energies Article Rock Pillar Design Using a Masonry Equivalent Numerical Model Ricardo Moffat 1, * , Cristian Caceres 1 and Eugenia Tapia 2   Citation: Moffat, R.; Caceres, C.; Tapia, E. Rock Pillar Design Using a Masonry Equivalent Numerical Model. Energies 2021, 14, 890. https://doi.org/10.3390/en14040890 Academic Editor: José A.F.O. Correia Received: 11 January 2021 Accepted: 2 February 2021 Published: 9 February 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Mining and Civil Engineering, Universidad Adolfo Ibáñez, Santiago 7941169, Chile; cristian.caceres@uai.cl 2 Civil Engineering, Universidad de Chile, Santiago 8370448, Chile; euge.beta@gmail.com * Correspondence: ricardo.moffat@uai.cl; Tel.: +56-2-87580155 Abstract: In underground mining, the design of rock pillars is of crucial importance as these are structures that allow safe mining by maintaining the stability of the surrounding excavations. Pillar design is often a complex task, as it involves estimating the loads at depths and the strength of the rock mass fabric, which depend on the intact strength of the rock and the shape of the pillar in terms of the aspect ratio (width/height). The design also depends on the number, persistence, orientation, and strength of the discontinuities with respect to the orientation and magnitude of the stresses present. Solutions to this engineering problem are based on one or more of the following approaches: empirical design methods, practical experience, and/or numerical modeling. Based on the similarities between masonry structures and rock mass characteristics, an equivalent approach is proposed as the one commonly used in masonry but applied to rock pillar design. Numerical models using different geometric configurations and state of stresses are carried out using a finite difference numerical approach with an adapted masonry model applied to rocks. The results show the capability of the numerical approach to replicate common types of pillar failure modes and stability thresholds as those observed in practice. Keywords: rock pillar; design numerical model; mining; underground stability 1. Introduction Rock pillars are generally left in underground mines to safely and economically extract as much of the orebody as possible, by stabilizing the mine openings and withstanding the in situ and induced stresses of the rock mass. In [1], rock pillars are defined as “the in situ rock between two or more underground openings.” Pillars are composed of an intact rock substance and naturally occurring discontinuities such as joints, fractures, and bedding planes. From field experience, it is well known that the wider the pillar, the more stable they are. However, a wider pillar becomes inefficient in terms of economic revenue as more ore will be left unmined. The design of pillars has been done using different methods such as experience and empirical design, analytical design and numerical analysis using different constitutive rock models. Each method of design has advantages and disadvantages, as they require different input information of the rock mass strength, geometry of the pillar and surroundings, and in situ and induced stresses. The many input parameters, some unknown at the time of design, makes this process very difficult to undertake. It is essential to apply more than one method that results in an equivalent conclusion, to be able to take correct decisions of the dimensions and geometry of pillars and mined areas. Underground rock design considers structural-controlled instability mechanisms and stress-controlled instability mechanisms. Structural-controlled mechanisms take into account the presence of discrete blocks formed by discontinuity planes that intersect the excavation contour. This type of failure may occur under low or high stress conditions and is usually stabilized by use of ground support with a combination of shotcrete, anchors, and wire meshes. On the other hand, stress-controlled instability mechanisms must take into account the in situ and induced stresses before and after mining activities. Stress on pillars have Energies 2021, 14, 890. https://doi.org/10.3390/en14040890 https://www.mdpi.com/journal/energies