Numerical modelling of critical conditions for the onset of a limit state in the rock mass surrounding unfilled underground voids in iron ore deposits
DOI:
https://doi.org/10.51301/ejsu.2026.i1.05Keywords:
numerical modelling; underground void; stratified heterogeneous rock mass; Hoek-Brown failure criterion; near-failure state; ground surface collapse; cemented paste backfillAbstract
The purpose of this study is to develop an approach for the quantitative assessment and prediction of rock mass condition surrounding unfilled underground voids, with a focus on a limit state associated with potential instability and ground surface collapse, using numerical modelling techniques. The investigation was carried out using finite element modelling of the stress-strain state of a stratified rock mass in the RS2 software package. To adequately reproduce the mechanical behaviour of fractured rocks of the Kryvyi Rih Iron Ore Basin, the stratified geological structure of the rock mass was incorporated into the model. The nonlinear Hoek-Brown failure criterion was applied, accounting for the Geological Strength Index (GSI). The existence of a transitional (near-failure) geomechanical state of the rock mass surrounding unfilled underground voids has been established. This state develops between stable and unstable conditions and is characterised by mechanical interaction between the void and the ground surface. A stable logarithmic relationship between the lower and upper bounds of the critical ratio H/Lc and the void depth has been identified, quantitatively reflecting the increase in rock mass resistance as the depth increases toward the limit state. An exponential relationship between the width of the ground surface subsidence trough and the parameter H/Lc has been identified, enabling the prediction of the extent of the potential collapse zone. An exponential relationship between the required strength of the cemented paste backfill and the H/Lc ratio has been established, defining the minimum bearing capacity of the backfill under near-failure conditions. For the first time, the existence of a distinct near-failure geomechanical regime of the rock mass surrounding unfilled underground voids has been quantitatively substantiated as an independent state preceding progressive ground surface collapse. The obtained relationships enable predicting the geomechanical condition of the rock mass above unfilled voids, determining the range of their critical geometric parameters, and timely identifying voids in a near-failure state. The developed approach can be applied in engineering practice to justify the parameters of cemented paste backfill from the surface to prevent sudden ground surface collapse.
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