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Tonia Perkins <br />July 31, 2024 <br />Page 10 <br />Agapito Associates, Inc. <br />NUMERICAL MODELING ANALYSIS <br />The empirical methods used for web pillar and barrier pillar design have been validated by <br />experience in a wide variety of mining scenarios and geological conditions. However, they do not <br />account for the variability of material properties or the interaction of multiple coal seams. Since <br />these factors are important to the stability of the proposed highwall mining at Trapper, numerical <br />modeling was used to evaluate the following items: <br />•Overall stability of empirical pillar designs <br />•The effects of multi-seam interaction <br />•The potential for cascading pillar failure <br />•Stability of the N pit slopes <br />Overall pillar stability, multi-seam interaction, and the potential for cascading failure were <br />evaluated using the LaModel boundary element software.2 LaModel employs non-linear methods <br />for the calculation of stress distribution and pillar stability in laminated strata. It allows for the <br />analysis of stress conditions imposed by mining on multiple horizons. Key inputs to the LaModel <br />analysis included excavation geometry, pillar dimensions, seam height, in situ coal strength, and <br />depth of cover. <br />Stability of the N-Pit slopes was evaluated using the FLAC3D finite difference program.3 <br />FLAC3D allows stress and displacement to be resolved with incremental changes in excavation <br />geometry and loading conditions using linear and non-linear methods. The three-dimensional (3D) <br />modeling approach also allows additional checks on the overall stability of web pillars, analysis <br />of interaction between the M and Q seams, and evaluation of cascading failure conditions on <br />highwall stability. <br />For numerical modeling purposes, conservative adjustments were made to seam heights, depths of <br />cover, pillar and entry widths, and interburden thickness to satisfy meshing constraints. Table 1 <br />shows the geometric parameters that were developed using empirical methods and adapted for <br />each numerical modeling approach for the south M and Q Seams. <br />Although the size of the LaModel and FLAC3D grids are only limited by computer memory, for <br />practical purposes, grid size was limited so that models converged in a reasonable amount of time. <br />There is a tradeoff between element size and the area that can be modeled, wherein a model with <br />smaller elements will give more detail but require more memory and run time. For this study, a <br />minimum element size of 1.5 ft was chosen for both LaModel and FLAC3D to provide sufficient <br />detail in the web pillar analysis. <br />2 Heasley, Keith A. "Numerical Modeling of Coal Mines with a Laminated Displacement-Discontinuity Code." 1990- <br />1999-Mines Theses & Dissertations (1998). <br />3 Itasca Consulting Group, Fast Lagrangian Analysis of Continua in 3D (FLAC3D), Finite difference software version <br />9.00.159 (2024)