Prerequisites for studying a two-phase model of steel reinforcement loading in deep excavations

Oleksandr Skobenko*, Lyubomyr Kurop

skobenko.o.v@nmu.one

Received 07.11.2025, Revised 17.03.2026, Accepted 28.04.2026, Published 29.05.2026
Abstract

Deep underground excavations at great depths are characterised by increased rock pressure, floor heave, and instability phenomena that significantly alter the loading conditions of steel arch supports. Conventional quasi-static calculation models do not fully account for the transition to impulsive loading associated with the loss of elastic-plastic stability of the surrounding rock mass. The objective of this study was to develop and substantiate a two-phase loading model for steel arch supports in deep underground excavations, accounting for nonlinear interaction with the rock mass. The methodology combined analytical modelling based on the theory of a curved beam on an elastic foundation, finite element simulations, and comparison with in situ monitoring data. This integrated approach enabled analysis of the stress-strain evolution of the “support-rock mass” system and identification of a phase transition criterion. The results demonstrate significant differences in the stress-strain state of the steel support between quasi-static and impulsive phases. A phase transition criterion based on a critical excavation contour displacement is proposed and substantiated. In the first phase, maximum bending moments are concentrated at the arch crown and depend on displacement amplitude and flexural stiffness. In the second phase, loading becomes impulsive, and peak bending moments shift towards the support zones depending on the roof collapse configuration. The redistribution of internal forces under nonlinear contact interaction, as well as the influence of anchor stiffness, are analysed. It is shown that impulsive loading may lead the support to its ultimate limit state even when quasi-static conditions appear acceptable. The findings can be applied in the design and assessment of steel supports in deep mine workings and in the development of monitoring systems for early prediction of stability loss

Keywords:
stress-strain state; heaving; geomechanical interaction; bifurcation model; bending moments

Retrieved from Volume 24, No. 1, 2026

Pages 63–72

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Skobenko, O., & Kurop, L. (2026). Prerequisites for studying a two-phase model of steel reinforcement loading in deep excavations. Journal of Kryvyi Rih National University, 24(1), 63-72. https://doi.org/10.31721/2306-5451-2026-1-24-63-72
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