Abstract

This paper presents a new equation to design rock pillars in underground excavations. The study is based on rigorous statistical analysis of empirical databases and equations used in the engineering design process. The new formula has three fitting functions that consider the rock mass quality, the shape of the rock pillar, and the scale effects. The new equation has two distinctive advantages: (1) It takes into account the Rock Mass Rating of Bieniawski-1989 (RMRB89), and (2) It unifies the strength of the intact rock, scaling the strength of laboratory tests to the scale of rock pillars. The results suggest that the proposed new formula (and corresponding fitting formulae) provide better estimations than empirical approaches, at both the laboratory and rock pillar scale levels. Specific recommendations to use the equations are based on the rock mass quality, geometrical properties, and spatial location of the rock pillars. The premise of this study was to overcome the three main disadvantages of empirical formulae used in the engineering design of rock pillars: (1) disregarding of the rock mass quality of rock pillars in the formulation. (2) Dependency on local site geomechanical conditions (site conditions dependent equations). (3) The non-uniformity between the intact rock strength measured in the laboratory and the pillar strength. The results of this work provide a step forward in the design of rock pillars, structures engineered with the natural in-situ rock mass, to sustain underground openings, and guarantee safe underground excavations. © The Author(s) 2025.