A Generalized Method for Calculating Pillar Cell Capacities for Boundary Element Modeling of Coal Mines

The problem of estimating pillar capacity in coal mines has motivated development of a variety of empirical equations. Most of these equations have arisen from experience and a very limited set of measurements that have, necessarily, been focused on particular regions or coal fields. Their applicability is often limited to a specific range of pillar sizes. This is of particular concern in the design of large gateroad pillars and small barrier pillars between panels. The result has been a variety of equations and equation coefficients that can calculate load estimates to size pillars. Inclusion of these equations in more sophisticated loading models, such as boundary element methods (e.g. LaModel and MULSIM) has been hampered by absence of a function that describes specific variation of coal strength within the pillar. A singular exception, to our knowledge, is a function corresponding to the Bieniawski pillar strength equation. Because of this, it is the only coal strength criteria inherently available in most boundary element models. This paper presents a general method for deriving local coal strength, as a function of distance from the pillar rib, for an arbitrary pillar strength equation. Integration of this function provides the strength of pillar regions, or cells, needed for boundary element models. The method is demonstrated for the Bieniawski, Maleki and Holland-Gaddy equations. The Maleki and Holland-Gaddy equations contrast strongly with Bieniawski as strengths are extrapolated to large pillars and barriers. This development provides a tool for incorporating any of the proposed empirical equations into a boundary element model, thereby allowing the analyst to choose the most appropriate equation for a particular region, coal seam and/or pillar size.