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• 5.2 LAMODEL Analysis <br />To check the web and barrier pillar design for each area, study seam interaction <br />effects. and check the design for cascading pillar failure potential, the LAMODEL <br />numerical modeling code was applied. V <br />LAMODEL (short for laminated model) is anon-linear boundary-element <br />displacement discontinuity code for estimating stress. displacement, and yielding in <br />tabular deposits such as coal (Neas)ey, 1996). LAMODEL ra'as developed by the former <br />U.S. Bureau of Mines (USBM}, now part of the National Institute of Safety and Health <br />(NIOSH). It has the ability to handle in-seam materials based on both linear and <br />nonlinear mechanical (stress-strain) behaviors. The geometry of the model is variable; <br />thus, incremental mode] changes can be used to determine optimal mining sequences, as <br />well as the impact of varying pillar sizes. variations in cover load. and seam interaction <br />effects. The program performs an iterative procedure to solve a set of equations <br />representing the stress-strain state of each element in a grid representing the mine <br />geometry, until asteady-state equilibrium is reached (loads no longer transfer). <br />Following an MSHA-recommended confined core approach to pillar strength <br />(Karabin, 1994), element properties can be arranged so that the weakest elements are <br />adjacent to the mine opening, with element strengths increasing into the pillar core. <br />Using strain-softening elements with increasing peak and residual strengths toward the <br />• core, elastic-plastic behaviors observed in pillar cores are approximated, and <br />correspondence with classical empirical pillar design methods is achieved. The effects of <br />width-to-height ratio are also accurately accounted for. <br />The plots of LAMODEL results presented in this report are plan-view <br />representations of yielding and safety factors in the coal structures. In the yield condition <br />plots. the color of each element show's either (l) how close the element is to yielding, (2) <br />that the element is in the process of yielding. or (3} that the element has completely <br />yielded. By comparing different areas within the model, and one model to another, the <br />plots give a very clear indication of relative stability. <br />Although the size of a LAA90DEL grid is only limited by computer memory, for <br />practical purposes, grid size should be limited so that models converge in a reasonable <br />amount of time. Therefore, there is a tradeoff between element size and the azea that can <br />be modeled (smaller element sizes give more detail. but cover a smaller area). In this <br />study. 28-in elements were used to give sufficient detail of web pillar stability. The <br />modeled areas were 630 ft into the highs+'all and 980 ft wide. Cover depth was varied <br />from the minimum of the design range at the highwall. to the maximum of the design <br />range ar the end of the miner openings. <br />Since LAMODEL models are made up of elements. the features that a model can <br />represent are limited to dimensions that are even multiples of the element size. The <br />• element size rugs selected to minimize the difference bety,-een the design and modeled <br />web pillar widths and tributary area loading factors. Once the element Size ryas <br />Seneca Coal Compane 1 6 NSA Engineering. Inc. <br />Highwatl ASine Dsien Repon June ?005 <br />