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• <br />Exhibit J shows the profile of the stream bed around the <br />part of the permit area where the largest impacts would <br />occur. <br />The profile of the subsidence trough has been calculated <br />using the hyperbolic function presented in Peng and showr: below: <br />5 = 1/2 S max (1 - tanh (2x/B)) <br />when S = the subsidence in feet at any point x <br />Smax = the maximum subsidence possible <br />8 = 1/2 of the critical width of excavation <br />~J <br />The origin point of xis the point where one-half <br />maximum subsidence occurs, which is taken as the point <br />underground where complete extraction ends. <br />Subsidence is calculated assuming both the upper and lower seams <br />are completely extracted, so that the total seam height removed <br />is 10 feet. Cover in the permit boundary area of the stream bed <br />is approximately 140 feet and the width of excavation is so large <br />that the critical width will be achieved and maximum subsidence <br />will occur. Maximum subsidence = .90 x total seam height. <br />Smax = .90 x 10 feet = 9.0 feet <br />• <br />At a cover depth of 140 feet, the critical width of excavation <br />is 115 feet. This corresponds to the minimum width of excava- <br />tion that cause maximum subsidence. <br />56~ <br />D. H. EMLING COMPANY <br />