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r1 <br />the variability in the overburden realistically. The analyzed areas including both the fine and <br />coarse mesh are shown in Figure lb, rotated for ease of mesh generation. Pore pressure effects <br />are excluded in these boundary element analyses but were :included in the finite difference <br />analyses of main pillars during the 2004 detailed analyses. <br />The boundary- element stress analyses results are described in Section 2 followed by conclusions <br />and recommendations in Section 3. <br />2.0 BOUNDARY ELEMENT STRESS ANALYSES <br />0 <br />Pillar stability was evaluated using an estimate of pillar strength and stress. Pillar strength was <br />estimated using a method developed by NIOSH (Mark - Bieniaswki formula, Mark and Chase <br />1997). 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 stream <br />valley by dividing pillar strength to stress. Because of the close proximity of the storage panel to <br />the longwall district, longwall retreat was simulated as well. <br />2.1 Modeling methods and scope <br />The pseudo- three - dimensional boundary- element code MUL',SIMTI was used for calculating <br />stress distributions over the area of interest. This program incorporates elastic, strain- softening <br />material and is suitable for multiple -seam excavations in dipping seams and variable <br />topographies ( Maleki and others 2003). Model input is shown in Table 1 for these elastic <br />analyses. <br />Table 1-Model input for boundary- element analyses <br />Property Value Ass material behavior <br />Roof and floor, Young's modulus, <br />10 psi 0.69 Elastic <br />Roof and floor, Poisson's ratio <br />Coal, Young's modulus, 10 psi <br />0.25 Elastic <br />0.13 Elastic <br />0 Premining vertical stress, psi 1.1 -psi stress Gradient <br />Maleki Technologies, Inc. Page 3 <br />