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The existing orientation of the mains is also favorable with respect to major joints and <br />cleats (approximately N70° E). At 30° deviation from the cleats, the potential for joint- <br />induced roof and rib instabilities are reduced. <br />4.2 Pillar Stability <br />Pillars stability was evaluated using an estimate of pillar strength and stress. Pillar <br />strength was estimated using a method developed by NIOSH (Mark and Chase 1997). <br />Pillar stress was calculated using a numerical model. The modeling resulted in vertical <br />stress distributions on the Upper B seam, including variations in topography, and mining <br />geometry. Pillar factor of safety was calculated during the development work beneath the <br />stream valley by dividing pillar strength to stress. <br />The pseudo-three-dimensional boundary-element code MULSIMTI was used for <br />calculating stress distributions over the area of interest. This proprietary program <br />incorporates elastic, strain-softening material and is suitable for multiple-seam <br />excavations in dipping seams and variable topographies (Maleki 2002). Model input is <br />shown in table 5 for this elastic analysis. <br />Figure 1 presents the planned mining geometries and the location of detailed models. <br />Mining geometry includes a set of mains being driven under the drainage. The total <br />modeled area is three times larger than shown in figure 1. <br />Modeling results are presented as vertical stress and factor of safety levels (figures 15 and <br />16). In figure 15, square elements are 6- by 6- by 9-ft coal elements, the color of which <br />depends on the stresses acting on them. Figure 16 presents the factor of safety for each <br />element while individual pillar dimensions and mining height are considered (9-ft). Pillar <br />strength is calculated using Mark-Bieniaswki formula (Mark and Chase 1997), which <br />depends on pillar dimensions and the excavation height. <br />0 <br />Maleki Technologies, Inc. Page 28