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4.2 Program Modifications <br /> 4.2.1 Calibration to Western Mines <br /> Much of the early work on subsidence prediction was done in the United <br /> Kingdm on long wall panels with the classic work being that of the National Coal <br /> Board of iondon resulting in the publication of the Subsidence Engineer's <br /> Handbook in 1965. This publication, although far more practical and useful than <br /> anything available previously, was still recognized to have relatively severe <br /> limitations particularly with respect to applications outside the United Kingdom <br /> and in areas of highly irregular topography and variable overburden thickness. <br /> Recognizing these limitations, J. E. Marr, a subsequent subsidence engineer <br /> with the National Coal Board, developed some modifications to earlier Stochastic <br /> methods proposed by Bats and others for subsidence prediction. The earlier work <br /> placed the inflection point (the point of half-maxim + subsidence) directly above <br /> the rib side when in actuality in most subsidence profiles this point occurs a <br /> significant distance frcrn the rib side toward the center of the mine panel. <br /> Previously, the weighting factors for the various zones were assigned on the <br /> basis of a linear function. Marr recognized that this relationship was not <br /> linear but was an exponential function. Good correlation was then obtained by <br /> calculating a value for the required exponent which we will refer to as the <br /> influence constant and then solving a set of seven simultaneous equations in <br /> order to obtain the "zone factors" for each of the seven concentric rings. For <br /> longwall panels in the United Kingdom, Marr o®nputed an influence constant of <br /> 2.296 and a set of zone factors a-g as follows beginning with the innermost <br /> circle: <br />