Proposed formulas for pillar stress estimation in a regular room-and-pillar pattern

Room-and-pillar mining is one of the oldest and most widely employed underground mining methods worldwide, while in recent years it has also been used for civil engineering projects and applications. The pillar design process is quite straightforward, requiring the assessment of two key elements, namely the pillar's strength and the anticipated loading imposed on it. Lots of research work has been elaborated for the estimation of pillars' strength and the main parameters associated with it, while, on the other hand, in terms of the loading the Tributary Area Theory (TAT) has been traditionally and successfully used as the dominant methodology to assess the post-mining pillar induced stresses. This paper focuses primarily on decoding the pillar loading regime by analyzing the identifying the stresses imposed to them through the use of modern computational tools offered by 2D and 3D numerical analyses, over a series of pillars' type (square, ribs), configurations and initial virgin stress fields. This allows for the development of a benchmarking framework that showcase the differences in the stress conditions and reveal the over-conservative behavior of TAT. More importantly though, it allowed for the expression of two (2) general analytical formulae for the direct estimation of the average vertical elastic stresses on pillars, both for the case of rib & square pillars layout; the most typical patterns applied in this method. They aim at providing an easy to use and more accurate estimation of the pillar stress - as compared to TAT - in alignment with the results obtained from numerical analyses. Thus, with the proposed formulas, the time-consuming numerical process needed for preliminary pillars' dimensioning is tackled in a swift and effective manner.