Analyzing Pillar Strength and Behavior using Wolfram Mathematica code

underground mining pillars necessitate a comprehensive
understanding of behavioral models and mechanical properties. This
study employs the Wolfram Mathematica code to investigate mining
pillar reliability, specifically focusing on elucidating the influence of
scale and shape on pillar strength. Drawing inspiration from
methodologies in the existing literature, our approach is based on the
Mohr-Coulomb theory and Griffiths's random field of rock strength.
This study highlights the significance of shape, where pillar strength
exhibits exponential growth with increasing width-to-height ratios.
Beyond a critical value, strength surges, especially under elevated
confining stress. Additionally, a critical mesh size significantly
affects the weakest pillar behavior. Our results confirm the 'size
effect,' wherein strength generally decreases with increasing pillar
volume. Thus, strength decreases with rising volume until a
threshold. Particularly noteworthy is the phenomenon observed in the
presence of cracks; initially, an increase in mesh size leads to a
decline in strength, corresponding to an increase in the number of
cracks. However, this decline stabilizes beyond a critical mesh size,
after which strength experiences a resurgence echoing behavior seen
in the homogeneous case.
In this paper, the reproduction of the scale effect by an algorithm
based on the Mathematica code was made to allow a probabilistic
study to be carried out because of the random existence of
discontinuities in nature – another hand to carry out stochastic
modeling of fractures and its influence on the rock mass strength.