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January 2, 2020 Page 4-2 <br />Agapito Associates, Inc. <br />Table 4-1. Normalized Coal Strengths Used in Web and Barrier Pillar Design <br />Area Seam UCS <br />(psi) <br />Normalized <br />In Situ Strength <br />(psi) <br />I Pit F 1,241 540 <br />J Pit G2 1,307 568 <br />N Pit <br />L 1,549 673 <br />M 1,762 766 <br />Q 1,956 850 <br />L Pit <br />H 1,245 541 <br />K 1,848 803 <br />Q 2,050 891 <br /> <br /> <br />Once pillar strength is determined, an estimate of pillar loading is required to calculate a <br />stability factor (SF). Pillar loading is estimated using tributary area load theory as follows: <br /> <br /> ܮ௉ ൌܵ௏ <br />ሺௐାௐಶ ሻ <br />ௐ (Eqn. 4-2) <br /> <br />where LP = average vertical load on the pillar (psi) <br /> SV = in-situ vertical stress (psi) <br /> W = pillar width (ft) <br /> WE = entry width (ft) <br /> <br />The vertical stress is assumed to be equal to the average overburden density multiplied by <br />the cover depth (or equivalent rock depth). The overburden density was assumed to be 162 pcf), <br />the default value in ARMPS-HWM, resulting in a stress gradient of 1.125 psi/ft of depth. Finally, <br />the SF is calculated as: <br /> <br /> ܵܨ ൌ <br />ௌು <br />௅ು <br /> (Eqn. 4-3) <br /> <br /> Using the Mark-Bieniawski formula and ARMPS-HWM SF criteria given in Table 4-2, <br />minimum web pillar widths were calculated for the expected range of cutting heights and cover <br />depths and are summarized as a set of design tables and charts. At lower cover depths and higher <br />mining heights, the SF criterion is sometimes satisfied by web pillars with width-to-height ratios <br />less than 0.8. Because some HWM designs have failed at low width-to-height ratios, AAI feels <br />that pillar widths should be adjusted to maintain a minimum ratio of 0.8. Barrier pillar loading was <br />calculated using a 21 abutment angle (the pillar supports all overburden directly above it and <br />within a 21 angle over the adjacent web pillars, as measured from vertical). <br /> <br />In practice, web and barrier pillars are designed on a panel-by-panel basis. Pillar <br />dimensions are determined using the design tables and charts. The input parameters to the tables <br />are the maximum mining height anticipated for each panel, and the design cover depth. Designing <br />for the maximum cover is somewhat conservative as the solid coal beyond the maximum HWM <br />