Date of Graduation


Document Type


Degree Type



Statler College of Engineering and Mineral Resources


Mining Engineering

Committee Chair

Ihsan Berk Tulu

Committee Member

Yi Luo

Committee Member

Keith A. Heasley

Committee Member

Gabriel S. Esterhuizen

Committee Member

Brijes Mishra


In this research, the equation for the increasing stress into the interior of a stone mine pillar, as a function of the pillar width-to-height ratio, is derived from the empirical pillar strength equation proposed by Esterhuizen et al. (2011). The gradient stress equations for the stone mine pillars were derived by following similar approaches to those presented by Mark et al. (1992) and Johnson et al. (2014). In these approaches, it is assumed that the variation of stresses within the pillar is a function of distance to the closest rib. The stress gradient function provides the stress distribution within the pillar and is used to derive concentric rings of zones to simulate stone mine pillar yielding in boundary element software. This stress gradient function assumes that there are no large discontinuities present and that discontinuities do not have an impact on the strength calculation. The pillar geometry and rock mass parameters for testing the stress functions are selected from the S-Pillar database. The functions are tested for pillars with different width-to-height ratios and different element sizes. Finally, a beta version of the “stone pillar wizard,” which will be implemented into LaModel's preprocessor, Lampre, is developed using the derived equations to obtain the Stone Pillar material properties. Using the new stone pillar wizard in Lamodel, the pillar stress distribution, pillar safety factors, overburden stress, and all the other output stress items available in the LaModel software can be determined for an underground limestone mine.

Embargo Reason

Publication Pending