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f3 CONTUVUUM MCCHANI(:S THSOa14;S 397 <br />such that S = I etx = 0 or maximum subsidence occurs above the center <br />of the excavation. Then <br />K, _~ I ~ ~S - I~~~t (9.3.3) <br /> <br /> <br />~ ` ~.: :, <br />, <br />where x r_x, are the points where S = } (i.e., half the maximum <br />subsidence). ]n determining K, and K„fiat find in the subsidence area the ~~ ' <br />points ss, where S = }, measure the slope BS/i3x, and calculate K, and K, <br />by Eqs. 9.3.3 and 9.3.6. The subsidence profile ran then be plotted using <br />Eq. 9.3.1. <br />The application of the theory is iltustreted in Fig. 9.3.2, whero the ' <br />broken lines are measured surface subsidence for a longwell panel 350 ft <br />~ <br />wide and 1973 ft deep with a coal seam S2 in. thick. The solid lines arc ~ <br />theoretical curves based on Eq. 9.3.1 using K, ~ 2 and K, = 10. !t must be j <br />natal that sevend trials of determining suitable values for K, end K, ere <br />almost ncccxwry before a close agreement between theory and field <br />tneasurcmenu is realized. <br /> <br />9.3.2 t'7ewk•Plastk Theory <br />i <br />Dahl and Choi rn found that mine subsidence is essentially time- 1 <br />independent end that measured surface attains frequently exceed the <br />•. V~r11CH •ub~ld~ne~: Praollnal (-•~-~. tMOrt,llo~lt^1 i <br />-1000 -500 -~• 0 ~" 500 Xtt~~t1 1000 ~~: <br />20 <br />-!{. l em t <br />i. <br />p ~ ~' <br />t <br />-1000 -500 • ~. ~ 500 Xtr~~t11000 <br />• 1 <br />av i axt enenrtnt ~ S <br />6. liorliOtltal atraln: prt,otlca•1 pdnta, tMortltleal eurv~ 1, <br />ph. a~.3 Surface tnoveteKnt meateeremenu eoenptred with theotetieat curve to K, ~ 3 <br />sad K ~ 10. Mar Beery (IS). ., <br /> <br />