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ift SURFACIi SUBSIDENCE <br />elastic limit. As a master of fact, surface borcholes drilled in the gob of a <br />r longwall face in the Pittsburgh coal scam indicated that ruck mass up to <br />l 3W Il above the coal scam w:u subjcclcd lu a vertical stnun ranging from <br />2000 to 10,000 µin./in. Dahl and Choi therefore suggested a model that <br />behaves in an clastic•elastoplustic manner. The madcl is linearly clastic <br />until the anisotropic Coulomb yield or the enisotropic Von Mises yield <br />criterion is satisfied. Because of the complexity in boundary conditions, <br />the finite-element method was used with an incremental constitutive rcla- <br />tionship: <br />whero (do) and (de) arc stress and strain tensors, respectively, and [EJ is <br />the matrix of proportionality constants of stress and strain. The linear <br />Hookean relationship [E] is used below the yield point, whereas for <br />applied stress above the yield point [E] is slrras depcndenl as sp~r:iliwl by <br />the yield criteria. <br />Using this model, Dahl and Choi (7) reported a case study of the <br />longwall panel in Blucksvillc Nu. I Mine, Blucksvillc, Wcst Virginia, <br />where the Pittsburgh coal seam 6 ft thick was mined. The surface subsi- <br />dence survey is shown in Fig. 9.3.3. Dotted lines arc surface topographic <br />contours, soli) Juts un: surveying stations, solid curvul lines an: subsi- <br />den~e contour lines, and heavy broken lines arc face locations. The <br />development of subsidence as the longwall retreat mining proceeded for a <br />period of 6 months is shown in A to E. Subsidence is symmetric wiW <br />~ mining activities and geometry and is not significantly affected by surface <br />topography. Furthermore, it is time-independent because subsidences <br />measured in Figs. 9.3.3D and E are essentially the same although They <br />were measured 4S days apart. Using the three-dimensional finiteclement <br />method, subsidence profiles in Fig. 9.3.3E was reproduced as shown in <br />,. Fig. 9.3.3F. However, the material properties asst and shown below <br />wcrn determined by trials and errors until they roprtxlucal the licld daW. <br />Caved Rock Intact Rock <br />Ytwng's modulus (psi) S x 10' 20 x 10' <br />Poisson rrliu U,25 0.23 <br />Tensile strength (psi 24 240 <br />From the two cases just discussed, it is dear that the validity of 4he <br />continuum mechanics theories hinges on the exact specifications of the <br />material properties of the subsiding grounds, applied loads, and boundary <br />conditions. D[Rercnt subsidence profiles ten be generated by varying <br />.: <br /> <br />r <br />