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2" SURFACE SUBSIDENCE <br /> Final face position <br /> 0 _ <br /> 10 Residual <br /> subsidence <br /> 20 <br /> e <br /> 40 Subsidence profit <br /> when face stoppec <br /> 50 , <br /> E wFinal subsldonc <br /> a 70 Profile 21 days <br /> after face stop <br /> 0 <br /> 90 <br /> 100 <br /> 2.0 1.5 1.0 0.5 0 0.5 1.0 1.5 2.0 <br /> Face advace <br /> Depth <br /> FfS. 9.2.7 Residual subsidence profile(12). Courtesy U.K. National Coal Board. <br /> i <br /> surface point and reduces to 2 to 3% if the face has passed the critical <br /> width. The rate of face advance determines the time needed to pass <br /> through the critical width. As long as the face is still within the critical <br /> width, further subsidence is expected. <br /> However, Brauner (13). citing Russian data, stated that in addition to <br /> the rate of advance and size of critical area, the duration of surface <br /> subsidence depends on strata conditions, depth of extraction, kinds of <br /> packings, and previous extraction and that it ranges from several days to <br /> several years. The duration is longer for thick-bedded or stronger over- <br /> burden, for greater depths, and for complete caving. For a small extrac- <br /> tion area of a relatively mobile overburden mined in a very short time,the <br /> rate of subsidence is proportional to the difference between the final <br /> subsidence S and the instantaneous subsidence S,: <br /> dSL = c(S — S,) (9.2.1) <br /> dt <br /> the solution of which is <br /> (: SO = C = 1 — e-0 (9.2.2) <br /> where a is a time factor and c is a constant characteristic of the strata. A <br /> typical a curve for soft strata is illustrated in Fig. 9.2.8. <br /> In the United States, earlier studies (10, 11) showed that subsidence <br /> I <br /> I <br />