Stochastic Continuous Modeling for Pillar Stress Estimation and Comparison with 2D Numerical, and Analytical Solutions in an Underground Stone Mine

Pillar collapses are events that due to their severe consequences can be classified as high risk. The design of pillars in underground room-and-pillar operations should migrate to risk-based design approaches. The authors of this work proposed a risk-based pillar design methodology that integrates stochastic discrete element modeling for pillar strength estimation, and stochastic finite volume modeling (FVM) for stress estimation. This paper focuses on the stochastic FVM component for stress estimation. The mining and geomechanical aspects of a case study mine (CSM) are described and pillar stresses are estimated by using three approaches: (1) analytical solutions, (2) 2D finite element modeling, and (3) 3D finite volume modeling. This operation extracts a 30 degrees dipping deposit, which makes current underground stone mine design guidelines inapplicable for this CSM. This work compares results from each stress estimation approach and discusses uses the point estimate method as a simplified stochastic approach to evaluate the effect of rock mass elastic properties variability on pillar stress distribution. Results from this work show that the three estimation approaches lead to different estimations, possibly, due to the wide range of assumptions each estimation approach considers. It was also determined that the horizontal to vertical stress ratio has a significant impact on pillar stress magnitude. Therefore, it is recommended to perform in situ stress measurements, or assume worst-case-scenario values to account and reduce uncertainty due to this parameter. The stochastic stress estimation approach used in this paper provides results that can integrate a risk-based pillar design framework.