2022-09-29_PERMIT FILE - C1980007 (5)

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Subsidence Evaluation for the Exhibit 60E Southern Panels, Apache Rocks West, & Sunset Trail Mining Areas Page 12 831-032.923 Wright Water Engineers, Inc. December 2021 5.3.1 Vertical Displacement, Tilt, and Horizontal Strain Differential vertical lowering of the continuous deformation and near surface zones causes vertical displacement (S), tilt (M), and horizontal strain (E). In flat or gently sloping terrain (slopes less than about 30 percent), surface profiles of subsidence depressions are similar to flexure of fixed- end, laterally constrained beams. Tensile stresses are present in areas of positive curvature, which become zero downward at the neutral surface, then reverse to compressive stresses below the neutral surface. In flat or gently sloping terrain, vertical displacement typically increases inward from the limit of the subsidence depression, is half the maximum value at the point of inflection, and is maximum in the middle of the depression (also called subsidence basin or subsidence trough). Tilt increases inward from the margin of the depression to a maximum at the point of inflection and become zero again at the point of maximum vertical displacement (Figure 3). Maximum values of tilt, curvature, and strain, discussed herein, apply only to slopes less than about 30 percent; values may be greater on slopes steeper than 30 percent. Positive curvature (convex upward) and horizontal tensile strain increase inward from the margin of the depression to a maximum about midway between the depression margin and the point of inflection and decrease to zero again at the point of inflection. Negative curvature (concave upward) and compressive horizontal strain increase inward from the point of inflection to a maximum about midway between the point of inflection and the point of maximum vertical displacement and decrease to zero again at the point of maximum vertical displacement. 5.3.1.1 Maximum Vertical Displacement (Subsidence) The following range of vertical displacements (subsidence values) are projected for the Southern Panels, Apache Rocks West, and Sunset Trail mining areas, based on the baseline data obtained from subsidence measurements above the B-seam longwall panels 1NW, 2NW, and 3NW (Figure 4, Table 1) and E-seam longwall panels E1 to E3 at West Elk Mine. Southern Panels Mining Area: As noted above, the E-Seam longwall panels E1 to E8 were originally approved as part of the South of Divide mining area, and subsequently panels E2 to E7 were approved to extend into the Dry Fork mining area. To simplify the discussion of subsidence projections, the full-length panels are addressed as the Southern Panels E1 to E8. Similarly, the proposed B-seam panels in this area are referred to as the Southern Panels B26 to B29. For purposes of the subsidence modeling evaluation, the overburden depth above the projected E- seam longwall centers ranges from approximately 370 to 1,800 feet. With a projected longwall panel width of approximately 1,080 feet, and assuming that the chain pillars (gate road pillars) are similar to those in longwall panel 17 of the Apache Rocks mining area, maximum subsidence (vertical displacement Sm = a • t) is predicted as follows (Table 2) for the Southern Panels mining area of panels E1 to E8 and E14 to E17: • Panels E1 to E8 and E14 to E17: These panels range in width from subcritical to supercritical (width-to depth ratio (W/d) ranges from 0.76 to 3.00).