Incorporation of a Water Condition Factor into the Stability Graph Method Using Software Mineroc®
Authors: Vallejos J. A. , Cepeda E. , Barberán A. , Espinoza J. 
Published: September 2023

ABSTRACT
Optimal stope dimensions for underground mining using the Sublevel Stoping method are selected to guarantee excavation stability. The stability graph method developed by Mathews et al. (1980) is used as an empirical tool for this purpose. The stability graph relates the stope walls’ hydraulic radius with the stability number N defined by N=AxBxCxQ′, where A, B and C are adjustment factors for stress to strength ratio, joint orientation and gravity effect over stope walls, respectively, and Q′ is the modified rock tunneling quality index (Barton, et al. 1974). In the stability method, the water condition is not considered since the registered cases presented dry conditions. The objective is to include the water condition in the stability graph method. This is accomplished by using the joint water reduction factor (Jw) and the inflow of water observed in the drifts. Therefore, the stability number with water conditions is defined by N=AxBxCxQ′xJw. A database of 25 case histories is collected and analyzed for a mine with the presence of underground water with software MineRoc®. Stability boundaries are proposed based on the Equivalent Linear Overbreak/Slough (ELOS). The impact of the water reduction factor is analyzed, and an overall improvement in the definition of the stability boundaries is observed.

INTRODUCTION
The potential for instability in the rock mass surrounding underground mine cavities is an ever-present hazard for the safety of people, equipment, and operations in sublevel open stoping (SLOS) mining. Several tools for the design of open stopes have been developed over the years with the purpose of reducing these threats, though none of them considers the presence of water, since the case histories used to propose the stability graph method presented dry conditions.
Mathews et al. (1981), based on a study of 26 case histories in SLOS, proposed the stability graph method in which a qualitative stability state for each open stope surface is given based on visual evaluations and/or reconciled data. The graph introduced by Mathews et al. (1981) became popular following the expansion of the original database and/or the re-calibration of the stability number factors. According to Madenova & Suorineni (2020), to date, five major stability graph variations exist: the Modified Mathews stability graph by Potvin (1988), the extended Mathews stability graph by Mawdesley & Trueman (2003), the equivalent linear overbreak slough (ELOS) stability graph proposed by Clark & Pakalnis (1997), the stability graph for cable bolt support design proposed by Diederichs et al. (1999), and the dilution-based stability graph introduced by Papaioanou & Suorineni (2015). Authors such as Nickson (1992), Suorineni (1998), Bewick & Kaiser (2009), Vallejos et al. (2016a, 2018a), Vallejos & Díaz (2020a), and Vallejos et al. (2022), among others, have also contributed adding new case histories to the original method, adapting some stability factors and proposing new qualitative stability boundaries. Note that in most cases the stability graph has been adapted for other SLOS operations (new site-specific conditions), narrow vein operations and even for caving operations.