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292 SURFACE SUBSIDENCE <br /> W <br /> i <br /> 1. Nonclosure <br /> i <br /> w ---•� <br /> T I-- 2b ---� <br /> 2. Partial closure <br /> 1� W <br /> F,K. 9.3.1 Bcrry's euxlclx of surface <br /> 3. Complete closure subsidence (IS). <br /> seam. h is the depth of excavation below surface, x is the horizontal <br /> distance from the center of the excavation, and K, and K. are two <br /> characteristic constants: <br /> K, _ (1 — v4)"' [E rIE„ — PA, (9.3.2) <br /> Ks a [EAM — v„(1 + vf)] (E.IE„ — v;,)-� (9.3.3) <br /> where E,,, v„ and E,r, v,, are the Young's moduli and Poisson ratios in <br /> vertical (perpendicular to beddings) and horizontal (parallel to beddings) <br /> directions, respectively, and M is the shear modulus. The restriction on <br /> these two constants is that both K, and K, + K, must be positive. It is <br /> seen from rq.9.3.1 that surface subsidence is highly dependent on K, and <br /> Ks. Therefore, the determination of K, and K. is very critical. Berry (15) <br /> suggested the conversion of Eq. 9.3.1 to a dimensionless quantity, S: <br /> S = hS.W <br /> 2112A(Kj +K,,),n <br /> —[K, C T� + 2K2 ( h� + (9.3.4) <br />