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C <br /> <br />:f~ <br />`~ -"~ <br />1. Nonclosurs <br />m <br />T I-- zo -I <br />1. Partial cloacars <br />~_ w _"~ <br />~, Complete oloeure <br />SURFACE SUI)SIDENCB <br />i1R. f~.l Berry'^ midcl^ ,~ w,fwx <br />wb^iJence l13). <br />seam. h is the depth of excavation below surface, .r is the horizontal <br />distance from the center of the excavation, and K, and K, ere two <br />characteristic constants: <br />K, ~ (1 - v;)"' [E,IE, - win <br />(9.3.2) <br />K, ~ [E,l2M - v,(I + v,)1(E,IE. - v;)'' (9.3.3) <br />where E„ v, and E,. v, are the Young'c moduli and Poisson ratios in <br />vertical (perpendicular to beddings) and horizontal (parallel to beddings) <br />dirccliuns, respectively, and M is the shear malulus. The restriction on <br />thex two constants is that both K, and K, + K, must be positive. It is <br />seen from Fq. 9.3.1 Ihrt surfrw xubsidence is high{y dependent can K, and <br />K,. Therefore, the Determination of K, and K, is very critics). Berry (IS) <br />auggated the conversion of F.q. 9.3.1 to a dimensionless quantity, S: <br />S _ hS,n <br />-[Kiih~+~s~hl +lr'~ <br />(9.3.4) <br />I <br />r 1 <br />~J <br /> <br />