Received: 20.05.2020 Accepted: 01.06.2020 Published: 01.07.2020 Copyright: © 2020 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. I NTRODUCTION he ice wall is an important engineering structure the integrity of which determines the safety of sinking operations in vertical mine shafts under construction. The effectiveness of the ice wall as a temporary protective lining depends on the adequate evaluation of its thickness. Optimal assessment of the wall thickness comes from the need to reduce the cost of mining operations at the design stage. This will help to exclude the failure of an ice wall and the breakthrough of groundwater into the mine. Furthermore, the savings in artificial freezing costs may be significant. Engineering calculations for ice walls are currently performed for two limit states - strain condition and strength condition. In strain calculations, it is necessary to determine the minimum thickness of the ice wall at which its deformation in the design phase does not exceed the value acceptable for shaft construction and promotes no dangerous movements of freezing columns. The objective of the limit strength design is to calculate the optimal minimum thickness of the ice wall which T