Laserfiche WebLink
January 2, 2020 Page 4-1 <br />Agapito Associates, Inc. <br />4 PILLAR DESIGN <br /> <br /> Empirical methods based on the Mark-Bieniawski pillar strength formula (Mark, Chase, <br />and Campoli 1995) were used to size web and barrier pillars for the various cover depths and <br />mining heights anticipated. The National Institute of Safety and Health (NIOSH) has developed a <br />similar procedure (NIOSH 2006), Analysis of Retreat Mining Pillar Stability-Highwall Mining <br />(ARMPS-HWM), which is readily accepted by the Mine Safety and Health Administration <br />(MSHA) as a design basis for HWM pillars. As discussed below, based on Western US HWM <br />experience, AAI recommends a more conservative approach to coal strength input than ARMPS- <br />HWM, and a minimum allowable pillar width-to-height ratio of 0.8. <br /> <br />4.1 Design Approach <br /> <br />Numerous pillar design equations have been developed over the years relating pillar <br />strength to coal strength, pillar height, and pillar width. The most widely accepted of these <br />formulas in the US today is the Mark-Bieniawski pillar design formula. A modified form of the <br />equation that represents infinitely long (effectively) web pillars is given by: <br /> <br /> Sp = Sc (0.64 + 0.54 H <br />W ) (Eqn. 4-1) <br /> <br />where Sp = pillar strength (psi) <br /> Sc = in-situ coal strength (psi) <br /> W = pillar width (ft) <br /> H = pillar height (ft) <br /> <br />One of the reasons for the wide acceptance of the Mark-Bieniawski formula is that in <br />addition to pillar width and height, the effect of pillar length is accounted for. In addition, pillar <br />strengths calculated with the formula have been compared with over 100 case histories of actual <br />pillar performance with high correlation. The Mark-Bieniawski formula is also the basis for pillar <br />strength estimation in ARMPS-HWM. <br /> <br />Although the formula appears straightforward, determining Sc (the in-situ coal strength) <br />can be difficult. Traditionally, this has been done by taking laboratory UCS test results and <br />applying a size reduction factor (usually one-sixth the square root of the sample diameter, <br />measured in inches). However, Mark and Barton (1997) concluded that laboratory test results are <br />a poor predictor of in-situ pillar performance, and that a constant in-situ coal strength of 900 psi <br />produces better results. As a result, the default in-situ coal strength in ARMPS-HWM is 900 psi. <br /> <br />An alternative approach is to apply site-specific coal strengths and normalize them to the <br />900-psi in-situ strength. Table 4-1 shows the target seam compressive strengths normalized to <br />900 psi. This was done by assuming that the average western coal UCS (2,070 psi in AAI’s <br />experience) can be represented by the 900-psi in-situ value. For example, the normalized strength <br />of the F Seam, 540 psi, is the laboratory UCS (1,241 psi) divided by the western coal UCS <br />(2,070 psi), multiplied by Mark-Barton’s (1997) recommended 900-psi in-situ strength. AAI <br />recommends, and applied, the normalized in-situ strengths shown in Table 4-1 to determine pillar <br />widths, since they account for the relative strength difference between seams.