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3" SURFACE SUBSIDENCE <br /> Therefore,the subsidence influence of an element dA on surface point P is <br /> dependent on an influence function P(r) whose magnitude is a function of <br /> the horizontal distance r between point P and element dA. The function <br /> P(r)is such that it reaches maximum when r = 0 or element dA is directly <br /> below surface point P. Stated differently,if P is located at the center of an <br /> opening with critical width, it is influenced by all elements and undergoes <br /> maximum subsidence 5,,,,,,. If P is at the edge, it is subjected to only <br /> one-half the maximum influence and undergoes one-half the maximum <br /> subsidence. In mathematical form, r <br /> Smox = 2a J 0 r P(r)dr (9.4.6) <br /> u � <br /> where r is the radial distance from a surface point where maximum <br /> subsidence occurs, and B is the critical radius. <br /> Several influence functions have been developed for the central Euro- <br /> pean coal fields(20). In these functions,r is usually expressed in terms of <br /> critical radius B,and P(r)by S..,/B', where Q - h cut y,h is depth below <br /> surface, and y is the complement of the angle of draw,r, or y = 90° —C. <br /> One function widely used in practice is <br /> P(r) x (9.4.7 <br /> (sin y cos y + 2 — yhr y(rY + U' tan' yY <br />