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Panel <br />Ribside <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />Vertical Stress <br />Re -distribution <br />/ I <br />Yield "Rigid" or <br />Pillar Abutment <br />Pillar <br />(a) After Development <br />Panel Panel <br />Strain <br />+E Curve Extension (Compression <br />E Subsidence \ �♦ <br />Curve I', I ♦♦ <br />'♦ so <br />Zone of Vertical Extension <br />I (bed separation) I <br />I I <br />I <br />IL too <br />O2 Zone of Bed Separation <br />I 1Q Zone of Caving I / <br />2 <br />O 3-sm <br />T777= FT <br />Pillar Yield and Floor <br />Punching Floor Heave Zone of Incomplete <br />(load transfer to cure) Convergence <br />Figure 1 <br />Generalized Vertical Stress Change and <br />Displacement during Longwall Mining <br />(Derived using information from Mark, 1992, <br />Bienawski, 1992, Shadbolt, 1977) <br />(b) After Longwall Extraction <br />1. Empirical Methods: Graphical Methods, Profile <br />Functions, Influence Functions and Zone Area <br />Methods. <br />2. Analytical Methods: Mechanistic Models, Finite <br />Element, Boundary Element, and Hybrids <br />(c) Zones of Fracturing <br />(Singh, 1986) <br />EXPLANATION: <br />rn = Extracted seam thickness <br />s = Subsidence <br />ov = In-situ vertical stress <br />6p = Side abutment stress <br />+E = Extension <br />-E =Compression <br />Table 1 provides a summary of the relative <br />capability of each method with regard to the <br />prediction of subsidence, displacement, and strain. <br />The interested reader is referred to the citations for a <br />detailed description of each method. <br />Table 1. Relative capability of the methods to predict subsidence, displacement and strain. <br />PREDICTION METHOD METHOD OF PREDICTING <br />(REFERENCE) Subsidence (S) Displacement Strain (E) <br />Graphical Method <br />Graphical based on w/h & <br />Not predicted, however, Figure <br />Maximum strains predicted <br />(Ref: NCB, 1975) <br />tabulated profile data <br />64 provides a monogram for <br />using Smax/h multiplier. Strain <br />calculating the change in length <br />profile predicted using tabulated <br />of influence. <br />of a subsided surface structure. <br />& graphical data. <br />Profile Functions <br />Uses mathematical equation <br />Calculated from predicted <br />Calculated from predicted <br />(Karmis, 1992; Singh, 1992) <br />based on empirical data. <br />slope. <br />curvature <br />Zone Area Method <br />Subsidence factor calculated by <br />Calculated from predicted Calculated from predicted <br />(Karmic & Hacocks, 1983; <br />superposition of the proportional <br />slope. curvature. <br />Marr, 1975) <br />extraction of a finite number of <br />concentric rings forming the area <br />of influence. <br />Influence Functions <br />Profiles constructed by <br />Calculated from predicted Calculated from predicted <br />(VPI, 1987; Salamon, 1992) <br />integrating the influence function <br />slope. curvature. <br />(see eq. 3-7 to 3-11) <br />Mechanistic Models Subsidence predicted based on Not addressed. Not addressed. <br />composite beam deflections. <br />Finite & Boundary Element Subsidence & related parameters Produced as model output. Computed from modeled <br />Models simulated directly through displacements. <br />(Su, 1992; Summers, 1990) analysis of the rock mass <br />response to underminine. <br />