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302 SURFACE SUBSIDENCE <br /> SURFACE <br /> O DATUM <br /> w O'2S S <br /> oc I <br /> W O•S <br /> � I I <br /> a 0,75 <br /> I <br /> I I <br /> I <br /> O SO 100 200 3O0 <br /> SCALE OF METRES <br /> Fir. 9.4.3 I'lollinS a subsidence profile (12). <br /> Profik and Influence Functions <br /> These two methods are based on principles of superposition and equiva- <br /> lence(13,20).The principle of superposition states that if two neighboring <br /> openings are excavated beneath a surface point, the total subsidence for <br /> the surface point is the sum of the subsidences due to the first and second <br /> openings. Figure 9.4.4 illustrates this principle. Subsidence S, is due to <br /> opening A,,and S„ is due to opening A,,. Total subsidence at P is then S = <br /> S, + S". <br /> According to the critical area concept,subsidence is related to the ratio <br /> of width to depth and the same width-to-depth ratio will produce the same <br /> amount of subsidence (Fig. 9.4.5a). The principle of equivalence extends <br /> this concept to state that any horizontal excavation area bounded by the <br /> same two straight lines radiating from a surface point produces the same <br /> amount of subsidence on that point; for example, excavation A, (Fig. <br /> 9.4.5b)produces the same amount of subsidence on P us excavation A.or <br /> A,. <br /> Profile Functions. Profile functions are based on two-dimensional exca- <br /> vations of critical width (Fig. 9.4.6). They are expressed as <br /> SW =JA x, S,o,,.. d) (9.4.1) <br />