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9J CONTINUUM MECHANICS THEORIES 293 <br /> such that S - 1 at - 0 or maximum subsidence occurs above the center <br /> of the excavation. Then <br /> K, - E 12x')S — l J u: (9.3.5) <br /> X, l ax rs� <br /> K, - h= [I — x dS (9.3.6) <br /> x, ax :-:, <br /> where x - ±x, are the points where S - f (i.e., half the maximum <br /> subsidence).In determining K, and K,,first find in the subsidence area the <br /> points tx, where S -}, measure the slope OS/ax,and calculate K, and K, <br /> by Eqs. 9.3.5 and 9.3.6. The subsidence profile can then be plotted using <br /> Eq. 9.3.1. <br /> The application of the theory is illustrated in Fig. 9.3.2, where the <br /> broken lines are measured surface subsidence for a longwall panel 550 ft <br /> wide and 1973 ft deep with a coal seam 52 in. thick. The solid lines are <br /> theoretical curves based on Eq.9.3.1 using K, =2 and K, = 10. It must be ; <br /> noted that several trials of determining suitable values for K, and K, are <br /> almost necessary before a close agreement between theory and field <br /> measurements is realized. <br /> 9.3.2 FAutic-Phtstic Theory <br /> Dahl and Choi (7) found that mine subsidence is essentially time- i <br /> independent and that measured surface strains frequently exceed the <br /> a. vertical subsidence: practical l— ——), theoretical( 1 <br /> -1000 -Soo -VL 0 w 500 X(feet) 1000 <br /> 40 <br /> -S.(cm) <br /> • - 0 � <br /> -1000 -500 ' • • • 500 X(feet)1000 <br /> • 1 <br /> aviaz(mmim) <br /> b. Horizontal strain: practical points , theoretical curve <br /> FI& 9J3 Surface movement measurements compared with theoretical curves for K, 2 <br /> wad K. - 10. After Berry(15). <br />