Assessment of Empirical Methods-Based Pillar Strength Estimation Through Numerical Modelling

ABSTRACT Over the past decades, many pillar strength relationships have been formulated from empirical observation of stable and failed case histories. These empirically derived equations are still widely adopted as a general technique for estimating pillar strength and simplified methods for evaluating the pillar stress (i.e., tributary area method). These generally accepted assessment methods might result in non-fully optimized solutions in terms of safe and, at the same time, economical designs. Numerical methods provide a better alternative to evaluate the mechanical behaviour of pillars in the context of progressive failure and, in turn, for a proper definition of the safety margins. In this paper, we propose using numerical modelling to determine the pillar strength through 3D analyses. An advanced constitutive model (Hoek-Brown with softening) is adopted to predict brittle mechanisms in rock masses. The results are compared with those obtained through empirical methods, providing insights about the implications of adopting empirical pillar design methods. INTRODUCTION In mining excavations, rock pillars are commonly adopted in most underground mining methods to support adjacent underground openings and thus guarantee the stability of the rooms for extracting the ore in a safe working environment. A system of pillars is designed to provide a suitable factor of safety that relates the pillar strength, defined as the maximum resistance to the axial compression, to the pillar stress. Over the past decades, stone mine pillars have been the subject of many studies that have led to the formulation of empirical strength equations (e.g., Hedley and Grant 1972; Von Kimmelmann et al. 1984; Krauland and Soder 1987; Potvin et al. 1989; Sjoberg 1992; Lunder and Pakalnis 1997; Walton and Sinha 2021), which generally refer to square pillars. However, several equations have been developed to predict the increase in strength from a square to a rectangular pillar (e.g., Mark and Chase 1997; Esterhuizen et al. 2011), which also include the effect of pillar length. Although all these empirically derived equations should only apply to design conditions consistent with the database supporting their development, they are still widely adopted as a general technique. Due to the complexity of the engineering problem, which is usually associated with rock fracturing and spalling failure process as the mine depth increases, it is difficult to consider which empirical method is the most appropriate. For such a reason, the significant limitations of the empirical methods have received the attention of several authors (e.g., Sinha and Walton 2019; Wang and Cai 2021; Wessels and Malan 2023) and should be carefully considered when pillar design is carried out.

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