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i <br /> 294 SURFACE SUBSIDENCE <br /> elastic limit. As a matter of fact, surface boreholes drilled in the gob of a <br /> longwall face in the Pittsburgh coal scum indicated that rock mass up to <br /> 300 ft above the coal scam was subjected to a vertical strain ranging from <br /> 2000 to 10,000 Ain./in. Dahl and Choi therefore suggested a model that <br /> behaves in an elastic-elastoplustic manner. The model is linearly clastic <br /> until the anisotropic Coulomb yield or the anisotropic 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 rela- <br /> tionship: <br /> (dakxl _ [E]exe(de) xl (9.3.7) i <br /> where NO and(de) are stress and strain tensors, respectively, and [E] 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 [/:l is stress dependent us specified by <br /> the yield criteria. <br /> Using this model, Dahl and Choi (7) reported a case study of the <br /> longwall puncl in Blacksville No. I Mine, Blacksville, West 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 are surface topographic <br /> contours, solid dots are surveying stations, solid curved lines urc subsi- <br /> dence contour lines, and heavy broken lines are 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 with <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 45 days apart. Using the three-dimensional finite-element <br /> method, subsidence profiles in Fig. 9.3.3E was reproduced as shown in <br /> Fig. 9.3.3F. However, the material properties used and shown below <br /> were determined by trials and errors until they reproduced the field data. <br /> Caved Rock Intact Rock <br /> Young's modulus (psi) 5 x HP 20 x I(P <br /> Poisson ratio 0.25 0.25 <br /> Tensile strength (psi) 24 240 <br /> From the two cases just discussed, it is clear that the validity of'the <br /> continuum mechanics theories hinges on the exact specifications of the <br /> material properties of the subsiding grounds,applied loads,and boundary <br /> conditions. Different subsidence profiles can be generated by varying <br />