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March 21, 2014 Page 37 <br />4.0 EMPIRICAL PILLAR DESIGN <br />4.1 Design Approach <br />In earlier highwall mining studies on the property (NSA 2003, NSA 2004a, NSA 2004b, <br />AAI 2004, AAI 2005a, AAI 2005c), the Mark - Bieniawski pillar design formula (Mark, et al. <br />1995) was applied to develop initial web and barrier pillar designs. In the case of highwall <br />mining, where the pillar length (miner penetration) is much greater than the pillar height or <br />width, the Mark - Bieniawski formula reduces to: <br />Sr = S, [(0.64 + (0.54 h A (Eqn. 2) <br />where Sp = pillar strength (psi) <br />S, = in -situ coal strength (psi) <br />h = pillar height (ft) <br />W = pillar width (ft) <br />However, after analyzing factors that may have contributed to subsidence over the West <br />Pit X Seam highwall mining area (AAI 2005e), AAI concluded that the Mark- Bieniawski <br />formula may overestimate pillar strength for some conditions at Colowyo, and recommended <br />that the modified van der Merwe formula (van der Merwe 2002) be used for future design on the <br />property. The modified van der Merwe formula is as follows: <br />Sp = SC h (Eqn. 3) <br />The van der Merwe formula and Mark - Bieniawski formulas produce equivalent pillar <br />strengths for a pillar width -to- height ratio of 1.4. Therefore, AAI recommends that the more <br />conservative of the two formulas be applied depending on the width -to- height ratio, and the <br />design curves discussed later in this report incorporate this recommendation. <br />In applying either the Mark - Bieniawski or van der Merwe formulas, determining Sc (the <br />in -situ coal strength) can be difficult. This traditionally has been done by taking laboratory <br />uniaxial compressive strength (UCS) test results and applying a size reduction factor (usually <br />one -sixth the square root of the sample diameter measured in inches). However, Mark and <br />Barton (1997) has found that laboratory test results are a poor predictor of in -situ pillar <br />performance and that a constant in -situ coal strength of 900 psi produces better results. AAI's <br />approach is to normalize coal strengths to 900 psi using the laboratory average of all seams <br />tested for highwall mining at Colowyo (2,070 psi). This allows for differences in strength test <br />results between seams to be reflected without straying too far from the 900 -psi value. Results <br />are presented in Table 7. <br />Considering the unplanned subsidence over the West Pit X Seam, and experience gained <br />in the western United States over the past several years, AAI believes it prudent to add an <br />additional measure of conservatism by capping the estimate of in -situ coal strength at 900 psi. <br />Agapito Associates, Inc. <br />