Comparison of the Mark-Bieniawski and Wilson Pillar Equations Using Site Specific Data

This paper compares the two most common pillar design equations used worldwide by John T. Boyd Company; the Mark-Bieniawski Equation, an empirical approach, and the Wilson Equation, an analytical approach. The equations are compared in two ways; by their stress profiles and by the Mark-Bieniawski Equation stability factor. Contrasting the two equations based on the visual comparison of their stress profiles is straight forward but evaluating their resulting pillar designs is problematic. Complications arise due to the differences between the use and development of stability factors for empirical equations and safety factors for analytical equations. To work around these differences, comparisons are made between the two equations by first calculating pillar sizes using the Wilson Equation and then determining the Mark-Bieniawski Equation stability factor for these pillars. Pillars designed using the Wilson Equation were based on site-specific data from 23 mines located in the Americas and Australia. Comparing sizes of pillars designed by the Wilson Equation to the Mark-Bieniawski Equation; the Wilson Equation pillar sizes were smaller in 77% of the cases, similar in 3%, and larger in 20% of the cases.