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Field studies by Dunrud (2006, p. 7) indicate that near-surface colluvium and alluvium, which <br />consist of predominantly clay and silt, can undergo significantly more extension without rupturing <br />than can the underlying material. In both the Somerset, Colorado and Sheridan, Wyoming areas <br />colluvium and alluvium 5 to 10 feet thick were observed to cover cracks as much as 10 to 14 inches <br />wide so that there was no indication of the underlying ruptures. <br />The zone of continuous deformation, which is transitional to the overlying near-surface zone and <br />also to the underlying zone of fracturing, undergoes differential vertical lowering and flexure as <br />laterally-constrained plates (in three dimensions) or beams (in two dimensions). With flexure, shear <br />occurs at the boundaries of rock units with different strength and stiffness, characteristics, such as <br />sandstones and shales. Zones of tension above the neutral surfaces of a rock unit, for example, <br />become compressive above the boundary with another rock unit and below its neutral surface <br />(Figure 2, Enlargement 2). Any cracks, therefore, which occur in the tension zone of a rock unit, <br />terminate at the neutral surface, because the unit is in compression below this point. <br />5.3.1 Vertical and Horizontal Displacement, Tilt, and Horizontal Strain <br />Differential vertical lowering of the continuous deformation and near surface zones causes vertical <br />displacement (S), horizontal displacement (Sh), tilt (M), and horizontal strain (E). In flat or gently <br />sloping terrain (slopes less than about 30 percent), surface profiles of subsidence depressions are <br />similar to flexure of fixed-end, laterally constrained beams. Tensile stresses are present in areas of <br />positive curvature, which become zero downward at the neutral surface, then reverse to <br />compressive stresses below the neutral surface. <br />In flat or gently sloping terrain, vertical displacement typically increases inward from the limit of the <br />subsidence depression, is half the maximum value at the point of inflection, and is maximum in the <br />middle of the depression (also called subsidence basin or subsidence trough). Horizontal <br />displacement and tilt increase inward from the margin of the depression to a maximum at the point <br />of inflection and become zero again at the point of maximum vertical displacement (Figure 3). <br />Maximum values of tilt, curvature, and strain, discussed herein, apply only to slopes less than about <br />30 percent; values may be greater on slopes steeper than 30 percent. <br />Positive curvature (convex upward) and horizontal tensile strain increase inward from the margin of <br />the depression to a maximum about midway between the depression margin and the point of <br />inflection and decrease to zero again at the point of inflection. Negative curvature (concave upward) <br />and compressive horizontal strain increase inward from the point of inflection to a maximum about <br />midway between the point of inflection and the point of maximum vertical displacement and <br />decrease to zero again at the point of maximum vertical displacement. <br />5.3.1.1 Maximum Vertical Displacement (Subsidence) <br />The following range of vertical displacements (subsidence values) are projected for the South of <br />Divide and Dry Fork mining areas, based on the baseline data obtained from subsidence <br />measurements above the 1 NW, 2NW, and 3NW longwall panels at West Elk Mine (Figure 4, <br />Table 1). The projected range of maximum vertical displacements, for the South of Divide mining <br />area is shown in Table 2. The projected range of vertical displacements for the Dry Fork mining <br />area is shown on Table 3. <br />South of Divide Mining Area: Overburden depth above the projected E Seam longwall centers <br />ranges from 400 to 1,425 feet. With a projected longwall panel width of 1,080 feet, and assuming <br />that the chain pillars (gate road pillars) are similar to those in longwall panel 17 of the Apache <br />Rocks mining area, maximum subsidence (vertical displacement Sm= a • t) is predicted as follows <br />(Table 2): <br />• Panels E1 to E8: These panels, which will trend roughly N80°W, will range in width from subcritical <br />to supercritical (width-to depth ratio (W/d) ranges from 0.76 to 2.7). <br />Tetra Tech - 090717/P