Evaluation of the Effects of Length on Strength of Slender Pillars in Limestone Mines Using Numerical Modeling

In this National Institute for Occupational Safety and Health (NIOSH) investigation, numerical modeling is used to evaluate the degree the pillar strength is increased with a rectangular pillar over a square pillar. Three-dimensional models are developed with pillar sizes and geometries typical of underground limestone mines in the United States. Physical properties for the models are based on geotechnical surveys of nearly 30 underground limestone mines. To examine the effects of pillar length on pillar strength with the modeling, a parametric study was conducted where the pillar width was held constant while the length and height were varied resulting in width-to-height ratios ranging from 0.5 to 1.5 and width to length ratios ranging from 1 to 6. There are two aspects to pillar strength and failure. At relatively low stresses, pillars can fail as a result of geologic structure. At greater depths and sufficient extraction ratios, the pillars can also fail as a result of the vertical stresses exceeding the pillar strength. The effects of increasing pillar length regarding both strength aspects are presented in this study. Equations were developed for the increase in pillar strength with both height and length based on the model results. The results from these equations were compared to those from previously developed empirical equations for rectangular pillars. For the more slender limestone pillars with a width-to-height ratio below one, there is little increase in pillar strength for length-to-width ratios above 2 and almost no increase with length for a width-to-height ratio of 0.5. Only with the more squat pillars is there a significant improvement in strength with length. The gain in pillar strength with length for the pillars is explained by the change in the ratio of the area of the pillar affected by the ends to the area of the pillar. For the squattest pillar, the change in strength is also affected by an increase in pillar confinement along the central length of the pillar as the pillar transitions from a square to a long rectangular pillar. With geologic structure, added pillar length can significantly improve the pillar strength, depending on the strike of that structure with respect to the long pillar axis. INTRODUCTION This investigation was conducted as part of an effort to improve safety in underground limestone mines by evaluating and improving the performance of the pillars. Highly stressed pillars that are approaching failure have an increased potential for spalling and fall of material from the ribs; thus increasing the hazard of ground fall injuries to workers while pillar failure can impact operations. In this investigation, the effects on pillar strength of the pillar length are evaluated. There are two aspects to pillar strength and failure. At relatively low stresses, pillars can fail as a result of geologic structure (Esterhuizen et al., 2006; Iannacchione and Coyle, 2002). A detailed analysis of the strength reduction of square limestone pillars with geological weaknesses has previously been conducted (Iannacchione, 1999). The analysis did not include the effects of pillar length. However the following comment was made about rectangular pillars “The orientation of a discontinuity is important when the pillars are rectangular in that the strength will be affected most if the discontinuity is aligned with the long axis of the pillar.” At greater depths and sufficient extraction ratios, the pillars can also fail as a result of the vertical stresses exceeding the pillar strength. The effects of increasing pillar length regarding both strength aspects will be presented in this study. Rectangular pillars have been used in situations where horizontal stress is an issue. Through the use of rectangular pillars, the roof exposed to failure from the maximum horizontal stress can be minimized (Iannacchione et al, 2003). Longer pillars can also increase the efficiency of ventilation in the limestone mines (Grau et al., 2002 and 2006). With longer pillars, the number of ventilation stoppings can be reduced. However, this study is designed to determine to what degree the pillar strength can be increased by using rectangular pillars over the more standard square pillars. The approach in this study is to use numerical modeling to evaluate the effects of pillar length on the pillar strength. There have been a number of equations developed to predict the increase in strength from a square to a rectangular pillar. Many of these equations have not been substantiated, or have been used for coal pillars which are much squatter pillars than used in limestone. The pillar sizes and geometries used in the models are typical of underground limestone mines in the United States.